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Seminar - Nonlinear Wave Scattering at the Interface of a Granular Dimer Chain and a Flexible Continuum by Prof. D. Michael MCFARLAND
日期:2016 年 08 月 30 日 ( 星期二)
Time:11:00 am – 12:00 pm


Uncompressed granular dimer chains composed of repeated pairs of heavy and light, spherical, linearly elastic beads exhibit interesting intrinsic responses. The dynamics of these highly discontinuous nonlinear media is governed by the mass ratio of each pair of beads. In this work we computationally study nonlinear scattering of incident pulses at the interface of an impulsively excited dimer chain with a dispersive elastic boundary; namely, a finite linear string resting on an elastic foundation. We develop an algorithm which accurately computes the highly discontinuous contact forces and displacements at the flexible interface, enabling computation of wave transmission and reflection, localization, and multi-scale nonlinear scattering. Depending on the mass ratio of the dimer and the stiffness of the elastic foundation, this scattering may lead to significant reduction of the maximum contact force at the interface, and, thus, it may drastically affect the energy transmitted and reflected at that boundary. Moreover, for sufficiently small mass ratios of the dimer chain transient breathers are realized close to the interface in the form of localized fast oscillations of light granules of the dimer that entrap shock energy and then release it on a slow time scale back to the chain and the flexible boundary.


Dr. D. Michael McFarland is an adjunct Research Professor in the Aerospace Engineering Department and the Civil and Environmental Engineering Department of the University of Illinois at Urbana-Champaign, Urbana, Illinois, USA, and a Distinguished Professor in the College of Mechanical Engineering of Zhejiang University of Technology, Hangzhou, China. He is a co-director of UIUC’s Linear and Nonlinear Dynamics and Vibrations Laboratory, and is a National High-end Foreign Expert of China, hosted by ZJUT. He holds BS and MS degrees in General Engineering and a PhD in Aerospace Engineering, all from UIUC. He was formerly on the faculty of Mechanical Engineering at the University of Connecticut and a participant in UConn’s Center for Grinding Research & Development and Precision Manufacturing Center. He is the author of over 100 journal papers and several books and book chapters, including a well-known monograph on smart structures. His expertise includes structural dynamics and control, experimental structural dynamic analysis, nonlinear dynamics, and computational mechanics. He is the president of two small engineering companies.