A Higher Order Theory for Free Vibration of Orthotropic, Homogeneous, and Laminated Rectangular Plates

1984 ◽  
Vol 51 (1) ◽  
pp. 195-198 ◽  
Author(s):  
A. Bhimaraddi ◽  
L. K. Stevens
Keyword(s):  
Free Vibration ◽  
Order Theory ◽  
Higher Order ◽  
Rectangular Plates ◽  
Higher Order Theory

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.

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

scholarly journals Vibration of Antisymmetric Angle-Ply Laminated Plates of Higher-Order Theory with Variable Thickness

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
A. K. Nor Hafizah ◽  
J. H. Lee ◽  
Z. A. Aziz ◽  
K. K. Viswanathan
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Plate Theory ◽  
Order Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Shear Stresses ◽  
Transverse Shear Stresses ◽  
Thickness Variations ◽  
Higher Order Theory

Free vibration of antisymmetric angle-ply laminated plates with variable thickness is studied. Higher-order shear deformation plate theory (HSDT) is introduced in the present method to remove the shear correction factors and improve the accuracy of transverse shear stresses. The thickness variations are assumed to be linear, exponential, and sinusoidal. The coupled differential equations are obtained in terms of displacement and rotational functions and approximated using cubic and quantic spline. A generalized eigenvalue problem is obtained and solved numerically by employing the eigensolution techniques with eigenvectors as spline coefficients to obtain the required frequencies. The results of numerical calculations are presented for laminated plates with simply supported boundary conditions. Comparisons of the current solutions and those reported in literature are provided to verify the accuracy of the proposed method. The effects of aspect ratio, number of layers, ply-angles, side-to-thickness ratio, and materials on the free vibration of cylindrical plates are discussed in detail.

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