Abstract
In this paper, the free vibration behaviors of composite laminated annular and circular plates under complex elastic boundary constraints are investigated. Firstly, Reddy’s high-order shear deformation theory (HSDT) and Jacobi polynomial method are effectively combined to establish the unified vibration analysis model of composite laminated annular and circular plates. Secondly, the simulation of complex elastic boundary and coupling boundary is realized by using artificial virtual spring technology. Then, the energy equation of the composite laminated plate is established by using Rayleigh–Ritz energy technology. Finally, the free vibration solution equation of the laminated plate is obtained through the Hamilton differential principle. The fast and uniform convergence of this method and the accuracy of the calculated results are verified by numerical examples and the model experimental method. On this basis, the parameterization study is conducted, and the effects of material parameters, geometric parameters, spring stiffness values, and lamination scheme on the vibration characteristics of the annular or circular plate are fully discussed, which can provide a theoretical basis for future research.
Highlights
According to the Ritz method and classical thin plate theory (CPT), Afsharmanesh et al [1] solved the forced vibration problem of laminated circular plates resting on a Winkler-type foundation
Arshid and Khorshidvand [3] studied the free vibration analysis of saturated porous functionally graded (FG) circular plates based on the differential quadrature method (DQM) and CPT
Draiche et al [8] presented an analytical model to predict the static analysis of laminated reinforced composite plates subjected to sinusoidal and uniform loads by using a simple first-order shear deformation theory
Summary
When the study model is changed from the annular plate to the circular plate, the inner radius is set to 0 and the stiffness of these boundary springs at this position is set to 0. According to the three-dimensional elasticity theory of the annular/circular plate, the strain-displacement relations in the cylindrical coordinate system can be obtained: zU εr. The present HSDT explains the parabolic distribution of transverse shear strains along the thickness of the composite laminated annular or circular plate. Erefore, the stress-strain relationship of the fiber reinforced layer of the laminated plate is focused. It assumes that the proposed plate has N layers. The relations between generalized force and strain can be written as the matrix form:
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