Computation of Eigenvalue-Eigenvector and Harmonic Motion Solution for Laminated Rubber-Metal Spring

Abstract

This paper presents the modeling of multi-degree-of-freedom on laminated rubber-metal spring in axial direction displacement. Two methods are used which are firstly the eigenvalues and eigenvectors solution and secondly called harmonic motion solution. In eigenvalues and eigenvectors approach, equation of motion of laminated rubber-metal spring is developed using spring-mass system. Then, the equation was rewritten again in matrix and harmonic motion in order to reduce the difficulty and become realistic to be solved using characteristic equation. On the other hand, harmonic motion approach is started from governing equation in term of mode shape. By using this concept, two important equations are finally derived which are displacement and velocity. Using these two methods, finally the maximum displacements of laminated rubber-metal spring are plotted as well as in frequency domain axis. Two types of analysis are considered in this study which are undamped and damped system. Based on the results obtained, the maximum displacement occurred at undamped system. By increasing the number of degree-of-freedom, the displacement is slowly reduced.