Free vibration analysis of thick spherical shells
TL;DR: In this paper, the axisymmetric and non-symmetric vibrations of spherical shells are analyzed using the thick shell theory and a semi-analytical method is used to reduce the dimension of the problem.
About: This article is published in Computers & Structures.The article was published on 1992-10-03. It has received 32 citations till now. The article focuses on the topics: Spherical shell & Shell (structure).
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193 citations
TL;DR: In this article, a higher order shear deformation theory is proposed to analyse the effects of various shell geometries and boundary conditions on the vibration responses, which results in cubic expressions for the transverse shear distribution through shell thickness.
67 citations
TL;DR: In this article, a three-dimensional method of analysis is presented for determining the free vibration frequencies and mode shapes of spherical shell segments with variable thickness, and the potential (strain) and kinetic energies of the spherical shell segment are formulated and upper bound values of the frequencies are obtained by minimizing the frequencies.
56 citations
TL;DR: In this article, a subparametric triangular plate bending element with first-order shear deformation has been used for free vibration analysis of very thin plates with cutouts, which is a distinct improvement over the existing practices of cutout modeling.
38 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
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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
TL;DR: In this paper, a simple two-node axisymmetric shell element with shallowly curved meridian assumptions and the inclusion of shear deformation and rotary inertia is presented.
Abstract: A simple two-node axisymmetric shell element with shallowly curved meridian assumptions and the inclusion of shear deformation and rotary inertia is presented. The principal developments include: (a) consistent resolution of the membrane and shear related excessive stiffening (locking) via anisoparametric interpolations of the displacement variables; (b) further upgrading of strain energy by means of a shear relaxation (correction) parameter. The resulting element possesses an improved condition of the stiffness matrix, increased efficiency in explicit time integration and enhanced accuracy in coarse discretizations. Comprehensive vibration examples are carried out to assess the element performance. The numerical results demonstrate a wide applicability range with respect to element slenderness and curvature properties.
35 citations