Building Vibration
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This project is to cover the graduation requirements for high Diploma of Higher College Of Technology. The research was on the earthquakes and it effects on the building. After that , designing system ...

This project is to cover the graduation requirements for high Diploma of Higher College Of Technology. The research was on the earthquakes and it effects on the building. After that , designing system that help us to control the effect of earthquakes. This system has structure components that should be under consideration. Also, installing the Tuned Mass Dumper TMD in the structure and superstructure of building. This consisting of mass, spring and viscous dumper. The viscous dumper will absorb the energy of the vibration due to earthquakes. Part of calculations, it’s important to study the Flexibility influence coefficient. It focuses on the behavior in terms of stiffness and flexibility. Another important subject is mass stiffness and matrices. This provides the simplest representation of a building for the purposes of investigating lateral dynamic responses.

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    Building Vibration Building Vibration Document Transcript

    • Higher Colleges of Technology, Abu Dhabi June 5 Building Vibration 2011 Project of Building Vibration for MECH N349 , Prepared For Dr. Molham Al Souk By Waleed Alyafee Humood AlShehhiMechanical Engineering studentsfor contact: ggc@windowslive.com
    • Building Vibration 2011ContentsAbstract ......................................................................................................................................................... 3Introduction .................................................................................................................................................. 4Literature Review .......................................................................................................................................... 6 Earthquake Proof Buildings and Structures: http://www.whatprice.co.uk/building/earthquake-proof- buildings.html............................................................................................................................................ 6How to Make Buildings & Structures Earthquake Proof:http://www.reidsteel.com/information/earthquake_resistant_building.htm ................................................. 7 Control of vibration in civil structures: http://journals.pepublishing.com/content/w61g17254m84506j/9 Active/passive vibration control systems for tall buildings: http://iopscience.iop.org/0964- 1726/7/5/003;jsessionid=BA6E2E5EC098268D422448A75FA80E9F.c2 ............................................. 10Control Algorithms ...................................................................................................................................... 17Passive control methods: ............................................................................................................................ 17 Lateral Load Resisting Systems: .............................................................................................................. 17 Tuned Mass Damper (TMD) .................................................................................................................... 18 Principle of operation ......................................................................................................................... 19 Viscous damper ................................................................................................................................... 20 FLUID VISCOUS DAMPER DESCRIPTION .............................................................................................. 20 Principle of operation: ........................................................................................................................ 21Active Control Systems ............................................................................................................................... 21SEMI-ACTIVE CONTROL: .............................................................................................................................. 22Flexibility influence coefficients:................................................................................................................. 23Mass and Stiffness Matrices ....................................................................................................................... 27MATLAB....................................................................................................................................................... 31 Applying MATLAB in the results .............................................................................................................. 32Conclusion ................................................................................................................................................... 43References: ................................................................................................................................................. 44 2 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011AbstractThis project is to cover the graduation requirements for high Diploma of Higher College OfTechnology. The research was on the earthquakes and it effects on the building. After that ,designing system that help us to control the effect of earthquakes. This system has structurecomponents that should be under consideration. Also, installing the Tuned Mass Dumper TMDin the structure and superstructure of building. This consisting of mass, spring and viscousdumper. The viscous dumper will absorb the energy of the vibration due to earthquakes. Part ofcalculations, it’s important to study the Flexibility influence coefficient. It focuses on thebehavior in terms of stiffness and flexibility. Another important subject is mass stiffness andmatrices. This provides the simplest representation of a building for the purposes of investigatinglateral dynamic responses. 