Vibration analysis of flexural-shear plates with varying cross-section

In this paper, multi-storey buildings with narrow rectangular plane configuration (narrow buildings) are treated as cantilever flexural-shear plates in analysis of free vibration. The governing differential equations for free vibration of flexural-shear plates with variably distributed mass and stiffness are established and reduced to Bessel's equations or Euler's equation by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass along the height of the plates. The general solutions of flexural-shear plates are derived. Numerical examples demonstrate that the calculated natural frequencies and mode shapes of narrow buildings are in good agreement with the experimentally measured data. It is also shown that it is possible to regard a building with rigid floors as a cantilever flexural bar that is a special case of a cantilever flexural-shear plate. Thus, the methods proposed in this paper are suitable for the calculation of free vibration of narrow buildings and common shear-wall buildings. © 1999 Elsevier Science Ltd. All rights reserved.