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

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Title: Simulation of plate bending vibration problems by the meshless backward substitution method.
Authors: Xu, Yitong1,2 (AUTHOR), Lin, Ji1,2 (AUTHOR) linji@hhu.edu.cn, Lu, Jun3 (AUTHOR), Reutskiy, Sergiy4 (AUTHOR)
Source: Computers & Mathematics with Applications. Sep2025, Vol. 194, p202-213. 12p.
Subjects: Vibration (Mechanics), Meshfree methods, Numerical solutions to equations, Structural analysis (Engineering), Iterative methods (Mathematics), Boundary value problems, Collocation methods
Abstract: 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. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract: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. [ABSTRACT FROM AUTHOR]
ISSN:08981221
DOI:10.1016/j.camwa.2025.06.019