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Journal ArticleDOI

Vibration analysis of laminated conical shells with variable thickness

08 Aug 1991-Journal of Sound and Vibration (JOURNAL OF SOUND AND VIBRATION)-Vol. 148, Iss: 3, pp 477-491
TL;DR: In this article, the effects of thickness variation on natural frequencies of laminated conical shells have been studied by using a semi-analytical finite element method, where Love's first approximation thin shell theory is used to solve the problem.
About: This article is published in Journal of Sound and Vibration.The article was published on 1991-08-08. It has received 52 citations till now. The article focuses on the topics: Shell (structure) & Radius.
Citations
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Journal ArticleDOI
TL;DR: In this article, an analytic method is presented for free and forced vibration analysis of stepped conical shells with general boundary conditions. And the results of this method agree fairly well with those in literature and calculated by finite element method.
Abstract: An analytic method is presented for free and forced vibration analysis of stepped conical shells with general boundary conditions. The method is involved in dividing the stepped shells into segments according to the locations of discontinuities, such as thickness and semi-vertex angle. Combining Flugge shell theory with power series method, displacements and forces at cross-section of conical segments are expressed in terms of eight unknown coefficients. Meanwhile, by employing artificial springs to restrain edge displacements, arbitrary boundary conditions, including classic and elastic ones, can be analyzed. All separate segments are assembled together through displacement continuity conditions and equilibriums of forces at junctions of discontinuities. To test the validity of present method, comparisons of some stepped conical shells subjected to classic and elastic boundary conditions are firstly presented. The results of present method agree fairly well with those in literature and calculated by finite element method. Furthermore, influences of semi-vertex angle, elastic boundary conditions, discontinuity, excitation and damping are investigated. Parametric studies reveal that meridional and circumferential displacements have significant effects on fundamental and beam mode frequency parameters, and effects of the location of discontinuity and semi-vertex angle depend on boundary conditions and thickness ratios.

24 citations

Journal ArticleDOI
TL;DR: In this paper, the buckling of an elastic truncated conical shell having a meridional thickness expressed by an arbitrary function, subject to a uniform external pressure, which is a power function of time, was considered.

19 citations

Journal ArticleDOI
TL;DR: In this paper, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduli and density varying in the thickness direction, subject to a uniform external pressure which is a power function of time, has been studied.
Abstract: In this research, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduli and density varying in the thickness direction, subject to a uniform external pressure which is a power function of time, has been studied After giving the fundamental relations, the dynamic stability and compatibility equations of a nonhomogeneous elastic orthotropic conical shell, subject to a uniform external pressure, have been derived Applying Galerkin`s method, these equations have been transformed to a pair of time dependent differential equations with variable coefficients These differential equations are solved using the method given by Sachenkov and Baktieva (1978) Thus, general formulas have been obtained for the dynamic and static critical external pressures and the pertinent wave numbers, critical time, critical pressure impulse and dynamic factor Finally, carrying out some computations, the effects of the nonhomogeneity, the loading speed, the variation of the semi-vertex angle and the power of time in the external pressure expression on the critical parameters have been studied

16 citations

Journal ArticleDOI
TL;DR: In this article, the displacements of a cylindrical shell with varying thickness and subjected to axial and external pressure are calculated analytically using the first-order shear deformation theory.
Abstract: In this paper, the displacements of a cylindrical shell with varying thickness and subjected to axial and external pressure are calculated analytically using the first-order shear deformation theory. The kinematics of the problem is defined by von Karman theory, and the constitutive equation obeys Hooke’s law. The governing equations, which are a system of nonlinear differential equations, are extracted by applying the virtual work principle; the matched asymptotic expansion method of the perturbation technique is used to calculate the analytical solution. The effects of different load profiles and thicknesses on the results are investigated. Also, a comparison with the FEM is performed.

16 citations

Journal ArticleDOI
TL;DR: In this article, free vibration analysis of fiber reinforced composite (FRC) conical shells resting on Pasternak-type elastic foundation is investigated, where two kinds of fiber distribution in the thickness direction, namely, uniformly distributed and functionally graded are considered.
Abstract: In this paper, free vibration analysis of fiber reinforced composite (FRC) conical shells resting on Pasternak-type elastic foundation is investigated. Two kinds of fiber distribution in the thickness direction, namely, uniformly distributed and functionally graded are considered. The material properties of FRC conical shells are estimated through a volume fraction power law. The equations of motion are derived through variational formulation. The governing equations are developed based on the classical shells theory and Sanders assumptions. Galerkin and Ritz methods are employed to solve the governing equations and determine natural frequencies of the conical shell. The conical shell assumed to be clamped at the both ends. Results are presented on the effect of fiber volume fraction, semi-vertex angle, thickness to radius ratio and elastic foundation stiffness parameters on the frequency characteristics of the conical shells. A comparative study between Ritz and Galerkin methods is carried out. Validity of the present study is confirmed by comparing the results with the data available in the open literature for a special case. A good agreement is observed between them.

13 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the free vibration analysis of joined conical-cylindrical shells is presented, where the governing equations of vibration of a conical shell, including a cylindrical shell as a special case, are written as a coupled set of first order differential equations by using the transfer matrix of the shell.

129 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a survey of the structural mechanics of composite materials, focusing on the macromechanical structural analysis of various structural elements, including response under conditions of stable static loading, buckling, and dynamics.
Abstract: Introduction T purpose of this Survey is to review and bring together in an orderly fashion some of the principal contributions to the field of structural mechanics of structures containing composite materials. The topics of micromechanics and fracture, while quite important, are not considered in this Survey. Emphasis is given to the macromechanical structural analysis of various structural elements, including response under conditions of stable static loading, buckling, and dynamics. The Survey unfolds in the following sequence: Straight and Curved Laminated Bars, Laminated Plates, Laminated Shells, Sandwich Structures, Applications to Practical Structural Systems, and Future Trends. The authors hope that this contribution will be a useful reference tool for researchers and engineers already involved in structural aspects of advanced composites, as well as for those who are just entering the field. No Survey can do full justice to such a wide field as compositematerial structural mechanics. The references cited give only a glimpse of the extensive literature in this field. The authors apologize for not citing a number of important contributions in the field.

115 citations

Journal ArticleDOI
TL;DR: In this paper, the free vibration of a truncated conical shell with variable thickness was analyzed by using the transfer matrix approach, and the effects of the semi-vertex angle, truncated length and varying thickness on the vibration were studied.

105 citations

Journal ArticleDOI
TL;DR: In this article, an analysis of axisymmetric and unsymmetric free vibrations of conical or cylindrical shells with various boundary conditions is presented, where Love's first-approximation shell theory, with transverse shear strain added, was used and solutions were obtained by Galerkin's method.

78 citations