Preprint Article Version 1 This version is not peer-reviewed

An Analytical Closed-Form Solution for Free Vibration of Functionally Graded Circular Plates with Even and Uneven Porosity Distributions

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. An Analytical Closed-Form Solution for Free Vibration of Functionally Graded Circular Plates with Even and Uneven Porosity Distributions. Preprints 2018, 2018090295 (doi: 10.20944/preprints201809.0295.v1). Żur, K.K. An Analytical Closed-Form Solution for Free Vibration of Functionally Graded Circular Plates with Even and Uneven Porosity Distributions. Preprints 2018, 2018090295 (doi: 10.20944/preprints201809.0295.v1).

Abstract

Free axisymmetric and non-axisymmetric vibration analysis of the unsaturated porous functionally graded circular plates has been presented on the basis of classical plate theory. The defined coupled equations of motion for the porous functionally graded circular plate were decoupled based on the properties of the physical neutral surface. The one general solution of the decoupled equation of motion was obtained as linear combinations of the multiparametric special Bessel functions for the functionally graded circular plate with even and uneven porosity distributions. The influences of the even and uneven distributions of porosity, gradient index, diverse boundary conditions and the negligible effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied. The obtained numerical results show the differences and significant effect of considered types of distributions of porosities, values of the gradient index and the porosity volume fraction on the distribution of eigenfrequencies of the circular plates. Additionally, the obtained multiparametric general solution of the defined differential equation will allow to study the influences of diverse additional complicating effects such as stepped thickness, cracks, additional mounted elements expressed by only additional boundary conditions on the dynamic behavior of the porous functionally graded circular/annular plates. The formulated boundary value problem, the method of solution and the obtained numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported. The present paper fills this void in the literature.

Subject Areas

porous FGM circular plate; free vibration; closed-form solution; multiparametric characteristic equations

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