Disordered Dynamic Systems Resulting From Approximate Modeling and Analysis

Abstract

Abstract Some dynamic systems exhibit curve veering behavior or avoided crossings when their natural frequencies are plotted against a system parameter, while some other show a curve crossing behavior or frequency coalescence. The curve veering behavior is also observed in disordered systems where the symmetry of the system is slightly perturbed and a mode localization takes place. In some systems while the exact analysis shows a curve crossing trend, approximate analyses show a curve veering behavior. Earlier studies have shown that there is a common pattern in curve veering systems and disordered systems. In the present study the exact analysis is recognized as representing the actual system while the approximate analysis of the same system renders it a disordered system by perturbing the eigenvalues and eigenfunctions from their true values. Since the responses of disordered systems can sometimes show violent changes for small perturbations in the system parameters, the response of a simply supported plate has been obtained both exactly and approximately using the Rayleigh Ritz method, and compared. The conclusions have far reaching implications from the point of the accuracy of the response quantities obtained by approximate methods such as finite element method, the Rayleigh Ritz and Galerkin methods.