螺旋细杆的均匀扭转振动

HOMOGENEOUS TORSIONALVIBRATION OF A HELICAL THINELASTIC ROD

讨论螺旋细杆的特殊形式扭转振动,即均匀扭转振动.以非圆截面杆和有原始曲率的圆截面杆为研究对象.杆作均匀扭转振动时各截面有相同的扭角变化规律,且杆中心线的几何形状不受振动过程的影响.研究表明,扭振来源于杆截面的非对称性及杆的原始曲率.杆的扭振规律与单摆运动相似,其动力学方程存在精确解.圆环杆的均匀扭振为螺,旋杆的倾角为零时的特例.

The homogeneous torsional vibration as a special case of the vibration of a helical thin elastic rod is discussed in this paper. A rod with noncircular cross section and a rod with circular cross section and intrinsic curvature are under investigation. In the process of ho- mogeneous torsional vibration all cross sections of the rod have a same torsional angle, and the configuration of cen-terline of the rod is not affected by the vibration. It is shown that the torsional vibration is caused by the asymmetry of the cross section and the intrinsic curvature of the rod. The torsional vibration of the rod is analogous to the motion of a simple pendulum, and there exists an exact solution for the dynamical equation. The similar vibration of an annular rod is a special case when the pitch angle of the helix is equal to zero.