Optimization of a mass matrix for properly assigning low order resonance frequencies by the addition of a rigid and small subsystem

Abstract

The car is assembled from a large number of supplier’s parts which are installed onto the OEM-designed body to form certain function. Therefore, it is inevitable that noise and vibration problems in the car will occur when the parts are installed. Thus, if the resonance frequency of a main system (OEM's car body) is predicted through characteristic of subsystem (supplier’s parts), this will save a considerable amount of effort and time during the initial design phase. In this paper, a method of predicting multiple resonance frequencies of a whole structure due to mounting of small parts is presented based on the monotonicity theorem proposed by Weyl, and numerical examples are used to verify this theory.