Circular Plates on Linear Viscoelastic Foundations

The solutions of the quasistatic bending problem of circular plates on linear viscoelastic foundations under arbitrary loading conditions are presented. The method of solution is developed by using the eigenfunctions found in the free lateral vibration problem of the circular plates with the same geometry and the same boundary condition, and the correspondence principle between linear elastic boundary value problem and viscoelastic one is utilized. Some results of numerical calculations for the variations in deflection and reactive force in space and with time are illustrated for the viscoelastic foundations of Kelvin (Voigt), Maxwell, and Standard linear solid types.