Mathematical Model of the Uniform Beam for Linear Vibration Analysis

Abstract

For a beam with uniformly distributed mass and stiffness, a linear mathematical model is derived that closely duplicates dynamic behavior through the two rigid-body modes and the first of two bending modes. The model has four terminals, transverse and angular displacement at each end, permitting it to be connected into assembly on a fixed-end basis. Eight degrees of freedom are used. It is shown that the response is superior to that obtained with the normal mode or lumped parameter approaches when a comparable number of degrees of freedom are used. Application of the results to a specific case involves only arithmetic operations.