A Group Theoretic Approach to the Linear Free Vibration Analysis of Shells with Dihedral Symmetry

Mohan, SJ and Pratap, R (2002) A Group Theoretic Approach to the Linear Free Vibration Analysis of Shells with Dihedral Symmetry. In: Journal of Sound and Vibration, 252 (2). pp. 371-341.

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Abstract

This paper deals with a group theoretic approach to the finite element analysis of linear free vibrations of shells with dihedral symmetry. Examples of such shell structures are cylindrical shells, conical shells, shells with circumferential stiffeners, corrugated shells, spherical shells, etc. The group theoretic approach is used to exploit the inherent symmetry in the problem. For vibration analysis, the group theoretic results give the correct symmetry-adapted basis for the displacement field. The stiffness matrix K and the mass matrix M are identically block diagonalized in this basis. The generalized linear eigenvalue problem of free vibration gets split into independent subproblems due to this block diagonalization. The Simo element is used in the finite element formulation of the shell equilibrium equations. Numerical results for natural frequencies and natural modes of vibration of several dihedral shell structures are presented. The results are shown to be in very good agreement with those reported in the literature. The computational advantages and physical insights due to the group theoretic approach are also discussed.

Item Type:	Journal Article
Publication:	Journal of Sound and Vibration
Publisher:	Elsevier
Additional Information:	Copyright of this article belongs to Elsevier.
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	03 Jun 2006
Last Modified:	19 Sep 2010 04:28
URI:	http://eprints.iisc.ac.in/id/eprint/7469

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