Vibration of a master plate with attached masses using modal sampling method

Abstract

At medium frequencies, several problems deal with systems having a large number of modes where classical modal methods must cope with the solution of large linear systems. The objective of the modal sampling method is to reduce these systems of equations in order to obtain a simplified model. The vibration response of a structure is reconstructed using a limited number of modes, called a sample, to interpolate the response of other modes. The accuracy of the prediction can be improved by increasing the size of the sample. The method, which has been developed in the case of a long beam, is presented here in the case of a nonhomogeneous structure such as a large, thin plate where point masses have been added. The structure is excited by a harmonic point force or a planar acoustic wave. A study of the convergence of the method shows that global quantities such as space—and/or frequency—averaged energy converge quickly. Thus predictions can be obtained with models having few degrees-of-freedom. Moreover, results show the ability of the method to take into account a master plate with attached point mass heterogeneities.