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)?
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).