Transverse Vibration Analysis in Beams

This course covers the comprehensive understanding of transverse vibration in beams, a key component of structural dynamics. It begins with an exploration of various beam theories such as Euler Bernoulli, Release, Shear, and Timoshenko, along with their assumptions. The course then delves into the derivation of the governing differential equation of motion for the Euler Bernoulli beam model using Newton's Second Law and Hamilton's equation. It further discusses the formulation of a boundary value problem and the process of obtaining non-trivial solutions for determining infinite eigenvalues and eigenfunctions of the beam. For instance, the course uses a cantilever beam to demonstrate how different boundary conditions can lead to diverse solutions. The course also covers the analysis of the transverse vibration of a beam under non-classical boundary conditions, such as a beam carrying a concentrated mass or resting on an elastic pad. It concludes with the derivation of the expression for damp free vibration response of Euler Bernoulli beam subjected to initial conditions.