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Journal ArticleDOI

Finite elements for the vibration of cones and cylinders

01 Jan 1975-International Journal for Numerical Methods in Engineering (John Wiley & Sons, Ltd)-Vol. 9, Iss: 4, pp 833-845
TL;DR: In this paper, a semi-analytical approach for the vibration of conical and cylindrical shells has been proposed based on mass matrices, and good agreement has been found between theory and experiment for thin-walled circular cylinders and cones, a conecylinder combination, and a cooling tower model.
Abstract: Elemental mass matrices have been produced for the vibration of conical and cylindrical shells, based on a semi-analytical approach. Frequencies and modes of vibration have been compared with existing solutions and also with experimental results obtained from other sources. Good agreement has been found between theory and experiment for thin-walled circular cylinders and cones, a cone-cylinder combination, and a cooling tower model. A theoretical investigation was also made on the vibration of a circular cylinder when subjected to uniform pressure.
Citations
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Journal ArticleDOI
TL;DR: A survey of studies on non-linear vibrations of shell-type structures can be found in this paper, where the most commonly used methods of modelling and solution are reviewed and commented.

79 citations

Journal ArticleDOI
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.

52 citations

Journal ArticleDOI
TL;DR: In this article, a semi-analytical finite element analysis is presented for determining the natural frequencies of thin circular isotropic cylindrical shells with variable thickness, where Love's first approximation shell theory is used to solve the problem.

40 citations

Journal ArticleDOI
TL;DR: In this paper, a parametric study examines the effects of varying the geometry, degree of thickness taper and end conditions on the natural frequencies and mode shapes, providing benchmark results for designers and future researchers.

35 citations

Journal ArticleDOI
TL;DR: In this article, the free vibration characteristics of orthotropic circular cylindrical shells are analyzed using Love's first approximation shell theory, and the effect of degree of orthotropy on natural frequencies of shells is also investigated.

23 citations

References
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Book
01 Jan 1971
TL;DR: In this paper, the authors describe how people search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads, and instead they cope with some infectious bugs inside their computer.
Abstract: Thank you very much for downloading the finite element method in engineering science. Maybe you have knowledge that, people have search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they cope with some infectious bugs inside their computer.

3,688 citations

Journal ArticleDOI
TL;DR: Starting from Flugge's three equations of motion for a uniform thin cylindrical shell, this article gave a general solution, from which the dependence of natural frequencies on shell dimensions and m...
Abstract: Starting from Flugge's three equations of motion for a uniform thin cylindrical shell, the paper gives a general solution, from which the dependence of natural frequencies on shell dimensions and m...

116 citations

Journal ArticleDOI
TL;DR: In this article, the authors describe the application of the matrix displacement method to the linear elastic analysis of shells of revolution, where the shell is idealized as a series of conical frusta, joined at nodal circles.
Abstract: The paper describes the application of the matrix displacement method to the linear elastic analysis of shells of revolution. The shell is idealized as a series of conical frusta, joined at nodal circles. In the present paper the use of the idealization to handle asymmetric deformations is demonstrated. Also shown is how approximations to the mass and stiffness matrices may be consistently derived; these may then be used to solve both static and dynamic problems. The effect on the results of static analyses of improving the approximation to the stiffness matrix, using the procedure suggested by Pian, is demonstrated and discussed. Results are presented of static analyses of several shell configurations, and these are compared with solutions by other methods. It is found that the method provides accurate solutions for shells of revolution under both axisymmetric and asymmetric loadings by using a reasonable number of elements.

83 citations

Journal ArticleDOI
TL;DR: In this article, an improved ring finite element analysis for shells of revolution, obtained by extending the polynomials representing the displacements, is presented, and the mass and stiffness matrices and their derivation for the elements with extended displacement functions are given.

37 citations