Nonlinear Dynamics of Flexible Spinning Discs

本研究项目的主要目的是研究旋转圆盘系统运动的局部和全局动力学，并从数值和实验上验证理论结果。这项研究的结果将在计算机磁盘存储设备、工业圆锯片和涡轮转子动力学等方面的应用中发挥作用。这项研究的目标有四个。首先，将系统地推导出控制圆盘动力学的一般非线性运动方程，以包括固有弯曲刚度、离心力引起的薄膜应力、平面内和横向位移的非轴对称、几何非线性、空气相对于圆盘静止和运动引起的气动阻尼、时变弹簧速率引起的参数激励等影响。其次，IS方程以及对称破缺分支也将被研究。第三，研究了五种非线性转盘整体分叉的机理，找出了系统的重要振型，确定了稳定边界，并验证了非线性响应的本质，验证了理论预测。验证研究将使用旋转盘制造商的实际数据进行。反过来，实验验证和验证指导理论的发展和完善，以纳入观察到的任何新现象。

The primary goal of this research project is to investigate the local and global dynamics in the motion of a spinning disc system and to numerically and experimentally verify the theoretical results. The results of this research will be useful in applications such as computer disc memory devices, industrial circular saw blades, and turbine rotor dynamics. The objectives of the research are four-fold. First, the general nonlinear equations of motion governing the disc dynamics will be derived systematically to include the effects due to inherent bending rigidity, membrane stresses arising from centrifugal forces, non-axismmetry of the inplane and transverse displacements, geometric nonlinearities, aerodynamic damping arising from air stationary and moving with respect to the disc, parametric excitation due to time varying spring rate, etc.. Second, is equations, along with symmetry-breaking bifurcations, will also be examined. Third the mechanisms which five rise to global bifurcations in nonlinear spinning disc to identify the important modes, locate the stability boundaries, and examine the nature of the nonlinear response to verity the theoretical predictions. Validation studies will be carried out using actual data from manufacturers of spinning discs. Experimental verification and validation in turn, guide the development and refinement of the theories to incorporate any new phenomena observed.