Abstract
The problem of axisymmetric vibration of a flat thin rigid circular plate located inside a vertically exponentially graded, transversely isotropic material of infinite extent is addressed by means of a displacement potential method. The contact condition on one side of the foundation is assumed to be the perfect adhesion with the media but known to be faced by a penny-shaped crack at the other side as it occurs in anchors. The mixed boundary value problem is formulated with the aid of Hankel integral transforms and is written in the form of a set of singular integral equations. The analytical procedure for the special case of vertical movement of the rigid plate results in a closed form solution. The solution is pursued numerically for the general elastodynamic case. The physical quantities, such as contact stress on the plate and the stress and displacement fields in the non-homogeneous medium are obtained for different materials.
| Original language | English |
|---|---|
| Pages (from-to) | 1338-1357 |
| Number of pages | 20 |
| Journal | ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |
| Volume | 97 |
| Issue number | 11 |
| Early online date | 11 May 2017 |
| DOIs | |
| Publication status | Published - 1 Nov 2017 |
Funding
Acknowledgement The authors wish to thank Prof. A.P.S. Selvadurai (McGill University) and Prof. M. Eskandari-Ghadi (University of Tehran) for their valuable comments during the preparation of the manuscript. This work has partially been supported by the NSF under grant IIP-1362146 (I/UCRC: Novel High Voltage/Temperature Materials and Structures).
Keywords
- exponentially graded material
- penny-shaped crack
- rigid plate
- transversely isotropic space
- wave propagation
- axisymmetric vibration