3 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Introduction One of the most frightening of natural disasters - an earthquake, leaves behind immediatedestruction, loss of life and despair on a scale that is mind boggling. And all of it due to collapsingstructures and dwellings unable to withstand the tremors of the earthquake. People lucky enough to beoutdoors manage to escape while people caught indoors get trapped or perish. Hence the importance ofconstructing earthquake resistant houses and buildings is known in earthquake experienced areas wherearchitects and engineers plan accordingly. Engineers would like to make every building earthquake-proof,but cant because its too expensive. Instead, they recommend making dams and public buildingsearthquake-proof. All other buildings should be earthquake resistant to avoid deaths. The cost of repair isa fraction of the cost of earthquake-proofing these buildings.In areas where earthquakes are likely, knowing where to build and how to build can help reduce injury,loss of life, and property damage during a quake. Knowing what to do when a quake strikes can also helpprevent injuries and deaths. Earth scientists try to identify areas that would likely suffer great damageduring an earthquake. They develop maps that show fault zones, flood plains (areas that get flooded),areas subject to landslides or to soil liquefaction, and the sites of past earthquakes. From these maps, land-use planners develop zoning restrictions that can help prevent construction of unsafe structures inearthquake-prone areas.Engineers have developed a number of ways to build earthquake-resistant structures. Theirtechniques range from extremely simple to fairly complex. Field inspection and analyses of theperformance of structures during earthquake shaking of their foundations have clearly shown thatbuilding design which blindly follows seismic code regulations does not guarantee safety againstcollapse or serious damage. First, there are large uncertainties in many of the aspects involved inthe numerical design of structures, particularly in establishing the design earthquake shaking andin estimating the demands and predicting the supplies of the real three-dimensional soil-foundation-building (superstructure) system; second, the performance of the system depends onits state when the earthquake strikes - thus construction and maintenance, which includes repair,retrofitting and/or modifications, must also be considered in addition to the design aspects. 4Design and construction of a structure are intimately related and the achievement of goodworkmanship depends, to a large degree, on the simplicity of detailing of the members and of MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011their connections and supports. For example, in the case of a reinforced concrete structure,although it is possible to detail complex reinforcement on paper and even to realize it inlaboratory specimens so that seismic behavior is improved, in the field such design details maynot be economically feasible. A design is only effective if it can be constructed and maintained.In a comprehensive approach to the design of a structure it is first necessary to establish thedesign criteria, that is, behavior of the structure - serviceability, damageability, and safety againstcollapse. Once the design criteria are established, depending on the limit state controlling thedesign, the selection of the design earthquake(s) should be done according to the comprehensiveapproaches. In this comprehensive attempt to overcome the uncertainties involved in modelingthe real three-dimensional soil-foundation-superstructure system and in the estimation of thedemands and supplies, usually derived from numerical analysis, the design cannot be based on asingle deterministic analysis of a single selected model. The designer should consider severalmodels, based on possible ranges over which the parameters governing the behavior of the realsystem can vary. In order to overcome or decrease the uncertainties to which the values of mostof the parameters in the estimation of the demands and supplies are subjected in any currentseismic-resistant design procedure, it is necessary to pay more attention to conceptual design.Conceptual design is defined as the avoidance or minimization of problems created by the effectsof seismic excitation by applying an understanding of the behavior rather than using numericalcomputations. From the analysis of the basic design equations and the general equation forpredicting response, it becomes clear that to overcome detrimental effects of the uncertainties inmany of the factors in these equations the following philosophy can be applied: (1) control ordecrease the demands as much as possible, and (2) be generous in the supply, particularly byproviding large ductility with stable hysteretic behavior (toughness).Because of the uncertainties regarding the dynamic characteristics of future earthquake groundmotions and their modifications as a result of the interaction of the soil with the foundation-superstructure system response, the conceptual idea would be to control the input to the structurefoundation. One promising method is through the use of base isolation techniques includingenergy absorbing devices in the system. In the case of buildings, a decrease in demand can be 5achieved by a proper selection of the configuration of the building and its structural layout andby the proper proportioning and detailing of the structural and non-structural components, that is, MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011by following the basic principles or guideline for achieving efficient seismic-resistantconstruction.Literature ReviewEarthquake Proofing Techniques: http://www.bookrags.com/research/earthquake-proofing-techniques-woi/This article talks about the ways on how to earthquake proof structures. The major thrust of earthquake-proofing by architects is to prevent the collapse of buildings. The ability of a building to withstand thestress of an earthquake depends upon its type of construction, shape, mass distribution, and rigidity.Various combinations of techniques are used. Square, rectangular, or shell-shaped buildings, andbuildings with few stories, can better resist vibrations than L-shaped structures or skyscrapers. To reducestress, a buildings ground floor can be supported by very rigid, hollow columns, while the rest of thebuilding is supported by flexible columns located inside the hollow columns. Another method is to userollers or rubber pads to separate the foundation columns from the ground, allowing the columns to shakehorizontally during an earthquake. It also talks on help to prevent collapse, roofs should be made of light-weight materials. Exterior walls can be made more durable by fortifying them with steel or woodenbeams, or with reinforced concrete. Interior walls can bolster exterior walls, and a continuous collar cancap a rectangular shaped structure, aiding its stability. If nonstructural walls (not used for support) areattached only to the floor or only to the ceiling, they can move sideways as the building sways. Flexiblewindow frames can hold windows in place without breaking during tremors.Earthquake Proof Buildings and Structures:http://www.whatprice.co.uk/building/earthquake-proof-buildings.htmlThis article says that nothing is guaranteed when it comes to earthquakes or other calamities. But luckily,there are certain building methods and materials to make structures more resistant to earthquakes. Beingaware about this information can potentially save you and your family. 