Analytical solution to vertical and rocking vibration of a rigid rectangular plate on a layered transversely isotropic half-space

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.

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Analysis of stress and deformation of an exponentially graded viscoelastic coated half plane under indentation by a rigid flat punch indenter tip

Çömez

2024

Mech Time-Depend Mater

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This paper solves the dynamic contact problem when a rigid flat punch indents into an exponentially graded (FG) viscoelastic coated homogeneous half-plane. A harmonic vertical force is applied to the FG coating, and the solution is obtained for the stress and displacement for both the FG viscoelastic coating and the half-plane using the Helmholtz functions and the Fourier integral transform technique. By applying specific boundary conditions, the contact mechanics problem is converted into a singular integral equation of the first kind. This equation is then solved numerically using the Gauss-Chebyshev integration formulas. The analysis provides detailed insights into how various parameters—such as external excitation frequency, loss factor ratio, Young’s modulus ratio, density ratio, Poisson’s ratio, indentation load, and punch length—affect the dynamic contact stress and dynamic in-plane stress.

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Analytical solution to vertical and rocking vibration of a rigid rectangular plate on a layered transversely isotropic half-space

Cited by 9 publications

References 52 publications

Dynamic contact problem for a viscoelastic orthotropic coated isotropic half plane

Dynamic contact problem for a viscoelastic orthotropic coated isotropic half plane

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

Analysis of stress and deformation of an exponentially graded viscoelastic coated half plane under indentation by a rigid flat punch indenter tip

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