On the Existence of Normal Modes of Damped Discrete-Continuous Systems

[+] Author and Article Information
H. T. Banks

Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8205

Zheng-Hua Luo

Department of Mechanical Engineering, Nagaoka University of Technology, Nagoka, Niigata 94021, Japan

L. A. Bergman

Department of Aeronautical and Astronautical Engineering, University of Illinois, Urbana, IL 61801

D. J. Inman

Department of Engineering Science and Mechanics, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061-0219

J. Appl. Mech 65(4), 980-989 (Dec 01, 1998) (10 pages) doi:10.1115/1.2791942 History: Received February 17, 1997; Revised August 13, 1997; Online October 25, 2007


In this paper we investigate a class of combined discrete-continuous mechanical systems consisting of a continuous elastic structure and a finite number of concentrated masses, elastic supports, and linear oscillators of arbitrary dimension. After the motion equations for such combined systems are derived, they are formulated as an abstract evolution equation on an appropriately defined Hilbert space. Our main objective is to ascertain conditions under which the combined systems have classical normal modes. Using the sesquilinear form approach, we show that unless some matching conditions are satisfied, the combined systems cannot have normal modes even if Kelvin-Voigt damping is considered.

Copyright © 1998 by The American Society of Mechanical Engineers
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