Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations

Abstract

Closed-form solutions for the vibration problem of initially stressed thick rectangular plates as described by Mindlin theory are presented. The plates are simply supported and resting on Pasternak foundations. The subset problem of buckling of Mindlin plates on Pasternak foundations is automatically solved by setting the frequency parameter to be equal to zero. The solution also applies to Winkler foundations where the shear modulus of the Pasternak model is taken to be zero. The closed-form solutions should be useful for checking the accuracy of numerical solutions. © 1994.