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Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Faculty of Mechanical Engineering, Bialystok University of Technology, 45C, 15-351 Bialystok, Poland
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Symmetry 2019, 11(3), 429; https://doi.org/10.3390/sym11030429
Received: 11 March 2019 / Revised: 18 March 2019 / Accepted: 20 March 2019 / Published: 22 March 2019
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported. View Full-Text
Keywords: eigenvalue problem; axisymmetric and non-axisymmetric vibrations; multiparametric special functions; circular plate; functionally graded porous material eigenvalue problem; axisymmetric and non-axisymmetric vibrations; multiparametric special functions; circular plate; functionally graded porous material
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Żur, K.K.; Jankowski, P. Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates. Symmetry 2019, 11, 429.

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