A comparative analysis of damping models for the vibratory properties of a bent beam

Much of Eric Unger's career was devoted to the study of dissipation mechanisms. This paper will explore the effect of various ways that damping effects have been incorporated in the solution of equations of motion. The analytical model of an L-shaped beam, cantilvered at one end and loaded at its free end by a force that is transverse to the plane of the bent beam, is the basis for the study. Equations of motion that account for coupling of flexure and torsion are created by merging the Ritz series method and the method of Lagrange multipliers. Energy is dissipated by a dashpot transversely mounted at the corner. An “exact” solution of the equations of motion using state-space modal analysis provides the reference for approximate methods including proportional damping, modal decoupling, and structural damping. Impulse response and complex frequency response at various levels of damping will be addressed.