Rectangular Plates on Linear Viscoelastic Foundations

This paper deals with the quasistatic bending problems of the rectangular plates and the infinite strips on the linear viscoelastic foundations of the Kelvin, the Maxwell and the standard linear solid types. The general solutions for them are developed by using the eigenfunctions derived from a free lateral-vibration problem of the plates with the same geometries and the same boundary conditions and by utilizing the correspondence principle between linear elastic boundary value problem and linear viscoelastic one. Numerical results for the variations of the deflection in space and time are illustrated for a rectangular plate and an infinite strip on the viscoelastic foundation of the standard linear solid type.