Nonlinear Frequencies for Transverse Free Oscillations of a Transporting Tensioned Beam

Abstract

Abstract. This study focuses on the natural frequencies of nonlinear free transverse oscillations of transporting tensioned beams via the standard fast Fourier transform (FFT). The transverse oscillations of transporting tensioned beams can be governed by a nonlinear partial-differential equation or a nonlinear integro-partial-differential equation. Numerical schemes are respectively presented for the two governing equations via the differential quadrature method. For each nonlinear equation, the nonlinear oscillations frequencies are investigated via FFT with the time responses histories. The numerical results depict the tendencies of the frequencies of nonlinear free transverse oscillations of transporting tensioned beams with the changing oscillations amplitude, transporting speed, the nonlinear coefficient and the flexural stiffness.