VIBRATION STUDIES OF CROSS-PLY LAMINATED SHEAR DEFORMABLE CIRCULAR CYLINDERS ON THE BASIS OF ORTHOGONAL POLYNOMIALS

• Published in: Journal of sound and vibration 1998-11, Vol.218 (2), p.219-243
• Main Authors: Soldatos, K.P., Messina, A.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.1998.1769

This paper deals with a study of the free vibration characteristics of transverse shear deformable cross-ply laminated circular cylindrical shells on the basis of the Ritz method. The analysis is based on the energy functional of the Love-type version of the unified shell theory presented in reference [28]. As a result, several kinds of shear deformable Love-type shell theories are employed along with their classical counterpart. The theoretical formulation is given in a general form but the variational approach is finally applied in conjunction with a complete functional basis made of the appropriate admissible orthogonal polynomials. The method is currently capable of treating cross-ply laminated circular cylindrical shells subjected to any set of variationally consistent edge boundary conditions. In this paper, particular emphasis is given to the free vibrations of shells having one or both of their edges free of external tractions. The efficiency of the proposed method is exhibited by comparing corresponding results with certain experimental data, as well as with the very few existing relevant analytical results obtained elsewhere, on the basis of an alternative mathematical method (the state space concept). Apart from the specific value of the present dynamic investigation, the analysis is further considered as a successful test towards its extension for the study of corresponding problems in which the state space concept cannot be applied directly.