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

In this paper, the general solutions of free vibrations of one-step cantile ver shear plates with variably distributed mass and stiffness are derived b y selecting suitable expressions, such as power functions and exponential f unctions, for the distributions of stiffness and mass along the height of t he plates. Then the general solutions of one-step shear plates are used to derive the general solutions and frequency equations of multi-step cantilev er shear plates by using transfer matrices. A numerical example demonstrate s that the calculated dynamic characteristics of a building with narrow rec tangular plane configuration (narrow building), which is considered as a ca ntilever shear plate with variable cross-section, are in good agreement wit h 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 an suitable for the calculation of free vibrations of narrow buildings and common shear-type buildings. (C) 1998 Elsevier Science Ltd. All rights rese rved.