Experimental Nonlinear Dynamics of a Highly Flexible Spinning Beam Using a 3-D Motion Analysis System

作者：Xin Qian, Xingwen Du, P. Frank Pai · 年份：2010 · DOI：10.2514/6.2010-2892 · 被引用次数：7 · 研究领域：Magnetic Bearings and Levitation Dynamics、Tribology and Lubrication Engineering、Gear and Bearing Dynamics Analysis

Here we introduce the use of a camera-based 3D motion analysis system for non-contact dynamic testing of a highly flexible spinning verti cal shaft. For dynamics characterization, we present a conjugate-pair decomposition (CPD) method for time-frequency analysis of measured dynamic responses. Experimental and numerical results show that the timevarying frequency and amplitude extracted by CPD are more accurate than those by Hilbert-Huang transform (HHT) and can be used for accurate dynamics characterization and nonlinearity identification. Furthermore, a geo metrically exact total-Lagrangian beam theory is formulated into a set of 12 first-order n onlinear ordinary differential equations, and a multiple shooting algorithm is used to solve for the steady-state operational deflection shape (ODS) corresponding to a spinning speed. The geometrically exact beam theory fully accounts for high-order geometric nonlinearities du e to bending and twisting and was derived using Jaumann stresses and strains, exact c oordinate transformation, and the concept of orthogonal virtual rotations. The numeri cally exact ODSs from multiple shooting analysis agree well with those experimentally measured ones.