Computer Modeling for the Complex Response Analysis of Nonstandard Structural Dynamics Problems
Publication: Journal of Aerospace Engineering
Volume 22, Issue 3
Abstract
Over the past several decades, two intriguing classes of problems, having a wide range of applications in engineering, have been of interest to many researchers: (1) coupled dynamics of a distributed parameter system traversed by one or more moving oscillators; and (2) transient dynamic analysis of axially moving media (and associated phenomena of parametric resonances). Bridge vehicle interaction falls into the first class of problems, and the analysis of flexible appendages deployed from a satellite or a spacecraft is typical of the second class. Mathematically, these two problems are dual to each other, and they often are highly nonlinear in nature and typically involve large overall motion in space with complex effects of convective inertia terms in their governing equations of dynamic equilibrium. The “nonstandard” analytical nature of these problems stems from the fact that we are dealing with one or more of the following peculiarities: (1) variable problem domain; (2) varying spatial distribution of forces over the time duration of the analysis; and/or (3) changing location and type of constraints. Many researchers are trying to formulate the response of these problems, each having a different approach, but applicable only to certain specific details. Moreover, few researchers have concluded that these problems are beyond the scope of the present commercial finite-element (FE) software packages. However, we believe that if the nature and details of these problems are studied properly and carefully, it is immediately possible to simulate these problems in available commercial FE programs. An added advantage would also be the avoidance of many unrealistic simplifying assumptions that are often introduced to reduce the mathematical complexity; e.g., neglecting possible separation (after periods of prior contacts) in beam-moving vehicle problems, assuming linear behavior of suspension systems, and restriction to beam configuration only, among many others. For demonstration, we use ABAQUS in a large number of test cases to be presented. The results are compared with those presented in literatures.
Get full access to this article
View all available purchase options and get full access to this article.
References
ABAQUS. (2004). ABAQUS analysis user’s manual, version 6.5, SIMULIA, Providence, R.I.
Akin, J. E., and Mofid, M. (1989). “Numerical solution for response of beams with moving mass.” J. Struct. Eng., 115(1), 120–131.
Behdinan, K., and Tabarrok, B. (1997a). “Dynamics of flexible sliding beams—Non-linear analysis. Part I: Formulation.” J. Sound Vib., 208(4), 517–539.
Behdinan, K., and Tabarrok, B. (1997b). “Dynamics of flexible sliding beams—Non-linear analysis. Part II: Transient response.” J. Sound Vib., 208(4), 541–565.
Behdinan, K., and Tabarrok, B. (1998a). “A finite-element formulation for sliding beams. Part I.” Int. J. Numer. Methods Eng., 43(7), 1309–1333.
Behdinan, K., and Tabarrok, B. (1998b). “Sliding beams. Part II: Time integration.” Int. J. Numer. Methods Eng., 43(7), 1335–1363.
Biondi, B., and Muscolino, G. (2005). “New improved series expansion for solving the moving oscillator problem.” J. Sound Vib., 281(1–2), 99–117.
Biondi, B., Muscolino, G., and Sidoti, A. (2004). “Methods for calculating bending moment and shear force in the moving mass problem.” J. Vibr. Acoust., 126(4), 542–552.
de Faria, A. R. (2004). “Finite element analysis of the dynamic response of cylindrical panels under traversing loads.” Eur. J. Mech. A/Solids, 23(4), 677–687.
de Faria, A. R., and Oguamanam, D. C. D. (2005). “Adaptive finite-element analysis of the dynamic response of spherical caps under traversing loads.” Finite Elem. Anal. Design, 41(11–12), 1027–1042.
Kumar, A., and Saleeb, A. F. (2009). “On the interaction dynamics of primary continuous structural systems traversed by oscillating subsystems—Part II: Axially-moving media problems.” Adv. Eng. Software, submitted.
Pesterev, A. V., Bergman, L. A., Tan, C. A., Tsao, T.-C., and Yang, B. (2003). “On asymptotics of the solution of the moving oscillator problem.” J. Sound Vib., 260(3), 519–536.
Saleeb, A. F., and Kumar, A. (2009). “On the interaction dynamics of primary continuous structural systems traversed by oscillating subsystems—Part I: Bridge–vehicle interaction problems.” Adv. Eng. Software, submitted.
Sofi, A., and Muscolino, G. (2007). “Dynamic analysis of suspended cables carrying moving oscillators.” Int. J. Solids Struct., 44(21), 6725–6743.
Vu-Quoc, L., and Li, S. (1995). “Dynamics of sliding geometrically-exact beams: Large angle maneuver and parametric resonance.” Comput. Methods Appl. Mech. Eng., 120(1–2), 65–118.
Wu, J.-J. (2006). “Use of moving distributed mass element for the dynamic analysis of a flat plate undergoing a moving distributed load.” Int. J. Numer. Methods Eng., 71(3), 347–362.
Yang, Y.-B., and Yau, J.-D. (1997). “Vehicle-bridge interaction element for dynamic analysis.” J. Struct. Eng., 123(11), 1512–1518.
Yu, L., and Chan, T. H. T. (2007). “Recent research on identification of moving loads on bridges.” J. Sound Vib., 305(1–2), 3–21.
Information & Authors
Information
Published In
Copyright
© 2009 ASCE.
History
Received: Sep 12, 2008
Accepted: Jan 22, 2009
Published online: Jun 15, 2009
Published in print: Jul 2009
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.