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TECHNICAL BRIEFS

Modal Analysis of Nonviscously Damped Beams

[+] Author and Article Information
S. Adhikari1

Department of Aerospace Engineering, Queens Building, University of Bristol, Queens Walk, Bristol BS8 1TR, UKs.adhikari@bristol.ac.uk

M. I. Friswell

Department of Aerospace Engineering, Queens Building, University of Bristol, Queens Walk, Bristol BS8 1TR, UK

Y. Lei

College of Aerospace and Material Engineering, National University of Defense Technology, Changsha 410073, PRC

1

Corresponding author.

J. Appl. Mech 74(5), 1026-1030 (Aug 15, 2006) (5 pages) doi:10.1115/1.2712315 History: Received February 08, 2006; Revised August 15, 2006

Linear dynamics of Euler–Bernoulli beams with nonviscous nonlocal damping is considered. It is assumed that the damping force at a given point in the beam depends on the past history of velocities at different points via convolution integrals over exponentially decaying kernel functions. Conventional viscous and viscoelastic damping models can be obtained as special cases of this general damping model. The equation of motion of the beam with such a general damping model results in a linear partial integro-differential equation. Exact closed-form equations of the natural frequencies and mode shapes of the beam are derived. Numerical examples are provided to illustrate the new results.

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Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 1

Euler–Bernoulli beam with nonviscous damping patch

Grahic Jump Location
Figure 3

The imaginary parts of the first four modes

Grahic Jump Location
Figure 2

The real parts of the first four modes

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