Free vibration analysis of shear-type buildings

In this paper, an analysis of free vibrations of shear-type buildings is presented and discussed. The differential equations for the free vibration of shear-type buildings with variably distributed mass and stiffness are established and reduced to Bessel's equations or differential equations with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distribution of shear stiffness and mass. An approach to determining the natural frequencies and mode shapes for shear-type buildings with variably distributed mass and stiffness is proposed. The derived general solutions are expressed in terms of Bessel functions and triangular functions. A numerical example shows that the selected expressions are suitable for describing the distributions of stiffness and mass of typical shear-type buildings and the methods proposed in this paper are convenient to engineering application.