Abstract: Some interesting results on the dynamics of continuous systems are reviewed. They involve: 1) vibration and stability of translating media with time-varying lengths and/or velocities; 2) nonlinear vibrations of systems with large degrees of freedom and general nonlinearities; 3) new spatial discretization and substructure methods for one- and two-dimensional continuous systems; and 4) new formulations of flexible multibody dynamics with application to elevator traveling cables. Two types of dynamic stability problems are addressed from the energy viewpoint in the first area: dynamic stability of translating media during extension and retraction, and parametric instabilities in continuous systems with periodically varying lengths and/or velocities. The incremental harmonic balance method is used and modified in the second area to handle periodic responses of high-dimensional models of nonlinear continuous systems and their stability and bifurcations, as well as quasi-periodic responses. The new spatial discretization and substructure methods in the third area ensure that all matching conditions of continuous systems are satisfied, and hence uniform convergence of solutions. New nonlinear models of slack cables with bending stiffness and arbitrarily moving ends are developed for moving elevator traveling cables in the fourth area. Some experimental results are presented to validate theoretical predictions.

Biography: Weidong Zhu is a Professor in the Department of Mechanical Engineering at the University of Maryland, Baltimore County, and the founder and director of its Dynamic Systems and Vibrations Laboratory and Laser Vibrometry Laboratory. He received his double major BS degree in Mechanical Engineering and Computational Science from Shanghai Jiao Tong University in 1986, and his MS and PhD degrees in Mechanical Engineering from Arizona State University and the University of California at Berkeley in 1988 and 1994, respectively. He is a recipient of the 2004 National Science Foundation CAREER Award. He has been an ASME Fellow since 2010, was an Associate Editor of the ASME Journal of Vibration and Acoustics from 2007‐2014, and is a Subject Editor of the Journal of Sound and Vibration. His research spans the fields of dynamics, vibration, control, applied mechanics, metamaterials, structural health monitoring, and wind energy, and involves analytical development, numerical simulation, experimental validation, and industrial application. He has published 180 SCI-indexed journal papers in these areas.