Forced Vibration Of A SDOF With A New Hysteretic Damping Subjected To Harmonic Loading

Abstract

The periodic solution for the new hysteretic damping model subjected to harmonic loading is analytically derived. The numerical solution using the Runge-Kutta method from the reanstient state to steady state is worked out for verification. The hysteresis loop is constructed and the dissipation energy of the area is shown to be indepedent of the exciting frequency theoretically and numerically. The stability and convergence for the pertrubation of the initial disturbance are demonstrated by means if a numerical example using the Range-Kurra method. The phase lags between input and output for different ranges of loss factors and exciting frequencies are examined. Also, the sticking phenomenom when the external force can nor overcome the friction damping is discussed. The subhatmonic solution is worked out using the numerical method.