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I was watching this video (the link to the video is https://www.youtube.com/watch?v=AoxTyIJprg8&list=PLMXj6GKKnHI6Lftj7CXr9WusMkXi5s9yH&index=60) which is part of a course on mechanical vibrations. Can someone explain how the expression for strain is derived in the video? Why is strain the derivative of u(x,t)? enter image description here

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  • $\begingroup$ Are you interested why $\epsilon$ is a derivative of u, t, or are you interested about the derivation of bending strain, or both? $\endgroup$ – NMech Apr 5 at 5:49
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Strain is the ratio of change in length of a layer of fiber in the beam with respect to its original length. And it is a function of displacement (elongation/shortening) in direction of the longitudinal axis, x, at time t (for the changes, length and sign, are dynamic in nature).

enter image description here

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