Question

Problem 1: Axial vibrations of a rod The rod of length L is fixed at ends x = 0 and x = L. The density of the rod is ρ(x), stiffness k(x) being subjected to a force f(x, t). Let's derive the equations for axial vibrations of a rod using almped model. We express the rod niy mol 41 in as a chain of masses m,mm, connected to each other through springs as shown in the figure. Let's say each mass m is subject to forces F(t). The position of each mass m, is marked by x and the displacement about this position is expressed as u(t) (1 a) Write the force balance equation for a mass m%- b) Following the same procedure as we did in class, derive the equation for motion in terms of density p(x) force per unit length (x,t) and stiffness k(x)

Answer 1

In this solution some basic concepts of Vibration Mechanics are used. For more information, refer to any standard textbook or drop a comment below. Please give a positive rating if solution is helpful.

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