- This document discusses modeling and energy methods for determining equations of motion and natural frequencies of systems. It provides alternative approaches to calculating these values when forces or torques are difficult to determine directly.
- Energy methods are useful for more complicated multi-degree of freedom and distributed mass systems that will be discussed later. Potential and kinetic energy equations are presented for springs and various mass configurations.
- The conservation of energy principle and Lagrange's equations can be used to derive equations of motion from the kinetic and potential energy of a system, providing alternative ways to model dynamic behavior. Examples are worked through for simple spring-mass and pendulum systems.
Response of dynamic systems to harmonic excitation is discussed. Single degree of freedom systems are considered. For general damped multi degree of freedom systems, see my book Structural Dynamic Analysis with Generalized Damping Models: Analysis (e.g., in Amazon http://buff.ly/NqwHEE)
What is a multiple dgree of freedom (MDOF) system?
How to calculate the natural frequencies?
What is a mode shape?
What is the dynamic stiffness matrix approach?
#WikiCourses
https://wikicourses.wikispaces.com/Lect04+Multiple+Degree+of+Freedom+Systems
https://eau-esa.wikispaces.com/Topic+Multiple+Degree+of+Freedom+%28MDOF%29+Systems
Response of dynamic systems to harmonic excitation is discussed. Single degree of freedom systems are considered. For general damped multi degree of freedom systems, see my book Structural Dynamic Analysis with Generalized Damping Models: Analysis (e.g., in Amazon http://buff.ly/NqwHEE)
What is a multiple dgree of freedom (MDOF) system?
How to calculate the natural frequencies?
What is a mode shape?
What is the dynamic stiffness matrix approach?
#WikiCourses
https://wikicourses.wikispaces.com/Lect04+Multiple+Degree+of+Freedom+Systems
https://eau-esa.wikispaces.com/Topic+Multiple+Degree+of+Freedom+%28MDOF%29+Systems
Specific Speed of Turbine | Fluid MechanicsSatish Taji
Watch Video of this presentation on Link: https://youtu.be/I0fHo0z6EgA
For notes/articles, Visit my blog (link is given below).
For Video, Visit our YouTube Channel (link is given below).
Any Suggestions/doubts/reactions, please leave in the comment box.
Follow Us on
YouTube: https://www.youtube.com/channel/UCVPftVoKZoIxVH_gh09bMkw/
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This chapter contains:-.
Analytical Methods of two dimensional steady state heat conduction
Finite difference Method application on two dimensional steady state heat conduction.
Finite difference method on irregular shape of a system
single degree of freedom systems forced vibrations KESHAV
SDOF, Forced vibration
includes following content
Forced vibrations of longitudinal and torsional systems,
Frequency Response to harmonic excitation,
excitation due to rotating and reciprocating unbalance,
base excitation, magnification factor,
Force and Motion transmissibility,
Quality Factor.
Half power bandwidth method,
Critical speed of shaft having single rotor of undamped systems.
Fluid Mechanics Chapter 4. Differential relations for a fluid flowAddisu Dagne Zegeye
Introduction, Acceleration field, Conservation of mass equation, Linear momentum equation, Energy equation, Boundary condition, Stream function, Vorticity and Irrotationality
Specific Speed of Turbine | Fluid MechanicsSatish Taji
Watch Video of this presentation on Link: https://youtu.be/I0fHo0z6EgA
For notes/articles, Visit my blog (link is given below).
For Video, Visit our YouTube Channel (link is given below).
Any Suggestions/doubts/reactions, please leave in the comment box.
Follow Us on
YouTube: https://www.youtube.com/channel/UCVPftVoKZoIxVH_gh09bMkw/
Blog: https://e-gyaankosh.blogspot.com/
Facebook: https://www.facebook.com/egyaankosh/
This chapter contains:-.
Analytical Methods of two dimensional steady state heat conduction
Finite difference Method application on two dimensional steady state heat conduction.
Finite difference method on irregular shape of a system
single degree of freedom systems forced vibrations KESHAV
SDOF, Forced vibration
includes following content
Forced vibrations of longitudinal and torsional systems,
Frequency Response to harmonic excitation,
excitation due to rotating and reciprocating unbalance,
base excitation, magnification factor,
Force and Motion transmissibility,
Quality Factor.
Half power bandwidth method,
Critical speed of shaft having single rotor of undamped systems.
Fluid Mechanics Chapter 4. Differential relations for a fluid flowAddisu Dagne Zegeye
Introduction, Acceleration field, Conservation of mass equation, Linear momentum equation, Energy equation, Boundary condition, Stream function, Vorticity and Irrotationality
This presentation gives an introduction to mechanical vibration or Theory of Vibration for BE courses. Presentation is prepared as per the syllabus of VTU.For any suggestions and criticisms please mail to: hareeshang@gmail.com or visit:ww.hareeshang.wikifoundry.com.
Thanks for watching this presentation.
Hareesha N G
Multiscale methods for next generation graphene based nanocomposites is proposed. This approach combines atomistic finite element method and classical continuum finite element method.
Slides of my talk at IISc Bangalore on nanomechanics and finite element analysis for statics and dynamics of nanoscale structures such as carbon nanotube, graphene, ZnO nanotube and BN nano sheet.
Finite element modelling of nonlocal dynamic systems, Modal analysis of nonlocal dynamical systems, Dynamics of damped nonlocal systems, Numerical illustrations
All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.
All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.
Instantaneous Gelation in Smoluchwski's Coagulation Equation Revisited, Confe...Colm Connaughton
Invited talk given at "Boltzmann equation:
mathematics, modeling and simulations
In memory of Carlo Cercignani", Institut Henri Poincare, Paris, February 11, 2011.
