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

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.

Investigation of dynamic behaviour of circular plates resting on Winkler and Pasternak foundations

“…In a related study, Yalcin et al [10] adopted differential transform method (DTM) for free vibration of circular plate. Also, Zur and Jankowski [11] investigated free vibration of porous functional graded material using exact method. DTM is equally a very versatile method, good in handling singularity and non-trivial differential system of equation but, requires the need to manipulate the governing equation before the singularity problem is resolved and subsequently, involve transforming the governing equation to algebraic form.…”