On the Existence of Normal Modes of Damped Discrete-Continuous Systems-Reference-Cited by-同舟云学术

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

Published:1998-12-01 Issue:4 Volume:65 Page:980-989
ISSN:0021-8936
Container-title:Journal of Applied Mechanics
language:en
Short-container-title:

Author:

Banks H. T.¹,Luo Zheng-Hua²,Bergman L. A.³,Inman D. J.⁴

Affiliation:

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

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

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

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

Abstract

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.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Link

http://asmedigitalcollection.asme.org/appliedmechanics/article-pdf/65/4/980/5880248/980_1.pdf

Reference33 articles.

1. Banks H. T. , GatesS. S., RosenI. G., and WangY., 1988, “The identification of a distributed parameter model for a flexible structure,” SIAM J. Control and Optimization, Vol. 26, pp. 743–762.

2. Banks, H. T., Smith, R. C., and Wang, Y., 1996, Smart Material Structures: Modeling, Estimation and Control, Masson/Wiley; Paris/Chichester.

3. Bellos, J., 1989, “Theoretical and Experimental Analysis of Non-Proportional Damping,” Ph.D. dissertation, Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, New York.

4. Bellos J. , and InmanD. J., 1989, “A survey on non proportional damping,” Shock and Vibration Digest, Vol. 27, No. 10, pp. 7–12.

5. Bergman L. A. , and McFarlandD. M., 1988, “On the Vibration of a Point Supported Linear Distributed System,” ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 110, pp. 485–492.

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