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Inverse differential quadrature solutions for free vibration of arbitrary shaped laminated plate structures

journal contribution
posted on 2022-11-18, 10:15 authored by Hasan KhalidHasan Khalid, Saheed OjoSaheed Ojo, Paul WeaverPaul Weaver

An essential aspect of design of laminated plate structures in many engineering applications is the analysis of free vibration behaviour in order to model the structure for random excitations. In this regard, numerical solutions to the systems of high-order partial differential equations governing free vibration response of the structure become important. Direct approximation of such high-order systems are prone to error arising from the sensitivity of high-order numerical differentiation to noise necessitating the demand for improved solution techniques. In this work, a novel generalised inverse differential quadrature method is developed to study the dynamic behaviour of first-order shear deformable arbitrary-shaped laminated plates. The ensuing underdetermined system is operated upon by Moore–Penrose pseudo-inverse preconditioning to form a squared eigenvalue system. Free vibration solutions of square, skew, circular, and annular sector plates for different boundary conditions are obtained and validated against exact and numerical solutions in the literature and ABAQUS. It is demonstrated with numerous examples that iDQM solutions are in excellent agreement with exact solutions for square plates and the results for arbitrary shaped plates are comparable with solutions in the literature while saving up to 96% degrees of freedom required for ABAQUS solution. Finally, refined parametric studies conducted reveal that, subject to varying geometric configurations, iDQM solutions are numerically stable and potentially converge faster than DQM 

Funding

Spatially and Temporally VARIable COMPosite Structures (VARICOMP)

Science Foundation Ireland

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History

Publication

Applied Mathematical Modelling

Publisher

Elsevier

Rights

This is the author’s version of a work that was accepted for publication in Applied Mathematical Modelling . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematical Modelling, 2022, https://doi.org/10.1016/j.apm.2022.11.013

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