Analysis of excited rod on the Laplace variable domain

Abstract

This work analyzes the continuum vibration of a uniform slender bar on the Laplace variable domain and validates the arising time response with the well-known time-domain analysis called the method of separation of variable. A novel form of the method of separation of variable is used alongside the popular form that assumes that the steady state response of the rod is of same form as the excitation to arrive at identical results that validate the presented s-domain analysis. Even though analysis is presented generally, a numerical case study is simulated and discussed. Both vibratory responses of displacement and stress are discussed. Possible application of method of this work is suggested to include the case of blades attached to an unbalanced shaft.