Transient Dynamics of Stochastically Parametered Beams
Publication: Journal of Engineering Mechanics
Volume 126, Issue 11
Abstract
The problem of determining the statistics of the transient response of randomly inhomogeneous beams is formulated. This is based on the use of stochastic dynamic stiffness coefficients in conjunction with the fast Fourier transform algorithm. The dynamic stiffness coefficients, in turn, are determined using a stochastic finite-element formulation that employs frequency-dependent shape functions. The approach is illustrated by analyzing the response of a random rod subject to a boxcar type of axial impact and, also, by considering the flexural response of a randomly inhomogeneous beam resting on a randomly varying Winkler's foundation and subjected to the action of a moving force. A discussion on the treatment of system property random fields as being non-Gaussian in nature is presented. Also discussed are the methods for handling nonzero initial conditions within the framework of the frequency domain response analysis employed in the study. Satisfactory comparisons between the analytical results and simulation results are demonstrated.
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References
1.
Adhikari, S., and Manohar, C. S. ( 1999). “Dynamical analysis of framed structures with statistical uncertainties.” Int. J. Numer. Methods in Engrg., 44, 1157–1178.
2.
Adhikari, S., and Manohar, C. S. ( 2000). “Transient dynamics of stochastically parametered structural systems: Analysis and Monte Carlo simulations.” Rep. No. ST-2000-1, Dept. of Civ. Engrg., Indian Institute of Science, Bangalore, India.
3.
Benaroya, H., and Rehak, M. ( 1988). “Finite element methods in probabilistic structural analysis: A selective review.” Appl. Mech. Rev., 41(5), 201–213.
4.
Brenner, C. E. ( 1991). “Stochastic finite elements (literature review).” Internal Working Rep. No. 35-91, Inst. of Engrg. Mech., University of Innsbruck, Innsbruck, Austria.
5.
Bucher, C. G., and Brenner, C. E. ( 1992). “Stochastic response of uncertain systems.” Arch. Appl. Mech., 62, 507–516.
6.
Chen, P. C., and Soroka, W. W. ( 1973). “Impulse response of a dynamic system with statistical properties.” Sound and Vibration, 31(3), 309–314.
7.
Deodatis, G., and Shinozuka, M. ( 1988). “Stochastic FEM analysis of nonlinear dynamic problems.” Stochastic mechanics, M. Shinozuka, ed., Vol. III, Princeton University, Princeton, N.J., 27–54.
8.
Deodatis, G., and Shinozuka, M. (1991). “Weighted integral method. II: Response variability and reliability.”J. Engrg. Mech., ASCE, 117(8), 1865–1877.
9.
Der Kiureghian, A., Li, C. C., and Zhang, Y. ( 1991). “Recent developments in stochastic finite elements.” Proc., 4th IFIP WG 7.5 Conf., R. Rackwitz and P. Thoft-Christensen, eds., Munich, Germany, 19–38.
10.
Fryba, L., Nakagiri, S., and Yoshikawa, N. ( 1993). “Stochastic finite elements for a beam on a random foundation with uncertain damping under a moving force.” Sound and Vibration, 163(1), 31–45.
11.
Ghanem, R., and Spanos, P. D. ( 1991). Stochastic finite elements: A spectral approach, Springer, Berlin.
12.
Grigoriu, M. ( 1995). Applied non-Gaussian processes, Prentice-Hall, Englewood Cliffs, N.J.
13.
Ibrahim, R. A. ( 1987). “Structural dynamics with parameter uncertainties.” Appl. Mech. Rev., 40(3), 309–328.
14.
Igusa, T., and Der Kiureghian, A. (1988). “Response of uncertain systems to stochastic excitations.”J. Engrg. Mech., ASCE, 114(5), 812–832.
15.
Iwan, W. D., and Jensen, H. ( 1993). “On the dynamic response of continuous systems including model uncertainty.” J. Appl. Mech., 60, 484–490.
16.
Katafygiotis, L. S., and Papadimitriou, C. ( 1996). “Dynamic response variability of structures with uncertain properties.” Earthquake Engrg. and Struct. Dyn., 25, 775–793.
17.
Kleiber, M., and Hien, T. D. ( 1992). The stochastic finite element method, Wiley, Chichester, England.
18.
Lee, C., and Singh, R. ( 1994). “Analysis of discrete vibratory systems with parameter uncertainties, part II: Impulse response.” Sound and Vibration, 174(3), 395–412.
19.
Liu, W. K., Belytschko, T., and Lua, Y. J. ( 1992). Stochastic computational mechanics for aerospace structures, Progress in aeronautics and astronautics series, American Institute of Aeronautics and Astronautics.
20.
Liu, W. K., Belytschko, T., and Mani, A. ( 1987). “Applications of probabilistic finite element methods in elastic/plastic dynamics.” J. Engrg. for Industry, 109, 2–8.
21.
Manohar, C. S., and Adhikari, S. ( 1998). “Dynamic stiffness of randomly parametered beams.” Probabilistic Engrg. Mech., England, 13(1), 39–51.
22.
Manohar, C. S., and Ibrahim, R. A. ( 1999). “Progress in structural dynamics with stochastic parameter uncertainties 1987–1998.” Appl. Mech. Rev., 52(5), 177–197.
23.
Matthies, H. G., and Bucher, C. ( 1999). “Finite elements for stochastic media problems.” Comp. Methods in Appl. Mech. and Engrg., 168, 3–17.
24.
Nakagiri, S. ( 1987). “Fluctuation of structural response, why and how?” Int. J., Tokyo, 30(261), 369–374.
25.
Prasthofer, P. H., and Beadle, C. W. ( 1975). “Dynamic response of structures with statistical uncertainties in their stiffnesses.” Sound and Vibration, 42(4), 477–493.
26.
Sarkar, A., and Manohar, C. S. ( 1996). “Dynamic stiffness matrix of a general cable element.” Archive of Appl. Mech., 66, 315–325.
27.
Schueller, G. I., guest ed. ( 1997). “A state-of-art report on computational stochastic mechanics.” Probabilistic Engrg. Mech., England, 12(4), 197–321.
28.
Shinozuka, M. (1987). “Structural response variability.”J. Engrg. Mech., ASCE, 113(6), 825–842.
29.
Shinozuka, M. ( 1991). “Freudenthal lecture: Developments in structural reliability.” Proc., 5th Int. Conf. on Struct. Safety and Reliability, Vol. 1, ASCE, New York, 1–20.
30.
Shinozuka, M., and Deodatis, G. (1988). “Response variability of stochastic finite element systems.”J. Engrg. Mech., ASCE, 114(3), 499–519.
31.
Soong, T. T. ( 1973). Random differential equations in science and engineering, Academic, New York.
32.
Takada, T. ( 1990). “Weighted integral method in stochastic finite element analysis.” Probabilistic Engrg. Mech., England, 5(3), 146–156.
33.
Udwadia, F. E. ( 1987). “Response of uncertain dynamic systems: I.” Appl. Math. and Comput., 22, 115–150.
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Received: Mar 25, 1998
Published online: Nov 1, 2000
Published in print: Nov 2000
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