Flexible Thin Shell Elements under Nonwhite and Nonzero Mean Loads
Publication: Journal of Engineering Mechanics
Volume 119, Issue 8
Abstract
A finite element formulation combined with stochastic linearization and normal mode methods developed earlier for the study of geometrically non‐linear random vibration responses of beam and frame structures subjected to simultaneously spatial and temporal Gaussian stationary nonwhite and nonzero mean random excitations is now extended to treat the plate and shell structures in the same fashion. Examples include dynamic random responses of simply supported square plate, cylindrical panel with all edges supported by rigid diaphragms, clamped spherical cap, and double‐curved square panel under different random loadings. To validate the present formulation and solutions, results are compared with alternative analytical solutions whenever available. The Monte Carlo simulation method is also used to generate solutions to compare with some of the present results when alternative solutions are not available.
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References
1.
Ahmadi, G., Tadjbakhsh, I., and Farshad, M. (1978). “On the response of nonlinear plates to random loads.” Acustica, 40, 316–322.
2.
Booton, R. C. (1954). “Nonlinear control systems with random inputs.” IRE Transactions on Circuit Theory, 1, 9–18.
3.
Chen, C. T. (1990). “Geometrically nonlinear random vibrations of structures,” PhD thesis, Purdue University, West Lafayette, Ind.
4.
Chen, C. C. T., and Yang, H. T. Y. (1991). “Flexible beam and frame elements under nonwhite and nonzero mean loads.” J. Engrg. Mech., ASCE, 117(6), 1346–1364.
5.
Dyer, I. (1959). “Response of plates to a decaying and convective random pressure field.” J. Acoustical Soc. of Am., 31(7), 922–928.
6.
Elishakoff, I. (1977). “On the role of cross‐correlations in the random vibrations of shells.” J. Sound and Vibration, 50(2), 239–252.
7.
Eringen, A. C. (1957). “Response of beams and plates to random loads.” J. Appl. Mech., 24, 46–52.
8.
Ghanem, R. G., and Spanos, P. D. (1991). Stochastic finite elements: a spectral approach. Springer‐Verlag, New York, N.Y.
9.
Herbert, R. E. (1965). “Random vibrations of plates with large amplitudes.” J. Appl. Mech., 32, 547–552.
10.
Hwang, C., and Pi, W. S. (1969). “Random acoustic response of cylindrical shell.” AIAA J., 7(12), 2204–2210.
11.
Kapania, R. K., and Yang, T. Y. (1984). “Time domain random wind response of cooling tower.” J. Engrg. Mech., ASCE, 110(10), 1524–1543.
12.
Kapania, R. K., and Yang, T. Y. (1986). “Formulation of an imperfect quadrilateral doubly curved shell element for postbuckling analysis.” AIAA J., 24(2), 310–311.
13.
Lin, Y. K. (1962). “Response of a nonlinear flat panel to periodic and randomly‐varying loading.” J. Aero/Space Sci., 29(9), 1029–1033, 1066.
14.
Mei, C., and Paul, D. B. (1986). “Nonlinear multimode response of clamped rectangular plates to acoustic loading.” AIAA J., 24(4), 643–648.
15.
Nemat‐Nasser, S. (1968). “On the response of shallow thin shells to random excitations.” AIAA J., 6(7), 1327–1331.
16.
Niordson, F. I. (1980). Introduction to shell theory. Solid Mechanics, Technical University of Denmark, Lyngby, Denmark.
17.
Olson, M. D. (1972). “A consistent finite element method for random response problems.” Computers and Structures, 2, 163–180.
18.
Pace, I. S., and Barnett, S. (1972). “Comparison of numerical methods for solving Liapunov matrix equations.” Int. J. Control, 15(5), 907–915.
19.
Roberts, J. B. (1984). “Techniques for nonlinear random vibration problems.” Shock and Vibration Dig., 16(9), 3–14.
20.
Roberts, J. B., and Dunne, J. F. (1988). “Nonlinear random vibration in mechanical systems.” Shock and Vibration Dig., 20(6), 16–25.
21.
Spanos, P.T.D. (1980). “Formulation of stochastic linearization of symmetric or asymmetric M.D.O.F. nonlinear systems.” J. Appl. Mech., 47(3), 209–211.
22.
Spanos, P. D. (1981). “Stochastic linearization in structural dynamics.” Appl. Mech. Rev., 34(1), 1–8.
23.
Stanisic, M. M. (1968). “Response of plates to random load.” J. Acoustical Soc. of Am., 43(6), 1351–1357.
24.
To, C. W. S. (1987). “Random vibration of nonlinear systems.” Shock and Vibration Dig., 19(3), 3–9.
25.
Tylikowski, A. (1971). “Nonlinear random vibration of the cylindrical shell.” Non‐linear Vibration Problems (Zagadnienia Drgan Nieliowych), Gliwice, Poland, 12, 137–146.
26.
Yang, T. Y., and Kapania, R. K. (1984). “Finite element random response analysis of cooling tower.” J. Engrg. Mech., ASCE, 110(4), 598–609.
27.
Yang, T. Y., and Liaw, D. G. (1988). “Elastic‐plastic dynamic buckling of thin‐shell finite elements with asymmetric imperfection.” AIAA J., 26(4), 479–486.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 119 • Issue 8 • August 1993
Pages: 1680 - 1697
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Dec 23, 1991
Published online: Aug 1, 1993
Published in print: Aug 1993
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