Exact solutions for buckling and vibration of stepped rectangular Mindlin plates

This paper presents the first-known exact solutions for buckling and vibration of stepped rectangular Mindlin plates with two opposite edges simply supported and the remaining two edges being either free, simply supported or clamped. The general Levy type solution method and a domain decomposition technique are employed to develop an analytical approach to deal with the stepped rectangular Mindlin plates. Exact buckling loads and vibration frequencies are obtained for two-, three- and four-stepped Mindlin plates with varying step thickness ratios. The influence of the step length ratios, step thickness ratios and the number of steps on the buckling and vibration behaviour of square and rectangular Mindlin plates is examined. The presented exact results may serve as benchmark solutions for such plates.