CE 102 covers the principle of virtual work and its applications to determine unknown forces and displacements in mechanical systems. The principle states that the total virtual work done by external forces acting on a system in static equilibrium must be zero for any virtual displacement that is kinematically admissible while maintaining constraints. Several example problems are provided to illustrate the use of virtual work to solve for unknown forces in ladder systems, lifting platforms, linkages, and other mechanical assemblies.
Unit 5- balancing of reciprocating masses, Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
This session covers the basics that are required to analyse indeterminate trusses to maximum of two degree indeterminacy which includes,
strain energy stored due to axial loads and bending stresses,
maxwell's reciprocal deflection theorem,
Betti's law,
castigliano's theorems,
problems based on castigliano's theorems on beams and frames,
unit load method,
problems on trusses with unit load method,
lack of fit in trusses,
temperature effect on truss members.
Unit 5- balancing of reciprocating masses, Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
This session covers the basics that are required to analyse indeterminate trusses to maximum of two degree indeterminacy which includes,
strain energy stored due to axial loads and bending stresses,
maxwell's reciprocal deflection theorem,
Betti's law,
castigliano's theorems,
problems based on castigliano's theorems on beams and frames,
unit load method,
problems on trusses with unit load method,
lack of fit in trusses,
temperature effect on truss members.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...
Virtual work modified [compatibility mode](1)
1. CE 102: EngineeringCE 102: Engineering
Mechanics
Principle of Virtual WorkPrinciple of Virtual Work
2. Work of a ForceWork of a Force
rdF=dU
= work of the force corresponding toF
p g
the displacement rd
dU = F ds cosα
α= 0, dU =+ F ds α=
π
2
, dU = 0α= π , dU = − F ds
2
dU = Wdy
3. Work of a CoupleWork of a Couple
Small displacement of a rigid body:Small displacement of a rigid body:
• translation to A’B’
t ti f B’ b t A’ t B”
ddFdFW
• rotation of B’ about A’ to B”
rdθF=dsF=rdF
rd+rdF+rdF=W
22
211
dθM
4. Principle of Virtual Workp
• Imagine the small virtual displacement of particle which
is acted upon by several forces.
• The corresponding virtual work,
δR
rδF+F+F=rδF+rδF+rδF=δU
321321
rδR
Principle of Virtual Work:
• If a particle is in equilibrium, the total virtual work of forces
acting on the particle is zero for any virtual displacement.
• If a rigid body is in equilibrium, the total virtual work
of external forces acting on the body is zero for any
virtual displacement of the bodyvirtual displacement of the body.
• If a system of connected rigid bodies remains connected
during the virtual displacement, only the work of theg p y
external forces need be considered.
5. Different types of forcesDifferent types of forces
• Forces that do work are called
active force.
• Reactive and internal forces doReactive and internal forces do
not do any work.
• Virtual displacements are to be• Virtual displacements are to be
given carefully so that the
active forces are only theactive forces are only the
known forces and the forces we
are interested in obtainingare interested in obtaining
• Similar to FBD we draw active
f di (AFD)force diagram (AFD).
7. Work of a ForceWork of a ForceForces which do no work:
• reaction at a frictionless pin due to rotation of a bodyp y
around the pin
• reaction at a frictionless surface due to motion of a
body along the surfacebody along the surface
• weight of a body with cg moving horizontally
• friction force on a wheel moving without slippingfriction force on a wheel moving without slipping
Sum of work done by several forces may be zero:
• bodies connected by a frictionless pin
• bodies connected by an inextensible cord
• internal forces holding together parts of a rigid body
8. Degrees of FreedomDegrees of Freedom
• DOF in this context is the total number• DOF in this context is the total number
of independent coordinates required to
specify the complete location of everyspecify the complete location of every
member of the structure.
F VW h d i hi ill• For VW method in this course we will
use only 1-DOF systems.
1 DOF 2 DOF
9. To summarizeTo summarize
P i i l f i t l k• Principle of virtual work
– The virtual work done by external active
forces on an ideal mechanical system inforces on an ideal mechanical system in
equilibrium is zero for any all virtual
displacements consistent with the
constraints.constraints.
• Ideal system:
All surfaces joints etc are frictionless– All surfaces, joints etc. are frictionless.
– We will deal with ideal system in this course.
• Consistent with constraints:Consistent with constraints:
– The virtual displacement should be such that they
should not do allow the non-active forces to do any
kwork.
10. Why principle of Virtual WorkWhy principle of Virtual Work
F l h i ( ill l• For complex mechanisms (we will solve some
problems) we do not need to dismember the
systemsystem.
