scholarly journals Free vibration analysis of truncated circular conical shells with variable thickness using the Haar wavelet method

2016 ◽  
Vol 18 (8) ◽  
pp. 5291-5305 ◽  
Author(s):  
Qingjie Cao ◽  
Qiyi Dai ◽  
Yushu Chen
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Haar Wavelet ◽  
Wavelet Method ◽  
Conical Shells ◽  
Haar Wavelet Method ◽  
Circular Conical Shells

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

2020 ◽  
pp. 146442072098049
Author(s):  
V Kumar ◽  
SJ Singh ◽  
VH Saran ◽  
SP Harsha
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Constant Thickness ◽  
Engineering Structures ◽  
Property Variation ◽  
Varying Thickness

The present paper investigates the free vibration analysis for functionally graded material plates of linearly varying thickness. A non-polynomial higher order shear deformation theory is used, which is based on inverse hyperbolic shape function for the tapered FGM plate. Three different types of material gradation laws, specifically: a power (P-FGM), exponential (E-FGM), and sigmoid law (S-FGM) are used to calculate the property variation in the thickness direction of FGM plate. The variational principle has been applied to derive the governing differential equation for the plates. Non-dimensional frequencies have been evaluated by considering the semi-analytical approach viz. Galerkin-Vlasov’s method. The accuracy of the preceding formulation has been validated through numerical examples consisting of constant thickness and tapered (variable thickness) plates. The findings obtained by this method are found to be in close agreement with the published results. Parametric studies are then explored for different geometric parameters like taper ratio and boundary conditions. It is deduced that the frequency parameter is maximum for S-FGM tapered plate as compared to E- and P-FGM tapered plate. Consequently, it is concluded that the S-FGM tapered plate is suitable for those engineering structures that are subjected to huge excitations to avoid resonance conditions. In addition, it is found that the taper ratio is significantly affected by the type of constraints on the edges of the tapered FGM plate. Some novel results for FGM plate with variable thickness are also computed that can be used as benchmark results for future reference.

scholarly journals Free Vibration Analysis of Composite Conical Shells with Variable Thickness

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Saira Javed ◽  
F. H. H. Al Mukahal ◽  
M. A. Salama
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Cone Angle ◽  
Spline Approximation ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Axial Direction ◽  
Thickness Variation ◽  
Node Number ◽  
Conical Shells

Free vibration of conical shells of variable thickness is analysed under shear deformation theory with simply supported and clamped free boundary conditions by applying collocation with spline approximation. Sinusoidal thickness variation of layers is assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and a generalized eigenvalue problem is obtained. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of composite conical shells consisting of three layers and five layers where each layer is made up of different materials is analysed. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length ratio, cone angle, circumferential node number, and different ply angles with different combinations of the materials. The results are presented in terms of tables and graphs.

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