抄録
Vibration of a system of one degree of freedom with damping proportional to the n-th power, mainly to the second, of the velocity is investigated. Unified asymptotic method is applied to the free vibration, and equivalent viscous damping method to the steady forced vibration under harmonic exitation. The results of unified asymptotic method well agree with those of numerical methods, that are Runge-Kutta-Gill method and Newmark's β method. It is shown by the analysis that the amplitude is inversely proportional to time when the velocity square damping exists in the system. The results of equivalent viscous damping method almost agree with those of numerical methods. The differencies of the two are small when the frequency of external force is the same as the natural frequency but relatively large when it is one-third of the natural frequency. The response of the system having the velocity square damping is influenced by the value of external force. The response of a system, which has one mass, two springs and one velocity-square damping is gained by the equivalent viscous damping method and the optimum damping coefficient is dscussed. This system seems favorable to isolate vibration, by earthquakes, machines and so on.
