Free vibration of a conical shell with variable thickness
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.
About: This article is published in Journal of Sound and Vibration.The article was published on 1982-05-08. It has received 105 citations till now. The article focuses on the topics: Conical surface & Transfer matrix.
Citations
More filters
TL;DR: In this article, a free vibration analysis for laminated conical and cylindrical shells was carried out using Love's first approximation thin shell theory and solved using discrete singular convolution (DSC) method.
158 citations
TL;DR: In this paper, free vibration analysis of conical and cylindrical shells and annular plates made of composite laminated and functionally graded materials (FGMs) is investigated for FGM cases.
Abstract: In this study, free vibration analysis of conical and cylindrical shells and annular plates made of composite laminated and functionally graded materials (FGMs) is investigated. Carbon nanotubes reinforced (CNTR) composite case is also taken consideration for FGM. The equations of motion for conical shell are obtained via Hamilton's principle using the transverse shear deformation theory. To obtain the eigenvalue problem of the system, the method of discrete singular convolution is employed. Material properties are graded in the thickness direction according to a volume fraction power law and four-parameter power law indexes for FGM cases. Five types of distributions of CNTR material are also considered. To verify the accuracy of this method, comparisons of the present results are made with results available in the open literature. Free vibrations of cylindrical shells and annular plates with FGM are treated as special cases. Results are also presented for carbon nanotubes reinforced (CNTR) composite cylindrical shells and annular plates. It is found that the convergence and accuracy of the present DSC method is very good for vibration problem of shells with functionally graded materials (FMG) and CNTR functionally graded materials.
158 citations
TL;DR: In this article, the free vibration analysis of thin conical shells under different boundary conditions is carried out using the element-free kp-Ritz method, and convergence studies are performed based on the influences of the support size and the number of nodes.
157 citations
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
References
More filters
Book•
[...]
TL;DR: In this paper, the vibrational characteristics and mechanical properties of shell structures are discussed, including the fundamental equations of thin shell theory, the characteristics of thin circular cylindrical shells, the complicating effects of noncircular cylinders, the properties of spherical shells and the solution of three-dimensional equations of motion for cylinders.
Abstract: The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.
1,114 citations
TL;DR: In this paper, the free vibration of arbitrary shells of revolution by means of the classical bending theory of shells is investigated, and a method is developed that is applicable to rotationally symmetric shells with meridional variations in Young's modulus, Poisson's ratio, radii of curvature, and thickness.
Abstract: This paper is concerned with a theoretical investigation of the free vibration of arbitrary shells of revolution by means of the classical bending theory of shells. A method is developed that is applicable to rotationally symmetric shells with meridional variations (including discontinuities) in Young's modulus, Poisson's ratio, radii of curvature, and thickness. By means of the method of this paper, the natural frequencies and the corresponding mode shapes of axisymmetric or nonsymmetric free vibration of rotationally symmetric shells can be obtained without a limitation on the length of the meridian of the shell. To illustrate the application of the method given in this paper to particular shells, stone results of free vibration of spherical and conical shells obtained earlier by means of the bending theory are reproduced by the general method of this paper, and a detailed comparison is made. In addition, paraboloidal shells and a sphere cone shell combination are considered, which have been previously analyzed by means of the inextensional theory of shells, and natural frequencies and mode shapes predicted by the bending theory are given.
120 citations
TL;DR: In this article, a method of iteration analogous to Stodola's method for beams is presented for the determination of the mode shapes and frequencies of free vibration of composite axisymmetric structures consisting of or tho tropic heterogeneous shells of revolution and elastic rings.
Abstract: A method of iteration, analogous to Stodola's method for beams, is presented for the determination of the mode shapes and frequencies of free vibration of composite axisymmetric structures consisting of or tho tropic heterogeneous shells of revolution and elastic rings. Numerical results are presented for 1) a spherical shell previously studied analytically (using Legendre functions) and also by means of a competitive numerical method; 2) a conical shell previously studied analytically (using the Galerkin technique) and also experimentally; and 3) a complete entry vehicle modeled as a continuous layered shell-ring-rigid mass structure, for which no previous results exist. In the case of the first example it is shown that what were previously reported to be the first three modes of axisymmetric vibration are, in reality, the first, second, and fourth modes. The missing third mode, which is presented in this paper, has, unexpectedly, no interior nodes of normal deflection. The second example serves to confirm and sharpen the qualitative result that edge constraint of circumferential deflection, in contrast to edge constraint of normal deflection, suppresses the tendency for vibration modes with a small number of circumferential waves to be essentially inextensional in the shell interior, thereby causing a large increase in frequency. At the same time it illustrates the deficiencies of the Donnell-type assumptions made in the Galerkin analysis for predicting frequencies of modes with a small number of circumferential waves.
74 citations