Nonlinear free vibration and stability of a rotating composite shaft with internal damping

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (1) : 117-127.

Ren Yongsheng, Shi Yuyan, Zhang Yuhuan

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Abstract

The nonlinear free vibration and stability of an internally damped rotating composite shaft were investigated. The shaft was assumed as an inextensional rotating beam with nonlinear curvature and inertia. The internal damping was described by the dissipative behavior of composite. Based on the constitutive relations and the strain-displacement relations of composite, the strain energy, virtual dissipative work and kinetic energy of the shaft were obtained. The equations of motion governing the nonlinear bending-bending vibration of the rotating composite shaft were derived using the extended Hamilton principle. The partial differential equations of motion were reduced into ordinary differential equations by the Galerkin’s method. In order to find the boundaries of stability, the corresponding linearized model of the composite shaft was used in eigenvalue analysis. The critical rotating speeds and instability thresholds of composite shaft were provided. The fourth-order Runge-Kutta method was used to integrate numerically the differential equations of motion. The displacement-time responses, phase plane curves and power spectra of the shaft were presented. The effects of the ply angle, ratio of length to outer radius and stacking sequence on the nonlinear bending vibration responses of the composite shaft were evaluated.

Key words

free vibration / motion stability / rotating composite shaft / internal damping / nonlinear curvature and inertia

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Ren Yongsheng, Shi Yuyan, