The three-dimensional (3D) nonlinear dynamics of an axially accelerating beam is examined numerically taking into account all of the longitudinal, transverse, and lateral displacements and inertia. Hamilton’s principle is employed in order to derive the nonlinear partial differential equations governing the longitudinal, transverse, and lateral motions. These equations are transformed into a set of nonlinear ordinary differential equations by means of the Galerkin discretization technique. The nonlinear global dynamics of the system is then examined by time-integrating the discretized equations of motion. The results are presented in the form of bifurcation diagrams of Poincaré maps, time histories, phase-plane portraits, Poincaré sections, and fast Fourier transforms (FFTs).
Nonlinear Dynamical Behavior of Axially Accelerating Beams: Three-Dimensional Analysis
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 15, 2014; final manuscript received February 14, 2015; published online June 30, 2015. Assoc. Editor: Stefano Lenci.
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Ghayesh, M. H., and Farokhi, H. (January 1, 2016). "Nonlinear Dynamical Behavior of Axially Accelerating Beams: Three-Dimensional Analysis." ASME. J. Comput. Nonlinear Dynam. January 2016; 11(1): 011010. https://doi.org/10.1115/1.4029905
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