Flexural-flexural-torsional Nonlinear Vibrations of Pre-twisted Rotating Beams with Asymmetric Cross-sections

Abstract

The equations of nonlinear flexural-flexural-torsional vibrations of rotating beams with asymmetric cross-sections are derived. As the cross-section is asymmetric the centre of gravity and shear centre of a beam cross-section are not assumed to coincide. The nonlinear vibrations are expanded into flexural-torsional vibrational mode series. Using the Galerkin technique, the large-scale system of ordinary differential equations is derived. The non-linear modes are used to study teh free vibrations of a rotating beam, and the backbone curves of the free vibrations and the surfaces of the non-linear modes are also presented.