6Generally, all buildings can withstand weak earthquakes. They do not fall apart and collapseinstantly. The reason for this is most buildings can support their own weight plus a few more. MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Even poorly built buildings and structures can defy the up-and-down movement caused byearthquakes. But it is the side-to-side movement that makes buildings collapse. Most buildingsare not designed to endure this. Structures and buildings should be supported to resist thesideways effect of an earthquake. There are other methods that we can use but the most commonrule is; the lighter the building, the less the loads are and the better for all.How to Make Buildings & Structures Earthquake Proof:http://www.reidsteel.com/information/earthquake_resistant_building.htmThis site discusses these issues mentioned.What is an earthquake?What makes a building or structure fail in earthquakes?So, how can we make buildings resistant to earthquakes?So, when looking at design and construction how do we earthquake proof buildings?There are a wide variety of earthquake effects - these might include a chasm opening up or adrop of many metres across a fault line. Therefore, it is not possible to design an earthquakeproof building which is guaranteed to resist all possible earthquakes. However, it is possibleduring your design and construction process to build in a number of earthquake resistantfeatures, which would increase enormously the chances of survival of both buildings and theiroccupants. Then it goes on to saying, nothing can be guaranteed to be fully resistant to anypossible earthquake, but buildings and structures like the ones proposed here by ReidSteel wouldhave the best possible chance of survival; and would save many lives and livelihoods, providinggreater safety from an earthquake.Earthquake, world book: http://www.nasa.gov/worldbook/earthquake_worldbook.htmlThis article discusses Earthquake (How an earthquake begins) (How an earthquake spreads) 7(Damage by earthquakes) (Where and why earthquakes occur) (Studying earthquakes). Mostearthquakes occur along a fault -- a fracture in Earths rocky outer shell where sections of rockrepeatedly slide past each other. Faults occur in weak areas of Earths rock. Most faults lie MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011beneath the surface of Earth, but some, like the San Andreas Fault in California, are visible onthe surface. Stresses in Earth cause large blocks of rock along a fault to strain, or bend. When thestress on the rock becomes great enough, the rock breaks and snaps into a new position, causingthe shaking of an earthquake. Most earthquakes occur along a fault -- a fracture in Earths rockyouter shell where sections of rock repeatedly slide past each other. Faults occur in weak areas ofEarths rock. Most faults lie beneath the surface of Earth, but some, like the San Andreas Fault inCalifornia, are visible on the surface. Stresses in Earth cause large blocks of rock along a fault tostrain, or bend. When the stress on the rock becomes great enough, the rock breaks and snapsinto a new position, causing the shaking of an earthquake. Earthquakes can damage buildings,bridges, dams, and other structures, as well as many natural features. Near a fault, both theshifting of large blocks of Earths crust, called fault slippage, and the shaking of the ground dueto seismic waves cause destruction. Away from the fault, shaking produces most of the damage.Undersea earthquakes may cause huge tsunamis that swamp coastal areas. Other hazards duringearthquakes include rockfalls, ground settling, and falling trees or tree branches. Earth scientiststry to identify areas that would likely suffer great damage during an earthquake. They developmaps that show fault zones, flood plains (areas that get flooded), areas subject to landslides or tosoil liquefaction, and the sites of past earthquakes. From these maps, land-use planners developzoning restrictions that can help prevent construction of unsafe structures in earthquake-proneareas. Engineers have developed a number of ways to build earthquake-resistant structures. Theirtechniques range from extremely simple to fairly complex. For small- to medium-sizedbuildings, the simpler reinforcement techniques include bolting buildings to their foundationsand providing support walls called shear walls. Shear walls, made of reinforced concrete(concrete with steel rods or bars embedded in it), help strengthen the structure and help resistrocking forces. Shear walls in the center of a building, often around an elevator shaft or stairwell,form what is called a shear core. Walls may also be reinforced with diagonal steel beams in atechnique called cross-bracing.How We Make Structures Earthquake Resistant: http://www.buildingssteel.com/earthquake-how.htm 8 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011This website talks about making structures to withstand earthquakes. It says that there areseveral killers in earthquakes to which non earthquake resistant buildings are more susceptible.The first is horizontal or vertical acceleration of the ground, which moves suddenly sideways orup. If the frame has insufficient sway strength, it falls down there and then at the first big jerk.Its easy to design sway resistance in steel. The second is vibration from shock waves; like atuning fork, a building will oscillate at its own frequency if relatively small shock waves come atthe resonant frequency (often leaving taller or shorter structures nearby much less affected).Oscillation can build up and produce greater and greater sway loads until the building fails insway or total overturning. This is where the ductility of the steel frame is so perfect; it deforms,absorbing energy and simultaneously changing the resonant frequency of the structure; botheffects reduce oscillation. Thus steel framed earthquake resistant buildings with their betterstructural performance help to solve these problems.Control of vibration in civil structures:http://journals.pepublishing.com/content/w61g17254m84506j/This paper reports recent trends in active vibration control mainly as developed in Japan for civilstructures. Firstly, it classifies vibration control methods and controllers, especially active dynamicabsorbers that are widely used in mechanical and civil engineering. Secondly, it addresses basic problemsin the control of vibration of flexible structures such as formulating the reduced-order model required fordesigning vibration controllers, the correct arranging of sensors and actuators, and how to preventspillover instability. Finally, the practical use of control theories such as linear-quadratic control theory,H∞ control theory, neural network theory and other topics are discussed.Experimental Active Vibration Control in Truss Structures Considering Uncertainties in SystemParameters: http://www.hindawi.com/journals/mpe/2008/754951.htmlThis paper deals with the study of algorithms for robust active vibration control in flexible structuresconsidering uncertainties in system parameters. It became an area of enormous interest, mainly due to thecountless demands of optimal performance in mechanical systems as aircraft, aerospace, and automotivestructures. An