FREE VIBRATION RESPONSE OF SHEAR-FLEXIBLE MODERATELY-THICK ORTHOTROPIC CYLINDRICAL SHELLS

2006 ◽  
Vol 06 (01) ◽  
pp. 121-138 ◽  
Author(s):  
Z. I. SAKKA ◽  
J. A. ABDALLA ◽  
H. R. H. KABIR
Keyword(s):  
Finite Element ◽  
Fourier Series ◽  
Analytical Solution ◽  
Free Vibration ◽  
Orthotropic Cylindrical Shell ◽  
Shell Element ◽  
Vibration Response ◽  
Fourier Series Expansion ◽  
Mode Shapes ◽  
Free Vibration Response

The free vibration response of shear-flexible moderately-thick orthotropic cylindrical shell panels, with fixed edges, is investigated using an analytical approach. The governing partial differential equations are developed based on Sander's kinematics and are solved using generalized Navier's with a boundary continuous double Fourier series expansion. The frequencies and mode shapes from the analytical solution for various parametric ratios, including degree of orthotropy (stiffness ratio), radius-to-segment ratio and segment-to-thickness ratio are compared with the finite element solutions that are based on an eight-node 48 degrees of freedom shell element. The rate of convergence of the analytical solution method with respect to the number of Fourier series terms, for various parametric ratios, is presented. The results of the analytical solution are very comparable to that of the finite element solution. It is clear that the presented analytical solution can be used as a benchmark to calibrate and validate numerical and finite element solutions that usually involve approximation to shell theories.

scholarly journals Investigation of Free Vibration Response of E-Glass/Epoxy Delaminated Composite Plates

2012 ◽  
Vol 21 (1) ◽  
pp. 096369351202100 ◽  
Author(s):  
Turan Ercopur ◽  
Binnur Goren Kiral
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Epoxy Composite ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Vibration Response ◽  
Mode Shapes ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Free Vibration Response

This paper deals with the finite element analysis of free vibration response of the delaminated composite plates. Free vibration analysis is performed by using ANSYS commercial software developing parametric input files. Natural frequency values and associated mode shapes of E-glass/epoxy composite delaminated plates are determined. Effects of delamination shape, dimension and location on the natural frequency and associated mode shapes are investigated and for the purpose of the observing the effect of the boundary conditions, cantilever and clamped-pinned delaminated composite plates are taken into consideration. Comparisons with the results in literature verify the validity of the developed models in this study. It is observed that the natural frequency decreases in the existence of the delamination and level of the decrease depends on the dimension, shape and location of the delamination.

scholarly journals Dynamic Response of Shear-Flexible Cylindrical Isotropic Shells with Clamped Edges

2006 ◽  
Vol 13 (2) ◽  
pp. 103-116 ◽  
Author(s):  
Zafer I. Sakka ◽  
Jamal A. Abdalla ◽  
H.R.H. Kabir
Keyword(s):  
Free Vibration ◽  
Cylindrical Shells ◽  
Shell Element ◽  
Double Fourier Series ◽  
Analytical Investigation ◽  
Fourier Series Expansion ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Bench Mark ◽  
Approximate Methods

It is fundamental to obtain the natural frequencies and the corresponding mode shapes for cylindrical shells in order to determine their response to different dynamic loading. In this paper an analytical investigation to the free vibration response of moderately-thick shear flexible isotropic cylindrical shells with all edges clamped is presented. The Sander’s kinematic relations for moderately thick cylindrical shell panels are utilized to develop the governing partial differential equations in conjunction with the boundary conditions. A recently developed generalized Navier’s approach, based on a boundary continuous double Fourier series expansion, is used as a solution methodology. A parametric study is presented with respect to various thicknesses, length and radius of curvature of the shell panel. The convergence of the solution method is established numerically for various parametric properties. The present results are compared with the results obtained from finite element method using a four-node isoparametric shell element. The results thus presented should serve as bench-mark solutions for future comparisons with numerical and approximate methods for calculation of free vibration parameters of moderately-thick isotropic cylindrical shells.

scholarly journals FINITE ELEMENT MODELLING FOR FREE VIBRATION RESPONSE OF CRACKED STIFFENED FGM PLATES

2020 ◽  
Vol 58 (1) ◽  
pp. 119
Author(s):  
Do Van Thom ◽  
Doan Hong Duc ◽  
Phung Van Minh ◽  
Nguyen Son Tung
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Finite Element Modelling ◽  
Vibration Mode ◽  
Vibration Response ◽  
Mode Shapes ◽  
Response Analysis ◽  
Vibration Responses ◽  
Method Effects ◽  
Free Vibration Response

This paper presents the new numerical results of vibration response analysis of cracked FGM plate based on phase-field theory and finite element method. Effects of geometrical and material properties on the vibration behaviors of the plate are investigated in this work. The computed results show that the crack and stiffener have a strong influence on both the vibration responses and vibration mode shapes of the structure. The computed results can be used as a good reference to study some related mechanical problems.

Solution for free vibration of spatial curved beams

2019 ◽  
Vol 37 (5) ◽  
pp. 1597-1616 ◽  
Author(s):  
Guangxin Wang ◽  
Lili Zhu ◽  
Ken Higuchi ◽  
Wenzhong Fan ◽  
Linjie Li
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cross Section ◽  
Circular Cross Section ◽  
Accurate Solution ◽  
Vibration Response ◽  
Curved Beams ◽  
Content Type ◽  
Variable Curvature ◽  
Free Vibration Response

Purpose The purpose of this paper is to propose and analyze the free vibration response of the spatial curved beams with variable curvature, torsion and cross section, in which all the effects of rotary inertia, shear and axial deformations can be considered. Design/methodology/approach The governing equations for free vibration response of the spatial curved beams are derived in matrix formats, considering the variable curvature, torsion and cross section. Frobenius’ scheme and the dynamic stiffness method are applied to solve these equations. A computer program is coded in Mathematica according to the proposed method. Findings To assess the validity of the proposed solution, a convergence study is carried out on a cylindrical helical spring with a variable circular cross section, and a comparison is made with the finite element method (FEM) results in ABAQUS. Further, the present model is used for reciprocal spiral rods with variable circular cross section in different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the results provide a relatively accurate solution. Originality/value The numerical results show that only a limited number of terms are needed in series solutions and in the Taylor expansion series to ensure an accurate solution. In addition, with a simple modification, the present formulation is easy to extend to analyze a more complicated model by combining with finite element solutions or analyze the transient responses and stochastic responses of spatial curved beams by Laplace transformation or Fourier transformation.

Vibration Analysis of Thick Arbitrarily Laminated Plates of Various Shapes and Edge Conditions

2011 ◽  
Vol 471-472 ◽  
pp. 1177-1183
Author(s):  
Tasneem Pervez ◽  
F.K.S. Al-Jahwari ◽  
Abdennour Seibi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Laminated Plates ◽  
Vibration Response ◽  
Element Formulation ◽  
Edge Conditions ◽  
Shear Deformation Theories ◽  
Free Vibration Response

Free vibration analysis of arbitrarily laminated plates of quad, penta and hexagonal shapes, which have combinations of clamped, simply supported and free edge conditions is performed. The finite element formulation is based on first and higher order shear deformation theories to study the free vibration response of thick laminated composite plates. A finite element code is developed incorporating shear deformation theories using an 8-noded serendipity element. The effect of plate shape, arbitrary lamination and different edge conditions on natural frequencies and mode shapes are investigated. A systematic study is carried out to determine the influence of material orthotropy and aspect ratio on free vibration response. For various cases, the comparisons of results from present study showed good agreement with those published in the literature.

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