Viscously damped free and forced vibrations of circular and annular membranes by a closed form exact method

Abstract

In the present paper, viscously damped free and forced vibrations of circular and annular membranes are investigated using a closed form exact method. Instead of undamped natural frequencies which are typically computed and applied in the free and forced vibration analysis, viscously damped natural frequencies are done. It is certain that the viscous damping affects the natural frequencies. The viscously damped natural frequency equation and the critical viscous damping equation are exactly derived. In the viscously damped free vibration analysis, effects on viscous damping on natural frequencies are studied. In the viscously damped forced vibration analysis, vibratory amplitudes are derived in a closed form exact manner. Accurate displacement amplitude vs. forcing frequency curves showing the forced response due to distributed harmonic loading are displayed.