important and difficult problem for designing active vibration control is to get arepresentative dynamic model. Generally, this model can be obtained using finite element method (FEM) 9or an identification method using experimental data. Actuators and sensors may affect the dynamicsproperties of the structure, for instance, electromechanical coupling of piezoelectric material must be MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011considered in FEM formulation for flexible and lightly damping structure. The nonlinearities anduncertainties involved in these structures make it a difficult task, mainly for complex structures as spatialtruss structures. On the other hand, by using an identification method, it is possible to obtain the dynamicmodel represented through a state space realization considering this coupling. This paper proposes anexperimental methodology for vibration control in a 3D truss structure using PZT wafer stacks and arobust control algorithm solved by linear matrix inequalities.Active/passive vibration control systems for tall buildings:http://iopscience.iop.org/0964-1726/7/5/003;jsessionid=BA6E2E5EC098268D422448A75FA80E9F.c2This article talks about the three examples of vibration control systems are described. The first is a hybridmass damper system, which is one type of active vibration control system, as installed on the top floor ofa complex triangular building of forty-three stories in order to reduce the response of the building tostrong winds and moderate earthquakes. The second is an unbonded brace damper, which is a kind ofelasto-plastic damper using low-yield-point steel. It has been installed in a fifteen-story building as anenergy absorption member to control severe earthquake motion. The last is a rotational variable damperusing an electrorheological fluid. The feasibility of applying this type of damper to a real scale structureas a semi-active control device has been investigated.www.ias.ac.in/resonance/Dec2004/pdf/Dec2004Classroom4.pdfEarthquake-Resistant Design of Buildings:Buildings should be designed like the ductile chain. For example, consider the common urban residentialapartment construction – the multi-storey building made of reinforced concrete. It consists of horizontaland vertical members, namely beams and columns. The seismic inertia forces generated at its floor levelsare transferred through the various beams and columns to the ground. The correct building componentsneed to be made ductile. The failure of a column can affect the stability of the whole building, but thefailure of a beam causes localized effect. Therefore, it is better to make beams to be the ductile weak linksthan columns. This method of designing RC buildings is called the strong-column weak-beam designmethod. By using the routine design codes (meant for design against nonearthquake effects), designersmay not be able to achieve a ductile structure. Special design provisions are required to help designers 10improve the ductility of the structure. Such provisions are usually put together in the form of a specialseismic design code, e.g., IS: 13920-1993 for RC structures. These codes also ensure that adequateductility is provided in the members where damage is expected. MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Quality Control in Construction:The capacity design concept in earthquake-resistant design of buildings will fail if the strengths of thebrittle links fall below their minimum assured values. The strength of brittle construction materials, likemasonry and concrete, is highly sensitive to the quality of construction materials, workmanship,supervision, and construction methods. Similarly, special care is needed in construction to ensure that theelements meant to be ductile are indeed provided with features that give adequate ductility. Thus, strictadherence to prescribed standards of construction materials and construction processes is essential inassuring an earthquake-resistant building. Regular testing of construction materials at qualifiedlaboratories (at site or away), periodic training of workmen at professional training houses, and on-siteevaluation of the technical work are elements of good quality control.Oscillations of Flexible Buildings:When the ground shakes, the base of building moves with the ground, and the building swings back and-forth. If the building were rigid, then every point in it would move by the same amount as the ground.But, most buildings are flexible, and different parts move back-and-forth by different amounts.Importance of Flexibility:The ground shaking during an earthquake contains a mixture of many sinusoidal waves of differentfrequencies, ranging from short to long periods. The time taken by the wave to complete one cycle ofmotion is called period of the earthquake wave. In general, earthquake shaking of the ground has waveswhose periods vary in the range 0.03-33sec. Even within this range, some earthquake waves are strongerthan the others. Intensity of earthquake waves at a particular building location depends on a number offactors, including the magnitude of the earthquake, the epicentral distance, and the type of ground that theearthquake waves travelled through before reaching the location of interest.www.ikb.poznan.pl/jacek.wdowicki/Pliki/materialy/.../Li03.pdfwind effects on Di Wang Tower:In this site the objective of the study is to investigate wind effects on Di Wang Tower under typhooncondition. Wind speeds, wind directions and acceleration responses presented in this paper weremeasured on top of the tall building during the passage of Typhoon Sally. Characteristics of the typhoon- 11generated wind, structural dynamic properties and wind-induced responses of this super tall building werepresented and discussed. Furthermore, the full-scale measurements are compared with the wind tunnel MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011test results.ncdr.nat.gov.tw/2icudr/2icudr_cd/PDF/P19.pdfEarthquake and Typhoon Effects on a 51-story Tall Building:This site investigates the vibratory characteristics of a 51-story steel high-rise building in response to amajor typhoon, earthquake and ambient vibrations.www.taylordevices.eu/pdfs/tall-building.pdfFluid Viscous Dampers to reduce Wind-induced Vibrations in Tall Buildings:The fluid viscous damping system proved to be a very cost effective method to effectively reduce wind-induced vibrations. For large force output at very low displacement, a motion amplification device hasbeen included in the design in order to reduce the quantity and cost of the dampers.e-book.lib.sjtu.edu.cn/nascc2004/data/.../WindResDsTallBldgsJapan.pdfImportance of Design Value of Damping:Structural damping is the most important, but most uncertain, parameter affecting dynamic responses ofbuildings. This uncertainty significantly reduces the reliability of structural design for dynamic effects.Accurate determination of structural damping is very important, not only for evaluating