Vibration analysis of hysteretically damped mass-loaded beams

Abstract

A procedure for determining the dynamic displacement and dynamic strain of a hysteretically damped mass-loaded free-free beam, subjected to simple harmonic, half-sine pulse and white noise excitations, is presented. Although free-free beams are considered in the analysis, the same procedure could also be used for vibration analysis of mass-loaded beams with other end conditions. The mode shapes for free vibration, displacement and strain due to simple harmonic and half-sine pulse force excitation are presented in graphical form. The maximum mean square displacement and mean square strain are tabulated for Gaussian white noise excitation. The analysis is used to analyze a space structure, which was modelled as a mass-loaded free-free beam. An exhaustive optimization search was made to obtain a structure with minimum dynamic response, when it is subjected to simple harmonic and half-sine pulse force excitations and minimum mean square response when subjected to Gaussian white noise excitation.