Free vibration analysis of a folded auxetic plate using the Levy-differential quadrature method

Authors

Department of Mechanical Engineering/Qom University of Technology

Abstract

In this study, the vibrations of a folded plate made of auxetic cells were examined. Initially, the elastic constants and density of the auxetic plate were determined based on the geometrical and material parameters of unit cell. The folded plate was considered as two jointed rectangular plates. Utilizing the first-order shear deformation theory and applying Hamilton's principle, the equations of motion governing each plate and the boundary conditions at the plate's edges were derived. Next, employing the combined Levy-differential quadrature method, the transformed equations of motion from the partial type to ordinary one has been solved. Assembling the equations of motion with boundary and continuity relations leads to an eigenvalue problem that its solution can present the frequency response function of folded plate. To validate the results obtained from the Levy-differential quadrature solution, the auxetic plate was simulated by a finite element analysis software (ABAQUS), and the comparison results demonstrated the accuracy of presented analytical method. Finally, the effects of plate's geometrical parameters on the natural frequencies of the folded plate were investigated. The results showed that by changing the folding angle from 180 degrees to less, or in other words, by converting the flat plate to a folded plate, the natural frequency first increases and then remains almost constant.

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References

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Journal of Solid and Fluid Mechanics
Volume 14, Issue 5
November and December 2024
Pages 155-165

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