Free Vibration of Cross-Ply Laminated Plates with Variable Thickness Based on Shear Deformation Theory

2016 ◽  
Vol 13 (03) ◽  
pp. 1650016 ◽  
Author(s):  
K. K. Viswanathan ◽  
Z. A. Aziz ◽  
Saira Javed ◽  
Shaharuddin Salleh ◽  
Siti Aisyah Binti Tumiran ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Free Vibration ◽  
Variable Thickness ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Frequency Parameter ◽  
Laminated Plates ◽  
Simply Supported ◽  
Thickness Variations ◽  
Plates Of Variable Thickness

Free vibration of laminated cross-ply plates of variable thickness including transverse problem is solved numerically to obtain eigenvalues as frequency parameter and associated eigenvectors which are spline coefficients. The variation of frequency parameters with respect to the aspect ratio, side-to-thickness ratio, ply-angle, number of layer and thickness variations for two different materials under simply supported boundary conditions are analyzed.

scholarly journals Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory

2021 ◽  
pp. 1-11
Author(s):  
Param D. Gajbhiye ◽  
Vishisht Bhaiya ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Shear Mode ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Thickness Shear

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.

A Trigonometric Shear Deformation Theory for Free Vibration Analysis of Functionally Graded Plates

2014 ◽  
Vol 680 ◽  
pp. 284-287
Author(s):  
Jiang Wu ◽  
Song Xiang
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Functionally Graded Plate ◽  
Simply Supported

A trigonometric shear deformation theory is presented to analyze the free vibration of functionally graded plate. The Navier-type analytical method is used to solve the governing differential equations. The natural frequencies of simply supported functionally graded plates are calculated and compared with the available results.

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.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

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