Preprint Article Version 2 This version is not peer-reviewed

Exact Analytical Solution for Free Axisymmetric and Non-Axisymmetric Vibrations of FGM Porous Circular Plates

Version 1 : Received: 15 September 2018 / Approved: 17 September 2018 / Online: 17 September 2018 (10:01:55 CEST)
Version 2 : Received: 17 October 2018 / Approved: 18 October 2018 / Online: 18 October 2018 (06:23:35 CEST)

How to cite: Żur, K.K..; Jankowski, P.. Exact Analytical Solution for Free Axisymmetric and Non-Axisymmetric Vibrations of FGM Porous Circular Plates. Preprints 2018, 2018090295 (doi: 10.20944/preprints201809.0295.v2). Żur, K.K..; Jankowski, P.. Exact Analytical Solution for Free Axisymmetric and Non-Axisymmetric Vibrations of FGM Porous Circular Plates. Preprints 2018, 2018090295 (doi: 10.20944/preprints201809.0295.v2).

Abstract

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 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 negligibled 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.

Subject Areas

FGM porous circular plate; free vibration; exact solution; multiparametric frequency equations

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