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.