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.
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TL;DR: In this paper, the dynamic stability and compatibility equations of a laminated elastic truncated conical shell with variable elasticity moduli and densities subject to an external pressure, employing Galerkin's method, were reduced to a system of time-dependent differential equations with variable coefficients.
Abstract: This study considers the dynamic stability of a laminated truncated conical shell with variable elasticity moduli and densities in the thickness direction, subject to a uniform external pressure, which is a power function of time Initially, the dynamic stability and compatibility equations of a laminated elastic truncated conical shell with variable elasticity moduli and densities, subject to an external pressure, have been obtained Then, employing Galerkin's method, those equations have been reduced to a system of time-dependent differential equations with variable coefficients Finally, applying a mixed variational method of Ritz type, the critical dynamic and static loads, the corresponding wave numbers and the dynamic factor have been found analytically Using those results, the effects of the variations in elasticity moduli and densities, the number and ordering of the layers, the semivertex angle and the power of time in the external pressure expression are studied via pertinent computations It is observed that these factors have appreciable effects on the critical parameters of the problem in the heading
13 citations
TL;DR: In this article, the free vibration of symmetric angle-ply laminated truncated conical shell is analyzed to determine the effects of frequency parameter and angular frequencies under different boundary condition, ply angles, different material properties and other parameters.
Abstract: Free vibration of symmetric angle-ply laminated truncated conical shell is analyzed to determine the effects of frequency parameter and angular frequencies under different boundary condition, ply angles, different material properties and other parameters The governing equations of motion for truncated conical shell are obtained in terms of displacement functions The displacement functions are approximated by cubic and quintic splines resulting into a generalized eigenvalue problem The parametric studies have been made and discussed
10 citations
Cites methods from "Vibration analysis of laminated con..."
...The versatile numerical method FEM was used by Sivadas and Ganesan [4] to study the vibration of laminated conical shells with variable thickness....
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TL;DR: In this article, the authors presented some modifications in the spline-based differential quadrature method (DQM) in order to accelerate the convergence of the method by solving set of equations arising from spline interpolation.
Abstract: Purpose – The purpose of this paper is to present some modifications in the spline‐based differential quadrature method (DQM), in order to accelerate the convergence of the method. The improvements are explained and examined by the examples of the free vibration of conical shells. The composite laminated shell, as well as isotropic one, are taken under consideration.Design/methodology/approach – To determine weighting coefficients for the DQM, the spline interpolation with non‐standard definitions of the end conditions is used. One of these definitions combines natural and not‐a‐knot end conditions, while the other one uses the boundary conditions for considered problem as the end conditions. The weighting coefficients can be determined by solving set of equations arising from spline interpolation.Findings – It is shown that the proposed modifications significantly improve the convergence of the method, especially when the boundary conditions are introduced at the stage of the computation of the weighting...
7 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, an asymptotic transfer function method is presented for modeling and analysis of conical shells, where displace-ment functions are first expanded in Fourier series in the circumferential direction, and the motion equations are decoupled into a group of partial differential equations with one space variable and one time variable.
Abstract: An asymptotic transfer function method is presented for modeling and analysis of conical shells. The displace- ment functions are first expanded in Fourier series in the circumferential direction, and the motion equations are decoupled into a group of partial differential equations with one space variable and one time variable. Introducing a small perturbation parameter and using the Laplace transformation and perturbation technique, the partial differential equations with variable coefficients are reduced to ordinary differential equations with constant co- efficients, which are solved by the transfer function method. The method is used to perform analysis of stepped conical shells with different conical angle or thickness and subjected to various initial and boundary conditions. Numerical methods are presented and compared with the finite element method. ONICAL shells have wide applications in aeronautic, astro- nautic, civil, and chemical engineering. The research on their mechanical behavior under various external excitations and bound- ary restrictions has great importance in engineering practice. As one type of revolutionary thin shells, conical shells have been studied by many researchers, and a lot of modeling and analysis methods have been developed. Chang1 gave a literature review of the vibration of conical shells. Liew2 reviewed recent developments in the free vibration analysis of thin, moderately thick shallow shells. Com- pared with cylindrical shells, conical shells are difficult to analyze in exact and closed form because of the mathematical complex- ity in geometry and variable surface curvature.2 Wan3-4 obtained a closed-form solution of the variable coefficient differential equa- tions of conical shells in terms of generalized hypergeometric func- tions. Tong5 obtained the solution of laminated conical shells in the form of power series. However, their solutions are very com- plicated and are difficult to use for complex loads, boundary con- ditions, and geometric configurations. Therefore, approximate or numerical methods, such as Raleigh-Ritz, Galerkin, finite differ- ence, and finite element methods, have been widely used in the analyses. Teichmann6 presented an approximate solution of funda- mental frequencies and buckling loads of cylindrical and conical shell panels. Srinivasan and Krishnan7 provided the free vibration frequencies of fully clamped open conical shells by using an inte- gral equation approach. Cheung et al.8 employed a spline finite strip method to investigate the natural frequencies of fully clamped singly curved shells, and design charts for specific fully supported conical shell configurations were presented. Xi et al.9 studied free vibra- tion of composite shells of revolution by the finite element method. Sivadas and Ganesan10 conducted vibration analysis of laminated conical shells with variable thickness. These methods provide ef- fective ways for engineering analysis in most cases. However, their defaults are obvious in some specific situations, such as analysis concerned with stress concentration, high-frequency response, etc. Based on the method proposed in Refs. 11 and 12, an asymp- totic distributed transfer function method for the analysis of conical shells is presented in this paper. First, the displacements, external excitations, and boundary conditions are expanded in Fourier se- ries in a circumferential direction. Because of the orthogonality of trigonometric functions, the governing equations for different wave numbers are decoupled and Laplace transformation is used to transform the time t to obtain ordinary differential equations with complex parameter s. Second, introducing the perturbation pa- rameter £ = Lsma/r(), those ordinary differential equations with variable coefficients are reduced to a group of ordinary differential
6 citations
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154 citations
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
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
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
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