ヒステリシス減衰を有する振動系の自由振動解析

抄録

This paper describes a new analytical method to derive free vibration of vibration systems that have hysteretic damping. We cannot obtain practical solutions as general solutions of homogeneous differential equations because general solutions diverge to infinity when vibration systems have hysteretic damping. Therefore, approximate solution that uses viscous damping instead of hysteretic damping has been used thus far when the damping is relatively small. In addition, the analytical method that uses Fourier inverse transform was proposed to obtain the free vibration that does not diverge. The validity of this conventional method has not been proved because there are no exact solutions. Apart from this problem, this method has disadvantages that step responses cannot be derived directly, and computational load is large. To solve these problems, we propose a new analytical method that uses the Fourier series expansion of the excitation terms. Using this method, the solution of free vibration is given as the superposition of the solutions of forced vibrations. Both impulse and step responses of discrete and continuous vibration systems were analyzed using the proposed method in this paper. The effectiveness of the proposed method was verified through numerical simulations.