An Exact Approach For Free Vibration Analysis of Multi-Step Nonuniform Shear Plates

Abstract

In this paper multi-story frame buildings are treated as shear plates with variably distributed mass and stiffness for free vibration analysis. An analytical model of a shear plate is proposed and an exact approach for determining natural frequencies and mode shapes of such shear plates is presented. The function for describing the distribution of mass of a shear plate along the plate height is an arbitrary one and the distribution of shear stiffness is expressed as a functional relation with the distribution of mass and vice versa. The exact solutions of one-step shear plates are obtained first for seven cases. Then the derived exact solutions of one-step shear plates are used to establish the frequency equations of multi-step shear plates by using the transfer matrix method. The numerical example shows that the natural frequencies and mode shapes of a shear plate calculated by the proposed methods are in good agreement with the measured data and those determined by the Ritz method and the finite element method, verifying the accuracy and applicability of the proposed methods.