松弛状态圆截面螺旋细杆的弹性波传播

研究松弛状态下的圆截面弹性螺旋细杆,即带有原始曲率和挠率的非圆截面弹性杆的动力学问题.基于Kirchhoff动力学比拟,建立欧拉角表达的弹性杆动力学方程.考虑截面的线加速度和角加速度的惯性效应.在一次近似意义下讨论松弛状态圆截面螺旋杆的静态和动态稳定性.证明在空间域内保持静态稳定,在波数大于1条件下亦满足时域内的动态稳定性条件.讨论弯扭变形弹性波在螺旋杆内的传播,导出波速与波数之间的对应关系.

Elastic wave propagation of a thin helical rod with circular cross section in relaxed state

The dynamics of a thin elastic helical rod with circular cross section in relaxed state, i.e., the dynamics of a rod with intrinsic curvature and twisting, was discussed. Based on the Kirchhoff's kinetic analogy, the dynamical equations of the elastic rod were expressed by the Euler's angles. The inertial effects of the linear and angular accelerations of the cross section were considered. The stability in spatial and time domain of a helical rod with circular cross section in relaxed state was discussed in the sense of first approximation. We proved that the stability conditions were satisfied in the spatial domain, and in the time domain when the wave number was larger than 1. The propagation of the elastic wave of bending/twisting deformation was discussed, and the relationship between the propagation speed and the wave number was obtained.