Simulation of plate bending vibration problems by the meshless backward substitution method

In this paper, the meshless backward substitution method is proposed for the first time to solve the fourth-order plate bending vibration problems. The numerical solution consists of approximation from the boundary conditions and the revised basis functions which satisfying the homogeneous conditions with weighted parameters which are obtained from the governing equations by the collocation method. Then the key issues are the organization of initial approximation and the revised basis function derived from the traditional basis functions. To demonstrate the accuracy and validity of the proposed method, several numerical examples are conducted and compared with existing methods in literature. The obtained results from numerical experiments confirm the potential of the proposed method in terms of both accuracy and efficiency.