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Analytical solution to vertical and rocking vibration of a rigid rectangular plate on a layered transversely isotropic half-space
https://orcid.org/http://orcid.org/0000-0001-5552-3683
This paper presents an analytical solution to the mixed boundary value problem for a dynamic rigid rectangular plate on the surface of a layered transversely isotropic half-space. For the contact problem, the mixed boundary conditions at the surface are converted into linear equations by means of Bessel series expansions. Solving these linear equations can get the expression of the contact stress, which can be further utilized to obtain the stresses and displacements of this model by the analytical layer element method of layered media. Additionally, the contact stresses can be used to evaluate the vertical and rocking compliances of a rectangular plate. A good agreement with existing solutions verifies the accuracy of the proposed method, and numerical examples are carried out to investigate the effect of angular frequency, length-to-width ratios, transverse isotropy and the stratification of media.
Analytical solution to vertical and rocking vibration of a rigid rectangular plate on a layered transversely isotropic half-space
https://orcid.org/http://orcid.org/0000-0001-5552-3683
This paper presents an analytical solution to the mixed boundary value problem for a dynamic rigid rectangular plate on the surface of a layered transversely isotropic half-space. For the contact problem, the mixed boundary conditions at the surface are converted into linear equations by means of Bessel series expansions. Solving these linear equations can get the expression of the contact stress, which can be further utilized to obtain the stresses and displacements of this model by the analytical layer element method of layered media. Additionally, the contact stresses can be used to evaluate the vertical and rocking compliances of a rectangular plate. A good agreement with existing solutions verifies the accuracy of the proposed method, and numerical examples are carried out to investigate the effect of angular frequency, length-to-width ratios, transverse isotropy and the stratification of media.
Analytical solution to vertical and rocking vibration of a rigid rectangular plate on a layered transversely isotropic half-space
https://orcid.org/http://orcid.org/0000-0001-5552-3683
This paper presents an analytical solution to the mixed boundary value problem for a dynamic rigid rectangular plate on the surface of a layered transversely isotropic half-space. For the contact problem, the mixed boundary conditions at the surface are converted into linear equations by means of Bessel series expansions. Solving these linear equations can get the expression of the contact stress, which can be further utilized to obtain the stresses and displacements of this model by the analytical layer element method of layered media. Additionally, the contact stresses can be used to evaluate the vertical and rocking compliances of a rectangular plate. A good agreement with existing solutions verifies the accuracy of the proposed method, and numerical examples are carried out to investigate the effect of angular frequency, length-to-width ratios, transverse isotropy and the stratification of media.
Analytical solution to vertical and rocking vibration of a rigid rectangular plate on a layered transversely isotropic half-space
Acta Geotech.
Ai, Zhi Yong (author) / Ye, Zi Kun (author)
Acta Geotechnica ; 17 ; 903-918
2022-03-01
16 pages
Article (Journal)
Electronic Resource
English
Analytical layer element method , Dual integral equations , Layered media , Rigid rectangular plate , Transverse isotropy Engineering , Geoengineering, Foundations, Hydraulics , Solid Mechanics , Geotechnical Engineering & Applied Earth Sciences , Soil Science & Conservation , Soft and Granular Matter, Complex Fluids and Microfluidics
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