Axisymmetric vibration of layered orthotropic spherical shells of variable thickness
TL;DR: In this article, the effect of thickness variation and lay-up on the natural frequencies of orthotropic spherical shells was analyzed. But the results were only for clamped and hinged boundary conditions.
About: This article is published in Computers & Structures.The article was published on 1992-12-03. It has received 9 citations till now. The article focuses on the topics: Spherical shell & Orthotropic material.
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212 citations
TL;DR: In this article, free and forced vibration analyses of functionally graded hollow cylinders and spheres are performed and analytical benchmark solutions are presented, where the material is assumed to be graded in the radial direction according to a simple power law.
Abstract: Free and forced vibration analyses of functionally graded hollow cylinders and spheres are performed and analytical benchmark solutions are presented. The material is assumed to be graded in the radial direction according to a simple power law. The Laplace transform method is used, and the inversion into the time domain is performed exactly using calculus of residues. The Complex Laplace parameter in the free vibration equation has directly given natural frequencies, and the results are given in tabular form. On the inner surface, various axisymmetric dynamic pressures are applied, and radial displacement and hoop stress are presented in the form of graphs. The exponent in the power law, called the inhomogeneity parameter, essentially refers to the degree of inhomogeneity. Increasing the inhomogeneity parameter provides a stress-shielding effect. Closed-form solutions obtained in the present paper are tractable, and they allow for further parametric studies. The inhomogeneity constant is a useful parameter from a design point of view in that it can be tailored for specific applications to control the stress distribution.
42 citations
TL;DR: A bibliographical review of the finite element methods applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given.
Abstract: Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.
36 citations
TL;DR: In this article, the free vibration characteristics of laminated composite spherical shells with variable thickness are investigated using the Haar wavelet discretization method (HWDM), as numerical solution technique.
Abstract: In this paper, the free vibration characteristics of laminated composite spherical shells with variable thickness are investigated using the Haar wavelet discretization method (HWDM), as numerical solution technique. The first-order shear deformation theory (FSDT) is adopted to establish theoretical formulation. The displacements and rotations at any point of spherical shell are extended Haar wavelet series in the meridional direction and Fourier series in the circumferential direction. The constants generating from the integrating process are disposed by adding the boundary conditions equations, and thus the equations of motion of total system including the boundary condition are transformed into an algebraic equations. Then, natural frequencies and corresponding mode shapes of the laminated composite spherical shell are directly obtained by solving these algebraic equations. Stability and accuracy of the present method are confirmed by performing of convergence and verification studies. The influences of some material parameters and geometric dimensions on the vibration behavior of laminated composite spherical shells with variable thickness are discussed. Some new results for laminated composite spherical shell with variable thickness and general boundary conditions are reported, which may serve as benchmark solutions.
7 citations
TL;DR: In this article, free and forced vibration behaviors of hollow spheres under dynamic internal pressure are investigated, where the material is assumed to be transversally isotropic with respect to the radial direction.
Abstract: In this article, free and forced vibration behaviors of hollow spheres under dynamic internal pressure are investigated. The material is assumed to be transversally isotropic with respect to the radial direction. Solutions are obtained in the Laplace domain and transformation into the time domain is performed exactly by the theory of residues. Frequency equations for free vibration are derived explicitly. Closed-form expressions for radial displacement and hoop stress due to various dynamic internal pressures are presented allowing for parametric studies. An anisotropy parameter involving circumferential and radial stiffness is defined and the effect of anisotropy is parametrically investigated. To validate the results material properties available in the literature are used.
3 citations
Cites methods from "Axisymmetric vibration of layered o..."
...On the free vibrations of orthotropic spheres the works by Nelson [2], Gautham and Ganesan [3] may be cited....
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...Gautham, P. and Ganesan, N. (1992)....
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272 citations
TL;DR: In this article, it was shown that for all opening angles the frequency spectrum consists of two coupled infinite sets of modes that can be labeled as bending (or flexural) and membrane modes.
Abstract: This paper is concerned with the vibration analysis of spherical shells, closed at one pole and open at the other, by means of the linear classical bending theory of shells. Frequency equations are derived ha terms of Legendre functions with complex indices, and for axisymmetric vibration the natural frequencies and mode shapes are deduced for opening angles ranging from a shallow to a closed spherical shell. It is found that for all opening angles the frequency spectrum consists of two coupled infinite sets of modes that can be labeled as bending (or flexural) and membrane modes. This distinction is made on the basis of the comparison of the strain energies due to bending and stretching of each mode. It is also found that the membrane modes are practically independent of thickness, whereas the bending modes vary with thickness. Previous analyses with the use of membrane theory have shown that one of two infinite sets of modes is spaced within a finite interval of the frequency spectrum. It is shown in this paper that this set of modes is a degenerate case of bending modes, and, if deduced by means of membrane theory, it is applicable only when the thickness of the shell is zero. When the bending theory is employed, then the frequency interval for this set of modes extends to infinity for every value of thickness that is greater than zero.
87 citations
TL;DR: In this paper, the problem of free, harmonic vibrations of thin, elastic, spherical shells is studied and the differential equations are derived in an invariant form together with the appropriate kinematic and static boundary conditions.
40 citations
21 citations