structuralresponses, but also for designing active and passive auxiliary damping devices to be installed in buildingsand structures. However, there is no theoretical method for estimating damping in buildings. Thus, it hasbeen estimated on the basis of actual measurements of widely dispersed damping ratios.www.mita.sd.keio.ac.jp/publications/data/c199501.pdf 12Vibration Control of Tall Building Using Mega SubConfiguration:An innovative vibration control system, which takes advantage of mega substructure configuration, was MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011proposed for tall and super tall building. This mega subcontrol system was designed in such a way thatthe vibration energy of the megastructure due to wind or earthquake loads can be transferred in tosubstructures and then dissipated in substructures by conventional damping devices.A LITERARY REVIEW OF STRUCTURAL CONTROL: EARTHQUAKE FORCEShttp://www.pbworld.com/news_events/publications/technical_papers/pdf/50_ALiteraryReview.pdfDamping is the corruption of energy from an oscillating system, primarily through friction. The kineticenergy is transformed into heat. Dampers can be installed to increase the damping rate. Attention has beendevoted to active control of engineering structures for earthquake hazard mitigation. This type of controlsystems are often referred to as protective systems and have the advantage of being able to dynamicallymodify the response of a structure in order to increase the safety and reliability.One of the most promising classes of semi-active control devices is the Magnetorheological (MR)damper. It overcomes the expenses and technical difficulties associated with other types of semi-activedevices. The fluids are materials that respond to an applied magnetic field with a dramatic change inrheological behavior. The outstanding characteristic of these fluids is their ability to reversibly changefrom free- flowing, linear viscous liquids to semi-solids having controllable yield strength in millisecondswhen exposed to a magnetic field.Another type of semi-active control device is a controllable tuned liquid damper. It utilizes a sloshingfluid or a column of fluid to reduce the responses of a structure. In a tuned mass damper, the liquid in asloshing tank is used to add damping to the structural system. It is not very effective for a wide variety ofloading conditions.The hybrid mass damper (HMD) is a common device used in full-scale civil engineering buildings. TheHMD is actually a combination of the tuned mass damper and an active control actuator. The efficiencyof the HMD relies on the forces from the control actuator. A typical HMD requires less energy to operatethan a fully active mass damper system.An active mass damper (AMD) is a small-auxiliary mass that is installed on one of the upper floors of abuilding. An actuator is connected between the auxiliary mass and the structure. Response and loads are 13measured at key locations on the building and sent to a control computer. The computer then processedthe information according to an algorithm and sends the appropriate signal to the AMD actuator. The MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011actuator then reacts by applying inertial control forces to the structure to reduce the structural responses ina desired manner.Passive control systems relate to uncontrolled dampers, which require no input power to operate. They aresimple and generally low in cost, but are unable to adapt to changing needs. Passive control systems aremost commonly used in new and existing buildings that are in low seismic areas. Passive systems includebase isolation systems, friction dampers, viscoelastic dampers, and bracing systems.Base Isolation systems are used to isolate the dynamic force transfer from the structure to the base.Friction dampers consist of a steel plate and two plates holding the 9 steel plate from both sides. Allplates work together to absorb energy by friction as the building deforms due to seismic activity.Viscoelastic dampers attenuate the force due to external and seismic loads. Bracing systems are used topermanently stabilize buildings from external forces such as wind loads and earthquakes.Variable semi-active devices have been used to utilize forces generated by surface friction to dissipatevibratory energy in a structural system. The ability of semi-active devices to reduce drifts within a highstory building that is seismically excited has been investigated. With much success, the frictioncontrollable system has been employed in conjunction with a seismic isolation system.Effect of Wind on Structure. http://www.sefindia.org/forum/files/Effect_of_wind_on_structure_141.pdfWind produces three different types of effects on structure which is static, dynamic and aerodynamic. Theresponse of load depends on type of structure. When the structure deflects in response to wind load thenthe dynamic and aerodynamic effects should be analyzed in addition to static effect. Sound knowledge offluid and structural mechanics helps in understanding of details of interaction between wind flow andcivil engineering structures or buildings Flexible slender structures and structural elements are subjectedto wind induced along and across the direction of wind. When considering the response of a tall buildingto wind gusts, both along-wind and across-wind responses must be considered. These arise from differentthe former being primarily due to buffeting effects caused by turbulence; the latter being primarily due toalternate-side vortex shedding. The cross-wind response may be of particular importance because it islikely to exceed along-wind accelerations if the building is slender about both axes.Any building or structure which does not satisfy either of the above two criteria shall be examined fordynamic effects of wind: 14a) Buildings and closed structures with a height to minimum lateral dimension ratio of more than about MECH N349 | HCT, Abu Dhabi
