Free vibration analysis of thin circular plates by the indirect Trefftz method

Abstract

The vibration of plates is important in many applications pertaining to mechanical, civil and aerospace engineering. Therefore, the vibration of plates is an important research area that has been studied by many researchers. To date, there are abundant plate vibration solutions available in the open literature based on Kirchhoff assumptions. The purpose of the present paper is free vibration analysis of thin circular plates by the indirect Trefftz method. In thin plate vibration problems, we will deal with the governing equation with the homogeneous boundary conditions. The Trefftz method basically employs the complete set of solutions satisfying the governing equation as the first step. To derive the boundary integral equation, either the reciprocity law, which is similar to those used in conventional BEMs, or the weight residual method can be used. The proposed approach has some merits when compared with other regular boundary element formulations reported so far. A main benefit for the Trefftz method is that it does not involve singular integrals due to the properties of its solution basis functions (T functions); thus, it can be categorized into the regular boundary element method. Besides, this advocated approach yields a solution that offers simultaneously the advantages of the classical FEM and BEM solutions, without having their drawbacks. Finally, several numerical examples are demonstrated to show the validity of the current approach.

Investigation of dynamic behaviour of circular plates resting on Winkler and Pasternak foundations

“…In another study, Gupta et al [6] analysed the vibration and buckling of circular plate embedded on Winkler foundation. On application of semi-analytical method, Ghannadi et al [7] used indirect Trefftz method to analyze free vibration of circular plate.…”