An analytical method for vibration analysis of arbitrarily shaped non-homogeneous orthotropic plates of variable thickness resting on Winkler-Pasternak foundation. (15th September 2022)

• Record Type: Journal Article
• Authors: Song, Yuyu; Li, Qiuhong; Xue, Kai
• Is Part Of: Composite structures. Volume 296(2022)
• Publication Date: 2022-09-15
• Subjects: Free vibration -- Gram-Schmidt orthogonalization process -- Penalty method -- Arbitrarily shaped plates -- Arbitrary boundary conditions -- Winkler-Pasternak foundation; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2022.115885
• Languages: English
• ISSNs: 0263-8223

Abstract

Highlights: A general purpose analytical method for vibration analysis is proposed. The penalty method and Gram-Schmidt orthogonalization process are combined. The normalization procedure of coordinates is avoid. The method applies to arbitrarily shaped composite plates with variable thickness. The method applies to various boundary conditions and elastic foundations. Abstract: A highly applicable analytical approach is proposed for the dynamic analysis of composite plate structures with complex variation of geometric characteristics (shape/boundary and thickness) and material characteristics (Young's modulus, shear modulus and density) resting on Winkler-Pasternak foundation with general elastic boundary conditions. Boundary conditions of the plates are treated by the penalty method, so that the admissible functions can use any complete set of orthogonal polynomials, which is obtained by Gram-Schmidt orthogonalization process. The interval where the in-plane coordinate variables of the plate domain are located can be selected as the orthogonalization intervals, so as to avoid the normalization procedure of coordinates and simplify the operation process. In order to calculate the energy integral of the arbitrarily shaped plate, the plate domain segmentation strategy is introduced. To verify the effectiveness and accuracy of the proposed method, convergence study and numerical verifications for different orthogonalization intervals, weight functions, penalty spring stiffness and the truncation number of orthogonal polynomials are carried out. Taking regular hexagonal plates as examples, the effects of the parameters of thickness, nonhomogeneity and foundations on the vibration characteristics of the plates are studied. These results can be used as reference data for future research.