NATURAL FREQUENCIES OF NONLINEAR TRANSVERSE VIBRATION OF AXIALLY MOVING BEAMS IN THE SUPERCRITICAL REGIME

摘要：

Natural frequencies are investigated for transverse vibration of axially moving beams in the supercritical ranges. In the supercritical transport speed regime, the straight equilibrium configuration becomes unstable and bifurcate in multiple equilibrium positions. The transverse motion can be governed by a nonlinear partial-differential equation or a nonlinear integro-partial-differential equation. For motion about each bifurcated solution, those nonlinear equations are cast in the standard form of continuous gyroscopic systems by introducing a coordinate transform. The natural frequencies are investigated for the beams via the 8-term Galerkin method to truncate the corresponding governing equations without nonlinear parts into an infinite set of ordinary-differential equations under the simple support boundary. Numerical results indicate that the nonlinear coefficient has little effects on the natural frequency, and the two nonlinear models predict qualitatively the same tendencies of the natural frequencies with the changing parameters. Quantitative comparisons demonstrate that results of the 4-term Galerkin method for the natural frequency for axially moving beams in the supercritical range are with rather high precision.

关键词： azially moving beam nonlinearity supercritical natural frequencies galerkin method

作者: Hu Dinga Li-Qun Chen

作者单位: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China Department of Mechan

会议类型: 国际会议

会议名称: The Fifth International Conference on VETOMAC-V(第五届振动工程及机械技术国际会议)

会议地点: 武汉

会议语种:英文

页码: 50-56

在线出版日期: 2009-08-27（万方平台首次上网日期，不代表论文的发表时间）