Dynamic analysis of an exponentially graded viscoelastic coated half plane pressed by a rigid flat punch

Abstract

This study analytically considers the dynamic contact problem between a rigid flat punch and an exponentially graded (FG) viscoelastic coated homogeneous half-plane. The punch transmits a harmonic vertical force to the FG coating. The general stress and displacement expressions for the FG viscoelastic coating and half plane are derived using Helmholtz functions and the Fourier integral transform technique. Thanks to the boundary conditions, the contact problem is transformed into the singular integral equation of the first kind, and it is solved numerically by implementing the Gauss-Chebyshev integration formulas. The effect of the parameters such as external excitation frequency, loss factor ratio, Young’s modulus ratio, density ratio, Poisson’s ratio, indentation load, and punch length on the dynamic contact stress and dynamic in-plane stress are discussed in detail.