Modal Analysis of Non-viscously Damped Beams
S Adhikari, MI Friswell (University of Bristol) & Y Lei (National University of Defense Technology, Changsha, PR China)
Journal of Applied Mechanics, Vol. 74, No. 5, September 2007, pp. 1026-1030
Linear dynamics of Euler-Bernoulli beams with non-viscous non-local 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.
This material has been published in the Journal of Applied Mechanics, Vol. 74, No. 5, September 2007, pp. 1026-1030. Unfortunately the copyright agreement with ASME does not allow for the PDF file of the paper to be available on this website.
Link to paper using doi:10.1115/1.2712315
Link to the Journal website