• We obtain the active unknown force in one
shot without bothering about the reactiveshot without bothering about the reactive
forces.
• Such type of analysis will be a stepping stone• Such type of analysis will be a stepping stone
to VW analysis using deformations when you
teach Solid Mechanics Structural Mechanicsteach Solid Mechanics, Structural Mechanics
etc. not to mention powerful Approximate
methods like the Finite Element Method.
11.
12.
13.
14. Problem 1Problem 1
• Assuming frictionless contacts,
determine the magnitude of P forg
equilibrium
This problem will beThis problem will be
referred to as the
Ladder problem
15.
16. Problem 2Problem 2
• The pressure p driving a piston of diameter
100 mm is 1 N/mm2. At the configuration
shown, what weight W will the system hold if
friction is neglected
This along with the ladderg
problem forms a framework
for many other problems
17.
18. Problem 3
(Shames)
• A hydraulic lift platform for loading trucks supports a weight 2W.
Only one side of the system has been shown; the other side is
id ti l Wh t f F h ld th h d li li d id tidentical. What force F should the hydraulic cylinder provide to
support the weight W. Assume that the hydraulic device is
inclined at a clockwise of α with respect to the horizontal. Neglect
f i i hfriction everywhere.
19.
20. Problem 4 MK5Problem 4 MK5
• A power operated loading platform designed for the back of a truck is• A power-operated loading platform designed for the back of a truck is
shown. The position of the platform is controlled by the hydraulic
cylinder, which applies force at C. The links are pivoted to the truck
frame at A, B, and F. Determine the force P supplied by the cylinder in
d t t th l tf i th iti h Th f thorder to support the platform in the position shown. The mass of the
platform and the links may be neglected compared with that of the 250
kg crate with center of mass at G.
21.
22. Problem 5 BJ8Problem 5 BJ8
• A f P i li d t lid C h Th t t f th• A force P is applied to slider C as shown. The constant of the
spring is 1.6 kN/m, and the spring is un-stretched when member
BD is horizontal. Neglecting friction between the slider and the
guide rod and knowing that BC = BD = 150 mm, determine theg g ,
magnitude of P so that θ = 25 deg when the system is in
equilibrium.
23. A small modifiction:A small modifiction:
I have used Q for the
resisting force and P
for the spring force.p g
24. Problem 6Problem 6
D t i Q f ilib i f th t• Determine Q for equilibrium for the system
shown. The pulleys are frictionless and have
masses W1 and W2. The sliding body has massmasses W1 and W2. The sliding body has mass
W3.
25. Problem 7Problem 7
• Find the force Q required to maintain
the system in equilibrium.y q
26.
27.
28. Problem 8Problem 8
• Determine the couple M which must bep
applied at O in order to support the
mechanism in the position θ = 30o. The
f th di k t C b OA d b BCmasses of the disk at C, bar OA, and bar BC
are mo, m, and 2m respectively.
29.
30. Problem 9Problem 9
• Determine force in member CD by usingDetermine force in member CD by using
the method of virtual work.
33. Problem 1
BJ8
Th b li k h i d b• The two-bar linkage shown is supported by a
pin and bracket at B and a collar at D that
slides freely on a vertical rod Determine theslides freely on a vertical rod. Determine the
force P required to maintain the equilibrium of
the linkage.g
38. Problem 3 MK5Problem 3 MK5
• Th l ti f th l tf f t d b th f• The elevation of the platform of mass m supported by the four
identical links is controlled by the hydraulic cylinders AB and AC
which are pivoted at point A. Determine the compression P in
each of the cylinders required to support the platform for they q pp p
specified angle θ
Meriam and KraigeMeriam and Kraige
39.
40. Problem 4
MK2
• Obtain the clamping force Q developed for
the pliers when the handle force is Pthe pliers when the handle force is P.
41.
42.
43.
44. Problem 5 MK5Problem 5 MK5
• The claw of the remote action actuator• The claw of the remote-action actuator
develops a clamping force C as a result of
the tension P in the control rod Express Cthe tension P in the control rod. Express C
in terms of P for the configuration shown
where the jaws are parallel.where the jaws are parallel.
45.
46. Problem 6 ShamesProblem 6 Shames
• Find the force delivered
at C in the horizontal
direction to crush thedirection to crush the
rock. Pressure p1= 100
M-Pa and p2= 60 M-Pa
( d b(measured above
atmospheric pressure).
The diameters ofThe diameters of
pistons are 100mm
each. Neglect the
weight of the rodsweight of the rods.
47.
48.
49. Problem 7 BJ10Problem 7 BJ10
D i h i l f• Determine the vertical movement of
joint C, if the member FG is lengthened
by 50 mm