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 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.
Highlights
Graded materials (FGMs) are a class of composite materials, which are made of the ceramic and metal mixture such that the material properties vary continuously in appropriate directions of structural components
The numerical results for the fundamental dimensionless frequencies of the porous Functionally graded materials (FGMs) circular plates presented in Tables 2–5 and Figures 3–6 show the following dependences:
The differences between the calculated dimensionless frequencies of free axisymmetric and non-axisymmetric vibration of the perfect FGM circular plate with and without the coupling effect are significant for the power-law index g ∈ [0, 20], but, for g ∈ [20, ∞], these differences decrease from 2% to 0%
Summary
Graded materials (FGMs) are a class of composite materials, which are made of the ceramic and metal mixture such that the material properties vary continuously in appropriate directions of structural components. In the processes of preparing functionally graded material, micro-voids and porosities may appear inside material in view of the technical issues. Reported that many porosities appear in material during the functionally graded material preparation process by the non-pressure sintering technique. A significant number of articles about the free vibrations of porous functionally graded (FGM) plates have appeared in the literature due to their wide applications in many fields of engineering such as aeronautical, civil, mechanical, automotive, and ocean engineering. The gradation of properties in functionally graded materials and the diverse distributions of porosity have a significant effect on distributions of the mass and the stiffness of plates and their natural frequencies.
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