Free Vibration Analysis on Combined Cylindrical-Spherical Shell

2012 ◽  
Vol 226-228 ◽  
pp. 3-8 ◽  
Author(s):  
Shi Hao Wu ◽  
Ye Gao Qu ◽  
Xiu Chang Huang ◽  
Hong Xing Hua
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Domain Decomposition Method ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Axial Direction ◽  
Energy Functional ◽  
Displacement Boundary ◽  
Finite Element Software ◽  
Boundary Equations

Based upon the Reissner-Naghdi-Berry’s shell theory, a domain decomposition method (DDM) is utilized to investigate the vibration characteristics of the combined cylindrical-spherical shell with different boundary conditions. The combined shell was first apart from prescribed-displacement boundary and then divided into some cylindrical and spherical shell subdomains, respectively. The boundary equations were introduced into the energy functional of the combined shell as well as the constraint equations derived from interface continuity conditions between two adjacent shell subdomains. Fourier series and Chebyshev orthogonal polynomials were employed as the admissible displacement functions for each shell subdomain in the circumferential direction and axial direction in order to obtain the discretization equations of motion of the combined shell. Exact free vibration solutions of the combined shell has been performed via the DDM and were compared with those obtained by the finite element software ANSYS to confirm the reliability and accuracy.

A Domain Decomposition Method for Forced Vibration Analysis of Joined Conical-Cylindrical-Spherical Shell

2012 ◽  
Vol 184-185 ◽  
pp. 3-10
Author(s):  
Shi Hao Wu ◽  
Ye Gao Qu ◽  
Hong Xing Hua
Keyword(s):  
Boundary Conditions ◽  
Spherical Shell ◽  
Domain Decomposition ◽  
Forced Vibration ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Double Series ◽  
Longitudinal Direction ◽  
Energy Functional ◽  
Finite Element Software

Based upon the Reissner-Naghdi-Berry shell theory, a semi-analytical domain decomposition method is presented to analyze the forced vibration of a joined conical-cylindrical-spherical shell with general boundary conditions. The joined shell was divided into some conical, cylindrical and spherical shell segments along the axis of revolution. The constraint equations derived from interface continuity conditions between two adjacent shell segments were introduced into the energy functional of the joined shell. Displacement variables of each shell segment are expressed as a mixed double series in the forms of Fourier series in the circumferential direction and Chebyshev orthogonal polynomial in the longitudinal direction. The forced vibration response of the joined shells subjected to various harmonic excitations and boundary conditions was calculated and compared with those FEM results obtained by finite element software ANSYS to confirm the reliability and accuracy of this analytical solution.

Free Vibration Analysis of a Carbon Nanotube Reinforced Composite Beam

2014 ◽  
Vol 592-594 ◽  
pp. 2041-2045 ◽  
Author(s):  
B. Naresh ◽  
A. Ananda Babu ◽  
P. Edwin Sudhagar ◽  
A. Anisa Thaslim ◽  
R. Vasudevan
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Formulation ◽  
Reinforced Composite ◽  
Vibration Responses

In this study, free vibration responses of a carbon nanotube reinforced composite beam are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced composite beam are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available literature. Various parametric studies are also performed to investigate the effect of aspect ratio and percentage of CNT content and boundary conditions on natural frequencies and mode shapes of a carbon nanotube reinforced composite beam. It is shown that the addition of carbon nanotube in fiber reinforced composite beam increases the stiffness of the structure and consequently increases the natural frequencies and alter the mode shapes.

Free Vibration of Moderately Thick Conical Shells Using a Higher Order Shear Deformable Theory

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
R. D. Firouz-Abadi ◽  
M. Rahmanian ◽  
M. Amabili
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
First Time ◽  
Circumferential Wave ◽  
Shear Deformable

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential wave numbers for clamped (C), and simply supported (SS) boundary conditions.

scholarly journals Analysis of Laminated Shells by Murakami’s Zig-Zag Theory and Radial Basis Functions Collocation

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
D. A. Maturi ◽  
A. J. M. Ferreira ◽  
A. M. Zenkour ◽  
D. S. Mashat
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Basis Functions ◽  
Transverse Displacement ◽  
Laminated Shells ◽  
Radial Basis

The static and free vibration analysis of laminated shells is performed by radial basis functions collocation, according to Murakami’s zig-zag (ZZ) function (MZZF) theory . The MZZF theory accounts for through-the-thickness deformation, by considering a ZZ evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by Carrera’s Unified Formulation and further interpolated by collocation with radial basis functions.

Free vibration analysis of Euler–Bernoulli nanobeam using differential transform method

2018 ◽  
Vol 07 (03) ◽  
pp. 1850020 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Differential Transform Method ◽  
Inverse Transformation ◽  
Algebraic Equations ◽  
Transform Method ◽  
Differential Transform

In this paper, a semi analytical-numerical technique called differential transform method (DTM) is applied to investigate free vibration of nanobeams based on non-local Euler–Bernoulli beam theory. The essential steps of the DTM application include transforming the governing equations of motion into algebraic equations, solving the transformed equations and then applying a process of inverse transformation to obtain accurate mode frequency. All the steps of the DTM are very straightforward, and the application of the DTM to both the equations of motion and the boundary conditions seems to be very involved computationally. Besides all these, the analysis of the convergence of the results shows that DTM solutions converge fast. In this paper, a detailed investigation has been reported and MATLAB code has been developed to analyze the numerical results for different scaling parameters as well as for four types of boundary conditions. Present results are compared with other available results and are found to be in good agreement.

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.

Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities

2019 ◽  
Vol 25 ◽  
pp. 69-83 ◽  
Author(s):  
Slimane Merdaci
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Porous Plate ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates

This article presents the free vibration analysis of simply supported plate FG porous using a high order shear deformation theory. In is work the material properties of the porous plate FG vary across the thickness. The proposed theory contains four unknowns unlike the other theories which contain five unknowns. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the plate are simply supported the Navier procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature for non-porous plates. Effects of the exponent graded and porosity factors are investigated.

Development of beam modal function for free vibration analysis of FML circular cylindrical shells

2017 ◽  
Vol 24 (14) ◽  
pp. 3026-3035 ◽  
Author(s):  
Masood Mohandes ◽  
Ahmad Reza Ghasemi ◽  
Mohsen Irani-Rahagi ◽  
Keivan Torabi ◽  
Fathollah Taheri-Behrooz
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
Fiber Metal Laminate ◽  
Circular Cylindrical Shells ◽  
Fiber Metal

The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable.

Free Vibration Analysis of Multilayered Functionally Graded Composite Cylinder

2010 ◽  
Author(s):  
M. H. Kargarnovin ◽  
M. Hashemi
Keyword(s):  
Free Vibration ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Longitudinal Direction ◽  
Element Model ◽  
Functionally Graded ◽  
Composite Cylinder ◽  
Shape Functions ◽  
Functionally Graded Composite

Free vibration of multilayered composite cylinder which volume fraction of fiber varies according to power law in longitudinal direction has been studied. Rule of mixture model and reverse of that are employed to represent elastic properties of this fibrous functionally graded composite. Strain-displacement relations employed are based on Reissner-Naghdi-Berry’s shell theory. The displacement finite element model of the governing equations of motion is derived by writing weak form of them. The Lagrangian shape functions for in-plane displacements and Hermitian shape functions for displacement in normal direction to the surface of mid-plane are utilized by defining a conformal quadrilateral element. The results show that by appropriate grading material properties of fiber in longitudinal direction the natural frequencies can be increased in comparison with traditional composite in which volume fraction of fiber does not vary.

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