Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Engineering Mechanics - Notes, Videos, MCQs & PPTs

Mechanical Engineering : Virtual Work and Displacements Mechanical Engineering Notes | EduRev

The document Virtual Work and Displacements Mechanical Engineering Notes | EduRev is a part of the Mechanical Engineering Course Engineering Mechanics - Notes, Videos, MCQs & PPTs.
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Virtual Work and Displacements

Using the concept of virtual displacements, and virtual work, we can derive the equations of motion of lumped parameter systems.

Example 1 Mass/Spring System

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Here number of degrees of freedom =1 Co-ordinate to describe the motion is x Now consider free-body diagram, at some time t

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

General one degree of freedom system If qis the co-ordinate used to describe the movement then the general form of δW is as follows:

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

we call δq1 – generalised displacement Q1 – generalised force. From principle of virtual work

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Example Referring to the mass/spring system again

x= q1

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Example 2

Simple pendulum

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

This is another one degree of freedom system. During a virtual displacement, δθ, the virtual work done is

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Example 3 – two degrees of freedom system

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

Virtual Work and Displacements Mechanical Engineering Notes | EduRev

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