Dynamic indentation of viscoelastic orthotropic layer supported by a Winkler–Pasternak foundation

In this study, the two-dimensional dynamic contact problem between a rigid flat punch and a viscoelastic orthotropic layer is investigated. The motivation of the study is to provide a better understanding of the vertical vibration of the two-parameter Winkler–Pasternak foundation, which has not yet been investigated. For the contact problem, the mixed boundary conditions on the top and bottom surfaces are transformed into linear equations using the Fourier transform technique and Helmholtz functions. Based on the Gauss–Chebyshev integration formula, the singular integral equation is obtained and solved numerically. As a result of the solutions, the effects of various parameters on the contact stresses are analyzed and examples are given. It was found that the Winkler foundation modulus does not affect the dynamic contact stress, while the Pasternak foundation modulus significantly affects the contact stress.