Abstract
The aim of this paper is to investigate the steady state response of beams under the action of random support motions. The study is of relevance in the context of earthquake response of extended land based structures such as pipelines and long span bridges, and, secondary systems such as piping networks in nuclear power plant installations. The following complicating features are accounted for in the response analysis: (a) differential support motions: this is characterized in terms of cross power spectral density functions associated with distinct support motions, (b) nonlinear support conditions, and (c) stochastically inhomogeneous stiffness and mass variations of the beam structure; questions on non-Gaussian models for these variations are considered. The method of stochastic finite elements is combined with equivalent linearization technique and Monte Carlo simulations to obtain response moments.
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Reference
Adhikari, S. and Manohar, C.S. (1999) Dynamical analysis of framed structures with statistical uncertainties, International Journal of Numerical Methods in Engineering, 44, 1157–1178.
Chang, C.C. and Yang, H.T.Y. (1991) Random vibration of flexible uncertain beam element, Journal of Engineering Mechanics, ASCE, 117(10) 2329–2349.
Deodatis, G. and Shinozuka, M. (1988) Stochastic FEM analysis of nonlinear dynamic problems, Stochastic Mechanics III, Shinozuka M (ed), Dept. of Civil Engineering and Operations Res., Princeton University.
Klosner, J.M., Haber, S.F. and Voltz,P. (1992) Response of nonlinear systems with parameter uncertainties. Int. J. Nonlinear Mech. 27(4), 547–563.
Koyluoglu, H.U., Nielsen, S.R.K. and Cakmak, A.S. (1995) Stochastic dynamics of nonlinear structures with random properties subject to stationary random excitation. Paper No 133, Dept. of Building technology and structural engineering, Aalborg University, Denmark.
Liu, W.K., Belytschko, T. and Mani, A. (1986) Random field finite elements. Int. J. Numer. Meth. Eng. 23 1831–1845.
Liu, W.K., Belytschko, T. and Mani, A. (1987) Applications of probabilistic finite element methods in elastic/plastic dynamics. ASME J. Eng. for Indus. 109 2–8.
Liu, W.K., Besterfield, G.H. and Belytschko, T. (1988) Variational approach to probabilistic finite elements. ASCE J. Eng. Mech. 114(12), 2115–2133.
Manohar, C.S. and Ibrahim, R.A. (1999) Progress in structural dynamics with stochastic parameter variations: 1987 to 1998, ASME Applied Mechanics Reviews, 52(5), 177–197.
Manohar, C.S. and Adhikari, S. (1997) Dynamic stiffness of randomly parametered beams, Probabilistic Engineering Mechanics, 13(1), 39–51.
Schueller, G.I., (Guest editor), (1997) A state-of-art report on computational stochastic mechanics, Probabilistic Engineering Mechanics, 12(4), 197–321.
Socha, L and Soong, T.T. (1991) Linearization in the analysis of nonlinear stochastic systems, Applied Mechanics Reviews, 44 399–422.
Shinozuka, M. and Yamazaki, F. (1988) Stochastic finite element analysis: an introduction, in Stochastic structural dynamics: Progress in theory and applications, Edited by Ariaratnam S T, Schueller G I and Elishakoff I, Elsevier Applied Science, London.
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Manohar, C.S., Gupta, S. (2001). Nonlinear Dynamics of Beams with Stochastic Parameter Variations. In: Narayanan, S., Iyengar, R.N. (eds) IUTAM Symposium on Nonlinearity and Stochastic Structural Dynamics. Solid Mechanics and its Applications, vol 85. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0886-0_11
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DOI: https://doi.org/10.1007/978-94-010-0886-0_11
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