旋转圆环受迫振动响应的行波解

FORCED VIBRATION ANALYSIS OF ROTATING RING WITH WAVE PROPAGATION METHOD

应用行波法求解旋转圆环的受迫振动响应问题。以静止坐标系中旋转、扩张弯曲梁的振动方程为基础,应用弹性固体中的波动理论,给出旋转圆环中波模式、波传递矩阵及受迫响应解。研究表明,在旋转弯曲梁段中,正方向与负方向上波的传播特性相异;将外激励等效为间断节点模型,考虑几何连续性条件和力的平衡条件,可获得旋转圆环上任意点处位移响应的表达式。通过行波方法求得的结果反映旋转圆环的动态特性,并可有效地计算旋转圆环的受迫振动响应。

The wave propagation was used to analyze the forced vibration characteristics of a rotating ring. Governing equations of motion, basing on the Hamilton principle and the Euler-Bernoulli beam theory, were developed for extensional curved beams with rotating speed under an absolute coordinate system. By using the theorem of wave motion in an elastic solid, the propagation characters of elastic wave guides, wave transfer matrix and forced vibration response were analyzed. The result of analysis showed that waves on the positive direction was different form ones on the negative direction. According to modeling external forces as discontinuous joints, and with consideration of the continuity condition and the equilibrium condition, an equation of displacement responses at any position within the ring was obtained. The numeric computation results illustrated that the equation, solved by wave propagation method, was able to determine forced vibration responses of the rotating ring; the wave propagation is efficiency in the prediction of forced vibration behaviors that are associated with rotating rings.