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

In this paper, multi-storey buildings with narrow rectangular plane con®guration (narrow buildings) are treated as cantilever ¯exural-shear plates in analysis of free vibration. The governing di€erential equations for free vibration of ¯exural-shear plates with variably distributed mass and sti€ness are established and reduced to Besselʹs equations or Eulerʹs equation by selecting suitable expressions, such as power functions and exponential functions, for the distributions of sti€ness and mass along the height of the plates. The general solutions of ¯exural-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 ¯oors as a cantilever ¯exural bar that is a special case of a cantilever ¯exural-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.