    • Building Vibration 20115.0.b) Buildings and closed structures whose natural frequency in the first mode is less than 1 Hz.Wind induced oscillationThere are three forms of wind induced motion as follows:-a) Galloping - is transverse oscillations of some structures due to the development of aerodynamic forceswhich are in phase with the motion. It is characterized by the progressively increasing amplitude oftransverse vibration with increase of wind speed. Non circular cross sections are more susceptible to thistype of oscillationb) Flutter is unstable oscillatory motion of a structure due to coupling between aerodynamic force andelastic deformation of the structure. Perhaps the’ most common form is oscillatory motion due tocombined bending and torsion. Long span suspension bridge decks or any member of a structure withlarge values of d/t ( where d is the depth of a structure or structural member parallel to wind stream and tis the least lateral dimension of a member ) are prone to low speed flutter.c) Ovalling - This walled structures with open ends at one or both ends such as oil storage tanks, andnatural draught cooling towers in which the ratio of the diameter of minimum lateral dimension to thewall thickness is of the order of 100 or more, are prone to ovalling oscillations. These oscillations arecharacterized by periodic radial deformation of the hollow structure.The dynamic component which essentially causes the oscillation of structure is generated due to threereasons:-1) Gust The wind velocity at any location varies considerably with time. In addition to a steady windthere are effects of gusts which last for few seconds, and yield a more realistic assessment of wind load.In practice the peak gust are likely to be observed over an average time of 3.5 to 15 sec depending onlocation and sizeof structure..The intensity of gusts is also related to the duration of gusts that affects structures. Largerstructure will be affected more by gust of larger duration and thus subjected to smaller pressure comparedto smaller structure. 15The gust effect factor accounts for additional dynamic amplification of loading in the along-winddirection due to wind turbulence and structure interaction. It does not include allowances for across-wind MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011loading effects, vortex shedding, instability due to galloping or flutter, or dynamic torsional effects.Buildings susceptible to these effects should be designed using wind tunnel results.This factor accounts for the increase in the mean wind loads due to the following factors:• Random wind gusts acting for short durations over entire or part of structure.• Fluctuating pressures induced in the wake of a structure, including vortex shedding forces.• Fluctuating forces induced by the motion of a structure.2) Vortex SheddingWhen wind acts on a bluff body forces and moments in three mutually perpendicular directions aregenerated- out of which three are translation and three rotation. For civil and structures the force andmoment corresponding to the vertical axis (lift and yawing moment) are of little significance. Thereforethe flow of wind is considered two-dimensional consisting of along wind response and transverse windresponse.Along wind response refer to drag forces, and transverse wind is the term used to describe crosswind. Thecrosswind response causing motion in a plane perpendicular to the direction of wind typically dominatesover the along-wind response for tall buildings.Consider a prismatic building subjected to a smooth wind flow. The originally parallel upwindstreamlines are displaced on either side of the building due to boundary layer separation. This results inspiral vortices being shed periodically from the sides into the downstream flow of wind creating a lowpressure zone due to shedding of eddies called the wake. When the vortices are shed across windcomponent are generated in the transverse direction. At low wind speeds, since the shedding occurs at thesame instant on either side of the building, there is no tendency for the building to vibrate in thetransverse direction. It is therefore subject to long-wind oscillations parallel to the wind direction. Athigher speeds, the vortices are shed alternately, first from one and then from the other side. When thisoccurs, there is a force in the along-wind direction as before, but in addition, there is a force in thetransverse direction.This type of shedding, which gives rise to structural vibrations in the flow direction as well as in the 16transverse direction, is called vortex shedding. The frequency of shedding depends mainly on shape andsize of the structure, velocity of flow and to a lesser degree on surface roughness, turbulence of flow. MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Control Algorithms There are three types of control methods structural that based in study: 1. Passive control methods 2. Active Control Systems 3. Semi-active control algorithmsPassive control methods: In this case, the passive device does not need an external power. This kind of method hassome features such as : 1. No need for external energy 2. Stable 3. Simple process and operationLateral Load Resisting Systems: It’s the system that combines structure components to face and overcome the effects ofearthquakes. This system must be studied when designing a building that can withstandearthquakes. The structure components are: 1. Shear walls 2. Braced frames 3. Moment resisting frames 4. Horizontal trussesThis type of system also involved in architect’s structural. When engineers design this system forany particular building, they should review the concept of architectural of the building. 17 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Tuned Mass Damper (TMD)It’s a passive control device that is connected to the structure of building to absorb its responses.TMD should have: 1. Mass that is 2 % of total mass of the Building. 2. Spring (K) that change the systems and modes of TMD of the controlled building. 3. Viscous damper ( C) 18 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Principle of operation From the laws of physics, we know that F = ma and a =F/m. This means that when an external force is applied to asystem, such as wind pushing on a skyscraper, there has to be anacceleration. Consequently, the people in the skyscraper wouldfeel this acceleration. In order to make the occupants of thebuilding feel more comfortable, tuned mass dampers are placed instructures where the horizontal deflections from the winds forceare felt the greatest, effectively making the building standrelatively still.When the building begins to oscillate or sway, it sets the TMDinto motion by means of the spring and, when the building isforced right, the TMD simultaneously forces it to the left.Ideally, the frequencies and amplitudes of the TMD and thestructure should nearly match so that EVERY time the wind pushes the building, the TMDcreates an equal and opposite push on the building, keeping its horizontal displacement at or nearzero. If their frequencies were significantly different, the TMD would create pushes that were outof sync with the pushes from the wind, and the buildings motion would still be uncomfortablefor the occupants. If their amplitudes were significantly different, the TMD would, for example,create pushes that were in sync with the pushes from the wind but not quite the same size and thebuilding would still experience too much motion.The effectiveness of a TMD is dependent on the mass ratio (of the TMD to the structure itself),the ratio of the frequency of the TMD to the frequency of the structure (which is ideally equal toone), and the damping ratio of the TMD (how well the damping device dissipates energy). 19 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Viscous damper Fluid viscous damping is a way to add energy dissipation to the lateral system of abuilding structure. A fluid viscous damper dissipates energy by pushing fluid through an orifice,producing a damping pressure which creates a force.FLUID VISCOUS DAMPER DESCRIPTION 1. Very strong shock absorber. 