Higher-Order Free Vibration Analysis of Porous Functionally Graded Plates

Abstract

The present work analyzes the free vibration response of functionally graded (FG) plates made of Aluminum (Al) and Alumina (Al2O3) with different porosity distributions, as usually induced by a manufacturing process. The problem is tackled theoretically based on a higher-order shear deformation plate theory, while proposing a Navier-type approximation to solve the governing equations for simply-supported plates with different porosity distributions in the thickness direction. The reliability of the proposed theory is checked successfully by comparing the present results with predictions available from literature based on further first-order or higher-order theories. A large parametric study is performed systematically to evaluate the effect of different mechanical properties, such as the material indexes, porosity volume fractions, porosity distributions, and length-to-thickness ratios, on the free vibration response of FG plates, as useful for the design purposes of most engineered materials and composite applications.

Metaheuristic Optimization of Functionally Graded 2D and 3D Discrete Structures Using the Red Fox Algorithm

“…Considering the structures that will be studied, one has to consider the first-order shear deformation to model their kinematical modelling [17][18][19][20][21]. The displacement field corresponding to this theory can be written as follows:…”

“…However, depending on the applications' characteristics, other material mixtures have been utilized as illustrated in the studies developed by [13][14][15][16][17], where mixtures of different metallic, polymeric, and ceramic materials were used. The FGM concept extended to materials with specific biocompatible characterisics can also be found with an increasing frequency, namely in [18][19][20], among others.…”

Nonlinear thermomechanical vibration of initially stressed functionally graded plates with porosities

“…Using $${\bar{N}}_{x0},{\bar{N}}_{y0}$$ from the Equations (24) into the Equation () yields $$$$\begin{equation}{I}_0h\frac{{{d}^2\overline W }}{{d{t}^2}} + {g}_{15}\overline W + {g}_{25}\overline W \left( {\overline W + \mu } \right) + {g}_{35}\overline W \left( {\overline W + \mu } \right)\left( {\overline W + 2\mu } \right) - {g}_{45}\left( {\overline W + \mu } \right)\Delta T = 0\end{equation}$$$$where …”

“…Also based on a quasi-3D approach and nonlocal elasticity theory, Dastjerdi et al [23] carried out the bending analysis of FGM plates with porosities. The linear free vibration response of simply supported FGM plates with porosities has been studied by Merdaci et al [24] using a HSDT and Navier-type analytical solution. Zghal and Dammark [25] developed an enhanced finite shell element for linear vibration analysis of FGM plates and shells including porosities.…”

“…The linear free vibration response of simply supported FGM plates with porosities has been studied by Merdaci et al. [24] using a HSDT and Navier‐type analytical solution. Zghal and Dammark [25] developed an enhanced finite shell element for linear vibration analysis of FGM plates and shells including porosities.…”