Forced Longitudinal Vibrations of Prismatic Slender Bars under the Influence of Quadratic and Equivalent Viscous Damping

摘要

Forced longitudinal vibrations of a prismatic, slender bar with quadratic skin damping and equivalent viscous damping are analyzed. The differential equation of motion with quadratic damping is solved numerically by the method of characteristics. The bar is assumed to be free of stress at one end and subject to sinusoidal motion at the other. Frequency-response curves are plotted for several values of the nonlinear damping coefficient. The equivalent linear system is analyzed by Laplace Transforms and the results are compared with those for the nonlinear system. The damping is linearized by equating the energies dissipated per cycle by quadratic and viscous damping. (Author)