2. Dumpers consists of stainless steel. 3. Live for 40 years. 4. The damping fluid is silicone oil 5. Very high technology seals that provide free leakage. 20 Viscous damper MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Principle of operation:The damping action is provided by the flow of fluid across the piston head. The piston transmitsenergy entering the system to the fluid in the damper, causing it to move within the damper. Themovement of the fluid within the damper fluid absorbs this kinetic energy by converting it intoheat. In automobiles, this means that a shock received at the wheel is damped before it reachesthe passengers compartment. In buildings this can mean that the building columns protected bydampers will undergo considerably less horizontal movement and damage during an earthquake.Active Control SystemsActive control systems have been studied extensively and are currently in use in a number ofstructures in Japan for protection against wind excitation and minor earthquakes. The term“active” is used to indicate that the operation of these systems requires a significant amount ofexternal power. The mechanical properties of these systems are typically adjusted based onfeedback from the structural system to which they are attached. Control forces are generallydeveloped by electro-hydraulic actuators which require a large power source for operation (onthe order of tens of kilowatts). Active control systems may also be designated as active energydissipation systems because the primary effect of these systems is to modify the level of dampingin a structure with only minor modification of stiffness. 21 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011SEMI-ACTIVE CONTROL:The use of passive control systems and active control systems represents two extremes in theapplication of control theory to earthquake hazard mitigation. A compromise between these twoextremes is available in the form of semi-active control systems which have been developed totake advantage of the best features of both passive and active control systems. The term “semi-active” is used to indicate that the operation of these systems requires a very small amount ofexternal power (on the order of tens of watts). As in an active control system, the mechanicalproperties are typically adjusted based on feedback from the structural system to which they areattached. As in a passive control system, semi-active control systems utilize the motion of thestructure to develop control forces. The control forces are developed through appropriateadjustment of damping or stiffness characteristics of the semi-active control system.Furthermore, the control forces always oppose the motion of the structure and therefore promotestability. Semi-Active control systems are typically considered to be fail-safe in the sense thatsemi-active devices can be designed to exhibit either prescribed damping or prescribed stiffnesscharacteristics in the event of a complete loss of power. 22 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Flexibility influence coefficients: This is used for expressing the elastic behavior in terms of stiffness and flexibility.The flexibility matrix written in terms of its coefficients aij is:  x  a a a  f 1  1   11 12 13      x2   a21 a22 a23  f 2        x3  a31 a33 a34  f 3     aij: The displacement at i due to a unit force applied at j when all other forces equal to zero.  First column: the displacements corresponding to f1=1 (f2=f3=0)  Second column: the displacements corresponding to f2=1 (f1=f3=0)  Third column: the displacements corresponding to f3=1 (f1=f2=0)Rule:  For the first column when f1=1 (f2=f3=0) 1  x   k1 0 0   1  1  1  f 1   x 2    0 0  0     k1 0 0    x3   1  0   k1     For the second column when f2=1 (f1=f3=0)  1     x  0  1  1 k1 0  0  1     x2   0    0 1      k1 k 2      x3  0 1 1  0  0          k1 k 2     For the third column when f3=1 (f1=f2=0)  1  x  0 0 k1    1  1 1   0  x 2   0 0   0  23   0 0 k1 k 2     x3   1  1  1  1   k1 k 2 k 3    MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011  The complete flexibility matrix is now the sum of the three prior matrixes: 1 1 1      x   k1 k1 k1  f1  1  1  1 1  1 1     x2          f 2    k1  k1 k 2  k1 k 2     x3  1 1 1  1  1  1  f 3        k1  k1 k 2  k1 k 2 k 3    For example:The flexibility matrix for a system shown below: 1)Given information:K1=2kK2=kK3=k 0.5 0.5 0.5Answer: 0.5 1.5 1.5    0.5 1.5 2.5   24 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011 2)Given information:K1=3kK2=kK3=k 0.3 0.3 0.3Answer: 0.31.3 1.3    0.31.3 2.3   3)Given information:K1=5kK2=3kK3=7k 25 0.2 0.2 0.2Answer: 0.2 0.5 0.5   0.2 0.5 0.7   MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011 4)Given information:K1=4kK2=2kK3=6k 0.25 0.25 0.25Answer: 0.25 0.75 0.75   0.25 0.75 0.92   5)Given information:K1=9kK2=3kK3=5k 0.1 0.1 0.1Answer: 0.10.4 0.4   0.10.4 0.6   26 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Mass and Stiffness Matrices Consider a building frame modeled by a set of rigid, massive floors supported by flexible,massless columns. This provides the simplest representation of a building for the purposes ofinvestigating lateral dynamic responses, as produced by earthquakes or strong winds. The lateralposition of mass i with respect to the ground will be given the variable ri, ki is the lateral stiffnessof the columns in story i, and the mass of mass i is mi.For a three-story building, this kind of representation is shown in Figure 1. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Figure 1. A simplified model of a building frame with massive rigid floors and light flexible columns.Exercise 1: Show that the mass matrix and stiffness matrix for this three story building can bewritten:Solution: let x1=1 and x2=x3=0. The forces required at 1,2 and 3, considering on the right aspositive, are: F1= k1+k2= k11 F2= - k2= k21 27 F3= 0 = k31Repeat with x2=1, x1=x3=0, the forces are now: MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011 F1= - k2= k12 F2= k2 + k3 = k22 F3= - k3 = k32For the last column of k’s, let x3=1 and x1=x2=0. The forces are: F1= 0 =k13 F2= - k3 = k23 F3= k3 = k33Therefore the mass matrix and stiffness matrix for a three story building is:Example 1.Solution: 28 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Example 2.Solution:Example 3. 