Dynamic analysis of viscoelastic foundation plate with fractional Kelvin–Voigt model using shifted Bernstein polynomials

Abstract

The fractional Kelvin–Voigt (FKV) viscoelastic constitutive model has been employed to build the fractional differential governing equation of viscoelastic foundation plate. Shifted Bernstein polynomial algorithm is implemented to solve the governing equations on a direct time domain numerically. Furthermore, the validity of the method is demonstrated by convergent analysis and error estimation of a math example. Finally, the dynamic analysis of viscoelastic foundation plate under different uniform loads. The movement of plate with different aspect ratios in viscoelastic foundation under the same load is studied. The stress of viscoelastic foundation plates of two materials under identical loading situations is investigated.