Abstract:

 Progresses in investigations on energetics and conserved quantities are summarized. The key issue in energetics, the time-rate of the total mechanical energy of axially moving structures, is determined for linear transverse vibration, nonlinear transverse vibration, and coupled planer vibration. The result shows that the mechanical energy is not a constant. Conserved quantities are constructed so that the quantities remain unchanged during those vibrations. The conserved quantities can be used to prove stability of the straight equilibrium configurations and to check the numerical algorithms. Some promising topics are suggested for future research.

Key words: energetics, conserved quantity, axially moving string, axially moving beam, nonlinearity

摘要：

综述了轴向运动弦线和梁的能量关系和守恒量的研究进展。分别对于横向线性振动、横向非线性振动和耦合平面振动, 确定能量变化的关键量以及轴向运动结构总机械能的时间导数, 结果表明总机械能不是常数。对于上述振动, 构造在振动过程中保持不变的守恒量, 可以用来证明直线平衡位形的稳定性以及检验数值算法。最后提出若干有望取得进展的研究课题。

关键词: 能量关系, 守恒量, 轴向运动弦线, 轴向运动梁, 非线性