装有阻力与位移成正比的减震器的车体振动的周期解

Periodic Solution of Vibration of a Two-Degreeof-Freedom Body with Dampers in Which Friction Is Proportional to the Displacement

本文研究装有摩擦减震器的车体的两个自由度强迫振动的周期解。讨论了路面的干扰简化为简谐支承运动、摩擦力的大小与车体的位移成正比的情况。文中首先建立了系统的运动微分方程。由于存在摩擦力,方程式中出现了带有记号函数Sgn(x)的非连续项,因而给方程的求解带来了困难。本文应用摄动法将所求的解展开为关于小参数ε的幂级数,并将记号函数Sgn(x)简化为第一近似解的记号函数Sgn(x_0_0)。最后得出系统的非共振周期解,获得了关于振动特性的一些结论。

This paper studies periodic solution of forced vibration of a two-degreeof-freedom body with friction dampers. It discusses the conditions that the road excitation is simplified to the harmonic support motion and the friction is proportional to the displacement of the body. Firstly, we derived the differential equation of motion of system. Because of the existanee of friction, discontinuous terms with sign function Sgn (x(?)) appear in the equation, so that there will be some difficulties in solving them. By means of the perturbation method, we expand the solution in a power series in small parameter ε and reduce the sign function Sgn(x(?)) to sign function Sgn(x_0(?)_0) of the first approximate solution. Finally, we obtain the nonresonance periodic solution of system and come to some conclusions for vibrational properties.