Free vibration analysis of multi-storey buildings with narrow rectangular plane configuration

In this paper, the general solutions of free vibrations of one-step cantilever shear plates with variably distributed mass and stiffness are derived by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass along the height of the plates. Then the general solutions of one-step shear plates are used to derive the general solutions and frequency equations of multi-step cantilever shear plates by using transfer matrices. A numerical example demonstrates that the calculated dynamic characteristics of a building with narrow rectangular plane configuration (narrow building), which is considered as a cantilever shear plate with variable cross-section, are in good agreement with the corresponding experimental data. It is shown that when the stiffness of each floor of a narrow building can be treated as infinitely rigid, such a building can be considered as a cantilever shear bar which is a special case of a cantilever shear plate. Thus, the proposed methods in this paper are suitable for the calculation of free vibrations of narrow buildings and common shear-type buildings.