On wave propagation and free vibration of piezoelectric sandwich plates with perfect and porous functionally graded substrates

2022 ◽  
pp. 1045389X2110721
Author(s):  
Mahmoud Askari ◽  
Eugenio Brusa ◽  
Cristiana Delprete
Keyword(s):  
Wave Propagation ◽  
Free Vibration ◽  
Analytical Solutions ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Fg Plates ◽  
Higher Order Theory

This paper aims to develop analytical solutions for wave propagation and free vibration of perfect and porous functionally graded (FG) plate structures integrated with piezoelectric layers. The effect of porosities, which occur in FG materials, is rarely reported in the literature of smart FG plates but included in the present modeling. The modified rule of mixture is therefore considered for variation of effective material properties within the FG substrate. Based on a four-variable higher-order theory, the electromechanical model of the system is established through the use of Hamilton’s principle, and Maxwell’s equation. This theory drops the need of any shear correction factor, and results in less governing equations compared to the conventional higher-order theories. Analytical solutions are applied to the obtained equations to extract the results for two investigations: (I) the plane wave propagation of infinite smart plates and (II) the free vibration of smart rectangular plates with different boundary conditions. After verifying the model, extensive numerical results are presented. Numerical results demonstrate that the wave characteristics of the system, including wave frequency and phase velocity along with the natural frequencies of its bounded counterpart, are highly influenced by the plate parameters such as power-law index, porosity, and piezoelectric characteristics.

scholarly journals The analysis of localized effects in composites with periodic microstructure

2013 ◽  
Vol 371 (1993) ◽  
pp. 20120373 ◽  
Author(s):  
Jacob Aboudi ◽  
Michael Ryvkin
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Single Cell ◽  
Order Theory ◽  
Higher Order ◽  
Thermomechanical Coupling ◽  
Transform Domain ◽  
Periodic Microstructure ◽  
Periodic Composite ◽  
Higher Order Theory

Several methods for the analysis of composite materials with periodic microstructure in which localized effects (such as concentrated loads, cracks and stationary/progressive damage) occur are resented. Owing to the loss of periodicity caused by these localized effects, it is no longer possible to identify and analyse a repeating unit cell that characterizes the periodic composite. For elastostatic problems, these methods are based on the combination of the representative cell method (RCM), the higher-order theory for functionally graded materials and often the high-fidelity generalized method of cells (HFGMC) micromechanical model. For elastodynamic problems, the combination of the dynamic RCM with a theory for wave propagation in heterogeneous media is used for the prediction of the time-dependent response of the periodic composite with localized effects. In the framework of the RCM, the problem for a periodic composite that is discretized into numerous identical cells is reduced to a problem of a single cell in the discrete Fourier transform domain. In the framework of the higher-order theory and the theory of wave propagation in composites, the resulting governing equations and interfacial conditions in the transform domain are solved by dividing the single cell into subcells and imposing the latter in an average (integral) sense. The HFGMC is often used for the prediction of the proper far-field boundary conditions based on the response of the unperturbed composite. The inverse of the Fourier transform provides the real elastic field at any point of a composite with localized effects. This research summarizes a series of investigations for the prediction of the behaviour of periodic composites with localized loading, fibre loss, damage and cracks subjected to static and dynamic loadings under isothermal and full thermomechanical coupling conditions.

Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials

2001 ◽  
Vol 68 (5) ◽  
pp. 697-707 ◽  
Author(s):  
J. Aboudi ◽  
M.-J. Pindera ◽  
S. M. Arnold
Keyword(s):  
Finite Element ◽  
Predictive Accuracy ◽  
Local Stress ◽  
Computer Code ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Infinite Matrix ◽  
Homogenization Technique ◽  
Higher Order Theory

A new micromechanics model is presented which is capable of accurately estimating both the effective elastic constants of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material’s periodic microstructure. The model’s analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading which, in turn, can be incorporated into a structural analysis computer code. The model’s predictive accuracy is demonstrated by comparison with reported results of detailed finite element analyses of periodic composites as well as with the classical elasticity solution for an inclusion in an infinite matrix.

FREE VIBRATION OF FUNCTIONALLY GRADED PLATES WITH A HIGHER-ORDER SHEAR AND NORMAL DEFORMATION THEORY

2013 ◽  
Vol 13 (01) ◽  
pp. 1350004 ◽  
Author(s):  
D. K. JHA ◽  
TARUN KANT ◽  
R. K. SINGH
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Normal Deformation ◽  
Fg Plates

Free vibration analysis of functionally graded elastic, rectangular, and simply supported (diaphragm) plates is presented based on a higher-order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of functionally graded (FG) plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson ratios of the FG plates are assumed to be constant, but their Young's modulii and densities vary continuously in the thickness direction according to the volume fraction of constituents which is mathematically modeled as a power law function. The equations of motion are derived using Hamilton's principle for the FG plates on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of Navier solution method. The accuracy of the numerical solutions is first established through comparison with the exact three-dimensional (3D) elasticity solutions and the present solutions are then compared with available solutions of other models.

A two-variable simplified nth-higher-order theory for free vibration behavior of laminated plates

2017 ◽  
Vol 182 ◽  
pp. 533-541 ◽  
Author(s):  
Mokhtar Bouazza ◽  
Yamina Kenouza ◽  
Noureddine Benseddiq ◽  
Ashraf M. Zenkour
Keyword(s):  
Free Vibration ◽  
Order Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Vibration Behavior ◽  
Higher Order Theory
Sign in / Sign up

Export Citation Format

Share Document