Vibration of Laminated Shallow Shells on Quadrangular Boundary
Publication: Journal of Aerospace Engineering
Volume 9, Issue 2
Abstract
A numerical solution to investigate the free vibrational characteristics of doubly curved laminated angle-ply shallow shells on quadrangular planforms is presented. The first-order composite shell theory is used in the formulation and the rotary inertia and shear deformation terms are included. The shell equation is solved by the Ritz method, in which the admissible displacement fields are defined in terms of the parametric Bezier surface patches. Owing to the special characteristics of Bezier functions, treatment of the geometric boundary conditions at a particular edge becomes very simple and straightforward by manipulating the coefficients that control the shape of the Bezier surface patch. Rapid convergence of the solution algorithm is found with only the fifth-order function. The natural frequencies are calculated for the four-layer angle-ply cantilevered cylindrical shells on square, rhombic, and trapezoidal boundaries. The numerical comparison indicates that the present solution method yields more accurate results than the ones obtained by the finite-element method using the eight-noded isoparametric shallow-shell element.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Crawley, E. F. (1979). “The natural modes of graphite epoxy cantilever plates and shells.”J. Composite Mat., Vol. 13, 195–205.
2.
Fan, S. C., and Luah, M. H.(1990). “New spline finite element for analysis of shells of revolution.”J. Engrg. Mech., ASCE, 116(3), 709–726.
3.
Kapania, R. K., and Singhvi, S.(1992). “Free vibration analyses of generally laminated tapered skew plates.”Composites Engrg., 2(3), 197–212.
4.
Kumar, V., and Singh, A. V.(1993). “Vibration analysis of non-circular cylindrical shells using Bezier functions.”J. Sound and Vibration, 161(2), 333–354.
5.
Leissa, A. W. (1973). Vibrations of shells, NASA SP-288, U.S. Govt. Printing Ofc.
6.
Leissa, A. W., Lee, J. K., and Wang, A. J.(1981). “Vibrations of cantilevered shallow cylindrical shells of rectangular planform.”J. Sound and Vibration, 78(3), 311–328.
7.
Mindlin, R. D.(1951). “Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates.”J. Appl. Mech., 18(1), 31–38.
8.
Mizusawa, T.(1988). “Application of spline strip method to analyze vibration of open cylindrical shells.”Int. J. Numer. Methods in Engrg., 26, 663–676.
9.
Peng-Cheng, S., and Jian-Guo, W.(1987). “Vibration analysis of flat shells by using B spline functions.”Comp. and Struct., 25(1), 1–10.
10.
Qatu, M. S.(1992). “Review of shallow shell vibration research.”Shock and Vibration Dig., 24(9), 3–15.
11.
Qatu, M. S., and Leissa, A. W.(1991a). “Free vibrations of completely free doubly curved laminated composite shallow shells.”J. Sound and Vibration, 151(1), 9–29.
12.
Qatu, M. S., and Leissa, A. W. (1991b). “Natural frequencies for cantilevered doubly-curved laminated composite shallow shells.”J. Composite Struct., Vol. 17, 227–254.
13.
Reissner, E.(1947). “On bending of elastic plates.”Quarterly of Appl. Math., 5(1), 55–68.
14.
Rogers, D. F., and Adams, J. A. (1990). Mathematical elements for computer graphics, 2nd Ed., McGraw-Hill Book Co., Inc., New York, N.Y.
15.
Singh, A. V. (1991). “On vibrations of shells of revolution using Bezier polynomials.”J. of Pressure Vessel Technol., Vol. 113, 579–584.
16.
Vinson, J. R., and Sierakowski, R. L. (1986). The behavior of structures composed of composite materials. Martinus Nijhoff Publishers, Dordrecht, The Netherlands.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 9 • Issue 2 • April 1996
Pages: 52 - 57
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Apr 1, 1996
Published in print: Apr 1996
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.