The Hybrid-Trefftz Finite Element Method For Forced Vibration Analysis Of Thin Plate

As a highly efficient and well established tool, the hybrid-Trefftz (HT) FEM, initiated about three decades ago, has now become more and more popular. The model uses two different shape functions in the non-conforming intra-element field and the auxiliary conforming frame field. Intra-element field is chosen so as to a priori satisfy the governing differential equentions, while the interelement continuity is enforced via the auxiliary conforming frame field. Using a variational principle or some other methods makes these two fields conformed, at last obtained the relationship between force and displacement. In the stiffness equation of the model, the nodal displacements are still the unknown variables, and the formulation only calls for integration along the element boundary which enables arbitrary polygonal or even curve-sided elements to be generated. As a result, it may be considered as a special, symmetric, substructure-oriented boundary solution approach and thus possesses the advantages of the conventional BEM. In contrast, however, HT FEM avoids the introduction of singular integral equations. The intra-element shape function and the element frame shape function feature the HT FEM model. Up to now, HT FEM has been thoroughly explored in a number of fields in engineering. However, it is starting prase to discuss the applications of the HT finite element approach to forced vibration analysis and its application to thin plates.The main content of this paper is two fold: some research on HT FEM itself and, development of forced vibration solution to shin plate algorithm based on it.This paper is based on HT FEM approach to forced vibration analysis of thin plates. The investigated approach consists in the combination of the T-element solution of a suitably modified equation of motion for a sequence of uniformly spaced discretized times with an unconditionally stable average acceleration method. And this paper also presents the modified Bessel function with order k and the Hankel function of the first kind with order k to form the particular solution and the homogeneous solution(T-complete system of homogeneous solution). At the end of this paper , the effectiveness and accuracy of the element model is assessed throuth some numerical examples.