From the Egyptian, Roman to the Victorian era, important engineering structures were built "solid" for strength and durability. Although many such structures have passed the test of time and therefore validate the underlying design philosophy, they may not always represent the most efficient way of utilising materials. Due to the unprecedented pressure on sustainability and global focus on net-zero, using less material for future engineering structures is mandatory. The rise of 3D printing technology provides a timely solution towards creating "hollow" or "porous" structural members, which have the potential to utilise lesser materials compared to their equivalent solid counterparts. However, the mechanical behaviour of such hollow structures must be understood well and subsequently. They need to be designed carefully to withstand static and dynamic loads to be experienced during their lifetime. This talk will outline some recent results from my group towards understanding the mechanics of lattice structures. New results on equivalent elastic properties, buckling and wave propagation will be discussed.
Homogeneous dynamic characteristics of damped 2 d elastic latticesUniversity of Glasgow
Lattice materials are characterised by their equivalent elastic moduli for analysing mechanical properties of the microstructures. The values of the elastic moduli under static forcing condition are primarily dependent on the geometric properties of the constituent unit cell and the mechanical properties of the intrinsic material. Under a static forcing condition, the equivalent elastic moduli (such as Young's modulus) are always positive. Poisson’s ratio can be positive or negative, depending only on the geometry of the lattice (e.g., re-entrant lattices have negative Poisson’s ratio). When dynamic forcing is considered, the equivalent elastic moduli become functions of the applied frequency and can become negative at certain frequency values. This paper, for the first time, explicitly demonstrates the occurrence of negative equivalent Young's modulus in lattice materials. In addition, we show the reversal of Poisson’s ratio. Above certain frequency values, a regular lattice can have negative Poisson’s ratio, while a re-entrant lattice can have a positive Poisson’s ratio. Using a titanium-alloy hexagonal lattice metastructure, it is shown that the real part of experimentally measured in-plane Young's modulus becomes negative under a dynamic environment as well as the reversal of the real part of the Poisson’s ratio. In fact, we show that the onset of negative Young's modulus and Poisson’s ratio reversal in lattice materials can be precisely determined by capturing the sub-wavelength scale dynamics of the system. Experimental confirmation of the negative Young's moduli and Poisson’s ratio reversal together with the onset of the same as a function of frequency provide the necessary physical insights and confidence for its potential exploitation in various multi-functional structural systems and devices across different length scales.
Special Plenary Lecture at the International Conference on VIBRATION ENGINEERING AND TECHNOLOGY OF MACHINERY (VETOMAC), Lisbon, Portugal, September 10 - 13, 2018
http://www.conf.pt/index.php/v-speakers
Propagation of uncertainties in complex engineering dynamical systems is receiving increasing attention. When uncertainties are taken into account, the equations of motion of discretised dynamical systems can be expressed by coupled ordinary differential equations with stochastic coefficients. The computational cost for the solution of such a system mainly depends on the number of degrees of freedom and number of random variables. Among various numerical methods developed for such systems, the polynomial chaos based Galerkin projection approach shows significant promise because it is more accurate compared to the classical perturbation based methods and computationally more efficient compared to the Monte Carlo simulation based methods. However, the computational cost increases significantly with the number of random variables and the results tend to become less accurate for a longer length of time. In this talk novel approaches will be discussed to address these issues. Reduced-order Galerkin projection schemes in the frequency domain will be discussed to address the problem of a large number of random variables. Practical examples will be given to illustrate the application of the proposed Galerkin projection techniques.
Eh4 energy harvesting due to random excitations and optimal designUniversity of Glasgow
This lecture is about vibration energy harvesting when both the excitation and the system have uncertainties. Two cases, namely, when the excitation is a random process and when the system parameters are described by random variables are described. Optimal design for both cases is discussed.
This talk is about the analysis of nonlinear energy harvesters. A particular example of an inverted beam harvester proposed by our group has been discussed in details.
Dynamic Homogenisation of randomly irregular viscoelastic metamaterialsUniversity of Glasgow
An analytical framework is developed for investigating the effect of viscoelasticity on irregular hexagonal lattices. At room temperature, many polymers are found to be near their glass temperature. Elastic moduli of honeycombs made of such materials are not constant, but changes in the time or frequency domain. Thus consideration of viscoelastic properties is essential for such honeycombs. Irregularity in lattice structures being inevitable from a practical point of view, analysis of the compound effect considering both irregularity and viscoelasticity is crucial for such structural forms. On the basis of a mechanics-based bottom-up approach, computationally efficient closed-form formulae are derived in the frequency domain. The spatially correlated structural and material attributes are obtained based on Karhunen-Lo\`{e}ve expansion, which is integrated with the developed analytical approach to quantify the viscoelastic effect for irregular lattices. Consideration of such spatially correlated behaviour can simulate the practical stochastic system more closely. Two Young's moduli and shear modulus are found to be dependent on the viscoelastic parameters, while the two in-plane Poisson's ratios are found to be independent of viscoelastic parameters. Results are presented in both deterministic and stochastic regime, wherein it is observed that the elastic moduli are significantly amplified in the frequency domain. The response bounds are quantified considering two different forms of irregularity, randomly inhomogeneous irregularity and randomly homogeneous irregularity. The computationally efficient analytical approach presented in this study can be quite attractive for practical purposes to analyse and design lattices with predominantly viscoelastic behaviour along with consideration of structural and material irregularity.
Transient response of delaminated composite shell subjected to low velocity o...University of Glasgow
Transient dynamic response of delaminated composite shell subjected to low velocity oblique impact - a finite element method is proposed and new results are discussed
Dynamic stiffness and eigenvalues of nonlocal nano beams - new methods for dynamic analysis of nano-scale structures. This lecture gives a review and proposed new techniques.