A Galerkin Method for Distributed Systems with Non-local Damping

Y Lei (National University of Defense Technology, Changsha, PR China), MI Friswell & S Adhikari (University of Bristol)

International Journal of Solids and Structures, Vol. 43, No. 11-12, June 2006, pp. 3381-3400


In this paper, a non-local damping model including time and spatial hysteresis effects is used for the dynamic analysis of structures consisting of Euler-Bernoulli beams and Kirchoff plates. Unlike ordinary local damping models, the damping force in a non-local model is obtained as a weighted average of the velocity field over the spatial domain, determined by a kernel function based on distance measures. The resulting equation of motion for the beam or plate structures is an integro-partial differential equation, rather than the partial differential equation obtained for a local damping model. Approximate solutions for the complex eigenvalues and modes with non-local damping are obtained using the Galerkin method. Numerical examples demonstrate the efficiency of the proposed method for beam and plate structures with simple boundary conditions, for non-local and non-viscous damping models, and different kernel functions.

Paper Availability

This material has been published in the International Journal of Solids and Structures, Vol. 43, No. 11-12, June 2006, pp. 3381-3400, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the Elsevier.

Link to paper using doi:10.1016/j.ijsolstr.2005.06.058

International Journal of Solids and Structures on ScienceDirect