29 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Example 4.Solution:Example 5.Solution: 30 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011MATLAB Matlab is a program that performs various numerical operations. Like a bigcalculator. Computer languages are generally divided into low-level languages, thatinteract with the specific hardware directly and need to be both written and compiled forthe specific setting you are using. This is very powerful, because it allows you to use theresources of your machine in whatever way you choose. High-level languages, on theother hand, can be transferred from machine to machine (and, in some cases, fromoperating system to operating system), but often will need to be compiled for a specificsetting. Matlab functions as a scripting language. Scripting languages are high-levelcomputer languages. However, above and beyond the portable nature of most high-level languages, a system specific interpreter interprets them online, as they run.Therefore, you will not need to compile the programs you write on Matlab. Scriptinglanguages are relatively easy to learn. However, they do not retain the same level offlexibility as low-level languages. Moreover, because they need to be interpreted asthey run, they are often slower than the equivalent program written in a compiled high-level language. 31 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Applying MATLAB in the resultsA=[-2 0.1;0.1 -2]; %Matrix determined by equations of motion. [v,d]=eig(A) %Find Eigenvalues and vectors. The eigenvectors arethe columns of "v," the eigenvectors are %the diagonal elements of "d"x0=[1 0] %Initial conditionsgamma=inv(v)*x0 %Find unknown coefficients gamma 32 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011A=[-2 0.1;0.1 -2]; %Matrix determined by equations of motion. [v,d]=eig(A) %Find Eigenvalues and vectors. The eigenvectors arethe columns of "v," the eigenvectors are %the diagonal elements of "d"x0=[1 0] %Initial conditionsgamma=inv(v)*x0 %Find unknown coefficients gamma 33 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011%Define Array from equations of motion.A=[0.5 1.5;1.5 2.5]; %2 masses[v,d]=eig(A); %Find Eigenvalues and vectors.omega=sqrt(diag(-d)); %Get frequenciesx0=[1 0] %Initial conditiongam=inv(v)*x0 %Find unknown coefficients 34 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011%Define Array from equations of motion.A=[0.3 0.3;0.3 0.3]; %2 masses[v,d]=eig(A); %Find Eigenvalues and vectors.omega=sqrt(diag(-d)); %Get frequenciesx0=[1 0] %Initial conditiongam=inv(v)*x0 %Find unknown coefficients 35 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011%Define Array from equations of motion.A=[0.3 1.3;1.3 0.3]; %2 masses[v,d]=eig(A); %Find Eigenvalues and vectors.omega=sqrt(diag(-d)); %Get frequenciesx0=[1 0] %Initial conditiongam=inv(v)*x0 %Find unknown coefficients 36 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011%Define Array from equations of motion.A=[0.3 1.3;1.3 2.3]; %2 masses[v,d]=eig(A); %Find Eigenvalues and vectors.omega=sqrt(diag(-d)); %Get frequenciesx0=[1 0] %Initial conditiongam=inv(v)*x0 %Find unknown coefficients 37 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011%Define Array from equations of motion.A=[0.2 1.2;1.2 0.2]; %2 masses[v,d]=eig(A); %Find Eigenvalues and vectors.omega=sqrt(diag(-d)); %Get frequenciesx0=[1 0] %Initial conditiongam=inv(v)*x0 %Find unknown coefficients 38 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011%Define Array from equations of motion.A=[0.2 0.5;0.5 0.2]; %2 masses[v,d]=eig(A); %Find Eigenvalues and vectors.omega=sqrt(diag(-d)); %Get frequenciesx0=[1 0] %Initial conditiongam=inv(v)*x0 %Find unknown coefficients 39 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011%Define Array from equations of motion.A=[0.2 0.5;0.7 0.2]; %2 masses[v,d]=eig(A); %Find Eigenvalues and vectors.omega=sqrt(diag(-d)); %Get frequenciesx0=[1 0] %Initial conditiongam=inv(v)*x0 %Find unknown coefficients 40 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011A=[-2 0.1;0.1 -2]; %Matrix determined by equations of motion. [v,d]=eig(A) %Find Eigenvalues and vectors. The eigenvectors arethe columns of "v," the eigenvectors are %the diagonal elements of "d" 41 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011A=[-2 0.1;0.1 -2]; %Matrix determined by equations of motion. [v,d]=eig(A) %Find Eigenvalues and vectors. The eigenvectors arethe columns of "v," the eigenvectors are %the diagonal elements of "d" 42 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011Conclusion All in all, earthquakes have so many negative results on building. In this case we canfind devices that can protect the building from the effects of vibration. During the earthquakes,the energy of the huge vibration will be sent to the building. Engineers designed devices thatabsorb this energy and kick it out in a form of heat. To translate the movements of earthquake,we need to study the types of algorithms that help us to reduce the effects of earthquakes. Todesign a building that has resistance of earthquakes, we need to design the Lateral LoadResisting Systems. This system gathers the structure components to absorb the energy andovercome the effects of the earthquakes. One of the passive control devices called Tuned MassDamper. This device consists of mass, spring and dumper device. One example is the viscousdumper. It’s part of the TMD, and its installed in the structure and superstructures of buildingwhere is the highest effect of the earthquake on the building. Part of calculations, it’s importantto study the Flexibility influence coefficient. It focuses on the behavior in terms of stiffness andflexibility. Another important subject is mass stiffness and matrices. This provides the simplestrepresentation of a building for the purposes of investigating lateral dynamic responses. Based onthe calculations, we can know what is the best way to choose the best module. 43 MECH N349 | HCT, Abu Dhabi
    • Building Vibration 2011References: 1. http://www.rwdi.com/cms/publications/18/t06.pdf 2. http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/Eva_Burk/Evas%201st%20page.htm 3. http://www.taylordevices.com/fluidviciousdamping.html 4. http://www.expertune.com/artCE87.html 5. http://nms.csail.mit.edu/papers/binomial-infocom01.pdf 6. http://www.benthamscience.com/meng/samples/meng%201-1/Kumar.pdf 7. http://www.bookrags.com/research/earthquake-proofing-techniques-woi/ 8. http://www.whatprice.co.uk/building/earthquake-proof-buildings.html 9. http://www.reidsteel.com/information/earthquake_resistant_building.htm 10. http://www.nasa.gov/worldbook/earthquake_worldbook.html 11. http://www.buildingssteel.com/earthquake-how.htm 12. http://journals.pepublishing.com/content/w61g17254m84506j/ 13. http://www.hindawi.com/journals/mpe/2008/754951.html 14. http://iopscience.iop.org/09641726/7/5/003;jsessionid=BA6E2E5EC098268D422448 A75FA80E9F.c2 15. http://www.ias.ac.in/resonance/Dec2004/pdf/Dec2004Classroom4.pdf 16. www.ikb.poznan.pl/jacek.wdowicki/Pliki/materialy/.../Li03.pdf 17. ncdr.nat.gov.tw/2icudr/2icudr_cd/PDF/P19.pdf 18. http://www.taylordevices.eu/pdfs/tall-building.pdf 19. e-book.lib.sjtu.edu.cn/nascc2004/data/.../WindResDsTallBldgsJapan.pdf 20. http://www.mita.sd.keio.ac.jp/publications/data/c199501.pdf 21. http://www.pbworld.com/news_events/publications/technical_papers/pdf/50_ALiterar yReview.pdf 22. http://www.sefindia.org/forum/files/Effect_of_wind_on_structure_141.pdf 44 MECH N349 | HCT, Abu Dhabi