Effect of Distributed Quadratic and Equivalent Viscous Damping on Longitudinal Vibrations of Prismatic Bars

Abstract

Forced longitudinal vibrations of a prismatic, slender bar with distributed quadratic damping and equivalent viscous damping are considered. The bar is free at one end and subjected to harmonic excitation at the other. The nonlinear differential equation with the velocity-squared term is solved numerically by the method of characteristics. The linearized equation is solved by Laplace transforms and the solution is compared to that of the nonlinear system. The damping is linearized by equating the energies dissipated per cycle by the two types of damping. Frequency-response curves, through the second natural mode, are given for several sets of the nonlinear and equivalent viscous damping coefficients.