Sensitivity Analysis of Dynamic Response by Change in Excitation Force and Cross-sectional Shape for Damped Vibration of Cantilever Beam

Abstract

This paper describes the time rate of change of dynamic response of a cantilever beam inserted with adamping element, such as bonding, which is excited under a general force at various locations. A sensitivityanalysis was performed in a finite element model to show that two types of second-order algebraic governingequations were used to predict the rate of change of dynamic displacement: one is related to the modalcoordinate linked to a physical coordinate, and the other to the design parameter of the time rate of change ofdisplacement. The sensitivity differential equation formulation includes more complicated terms compared withthat of the undamped cantilever beam. The sensitivities of the dynamic response were observed by changing thelocation of the excitation force, displacement extraction, and cross-sectional area of the beam. The analyticalresults obtained by this suggested theory showed a relatively good agreement when compared with thoseobtained using the commercial finite element program. The suggested analysis procedure enables the prediction ofthe response sensitivity for any finite element model of the dynamic system.