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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
Abstract: Effects of thickness variation on natural frequencies of laminated conical shells have been studied by using a semi-analytical finite element method. Love's first approximation thin shell theory is used to solve the problem. Effects of various parameters, such as the number of layers of the shell, the semi-vertex angle, the slant length to small end radius ratio and the thickness variation parameter (maximum to minimum thickness ratio), are studied, particularly on the lowest natural frequency. Shells of linear symmetrically varying thickness, about the mid-length of the shell, have been considered for the analyis. During the computation, the mass of the shell was kept constant for a particular slant length to small end radius ratio in order to provide useful examples of the effect of the thickness distribution on the natural frequencies.
Topics: Shell (structure) (58%), Radius (51%)
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Abstract: In this paper, we consider the free vibration analysis of thin conical shells under different boundary conditions. The analysis is carried out using the element-free kp-Ritz method. The present study is based on the classical thin-shell theory. The kernel particle (kp) functions are employed in hybridized form with harmonic functions to approximate the two-dimensional displacement field. In order to examine the numerical stability of the present approach, convergence studies are performed based on the influences of the support size and the number of nodes. To verify the accuracy of this method, comparisons of the present results are made with results available in the open literature. This study also examines in detail the effects of semi-vertex angles and boundary conditions on the frequency characteristics of the conical shells.

138 citations

Journal ArticleDOI
Abstract: In this paper, the global method of generalized differential quadrature (GDQ) is applied for the first time to study the free vibration of isotropic conical shells. The shell equations used are Love-type. The displacement fields are expressed as product of unknown functions along the axial direction and Fourier functions along the circumferential direction. The derivatives in both the governing equations and the boundary conditions are discretized by the GDQ method. Using the GDQ method, the natural frequencies can be easily and accurately obtained by using a considerably small number of grid points. The accuracy and efficiency of the GDQ method is examined by comparing the results with those in the literature and very good agreement is observed. The fundamental frequency parameters for four sets of boundary conditions and various semivertex angles are also shown in the paper.

83 citations

Journal ArticleDOI
Abstract: In this paper, a method is presented to study the free vibrations of a rotating truncated circular conical shell with simply-supported boundary conditions. The method is based on the use of Love’s first approximation theory and it includes the effects of initial hoop tension and the centrifugal and coriolis accelerations. Results are obtained for the frequency characteristics at different modes and various geometric properties, the effects of cone angle on the frequency characteristics are also discussed. To validate the present analysis, comparisons are made with a very long rotating cylindrical shell and a non-rotating truncated circular conical shell and very good agreement is obtained.

73 citations

Journal ArticleDOI
Abstract: In this paper acoustic behavior of the laminated composite cylindrical shell, excited by an oblique plane sound wave, is investigated. The cylindrical shell is assumed to be infinitely long with uniform airflow in the external fluid medium. To provide an analytical solution of Sound Transmission Loss (STL) based on Third-order Shear Deformation Theory (TSDT), the displacements are developed as the cubic order of the thickness coordinate. Furthermore, the equations of wave propagation are expanded to determine STL beside vibration equations of laminated composite cylindrical shell, simultaneously. Then, the obtained result is compared with that of previous models. However, the importance of using Third-order Shear Deformation Theory (TSDT) reveals the fact that the present model demonstrates more accurate results, particularly for thick shell where the effects of the shear and rotation become more significant in lower R/h. Moreover, with changing the R/h ratios, the difference between the present study (TSDT) and other shell theory such as First-order Shear Deformation Theory (FSDT) is increased. Eventually, numerical results are discussed to indicate the effectiveness of different structural properties and geometrical properties on STL.

42 citations

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144 citations

Journal ArticleDOI
01 Sep 1974-AIAA Journal
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.

114 citations

Journal ArticleDOI
Abstract: An analysis is presented for the free vibration of joined conical-cylindrical shells. 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. Once the matrix has been determined, the entire structure matrix is obtained by the product of the transfer matrices of the shells and the point matrix at the joint, and the frequency equation is derived with terms of the elements of the structure matrix under the boundary conditions. The method has been applied to a joined truncated conical-cylindrical shell and an annular plate-cylindrical shell system, and the natural frequencies and the mode shapes of vibration calculated numerically. The results are presented.

104 citations

Journal ArticleDOI
Abstract: An analysis is presented for the free vibration of a truncated conical shell with variable thickness by use of the transfer matrix approach. The applicability of the classical thin shell theory is assumed and the governing equations of vibration of a conical shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the matrix has been determined by quadrature of the equations, the natural frequencies and the mode shapes of vibration are calculated numerically in terms of the elements of the matrix under any combination of boundary conditions at the edges. The method is applied to truncated conical shells with linearly, parabolically or exponentially varying thickness, and the effects of the semi-vertex angle, truncated length and varying thickness on the vibration are studied.

97 citations

Journal ArticleDOI
Abstract: In this paper is presented an analysis of axisymmetric and unsymmetric free vibrations of conical or cylindrical shells with various boundary conditions. The shell construction may be either homogeneous or symmetrical sandwich, and the facing and core may be either isotropic or specially orthotropic. Love's first-approximation shell theory, with transverse shear strain added, was used and solutions were obtained by Galerkin's method. Comparisons were made with existing experimental results for the following boundary conditions: freely supported at both ends; clamped-clamped; and free-free.

76 citations

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