Vertical vibration of a rigid circular disc at the interface of a transversely isotropic bi-material

A theoretical formulation is presented for the determination of the dynamic interaction of a vertically loaded rigid disc embedded at the interface of a transversely isotropic bi-material full-space. With the aid of Hankel integral transforms, a relaxed treatment of the mixed-boundary value problem...

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Bibliographic Details
Published in:International journal of solids and structures 2013-08, Vol.50 (18), p.2772-2780
Main Authors: Hajimohammadi, A.R., Khojasteh, A., Rahimian, M., Pak, R.Y.S.
Format: Article
Language:English
Subjects:
Bi-material
Discs
Disks
Dual integral equations
Dynamic tests
Dynamics
Green’s function
Impedance function
Integral equations
Integrals
Mathematical analysis
Mathematical models
Rigid disc
Transversely isotropic
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Summary:A theoretical formulation is presented for the determination of the dynamic interaction of a vertically loaded rigid disc embedded at the interface of a transversely isotropic bi-material full-space. With the aid of Hankel integral transforms, a relaxed treatment of the mixed-boundary value problem is formulated as dual integral equations, which can be reduced to a Fredholm integral equation of the second kind. The dynamic contact pressure under the disc and the impedance function are analytically evaluated in the general dynamic case. It is shown that the impedance functions are in exact agreement with the existing solutions for a an elastic half-space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with previously published solutions.
ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2013.04.024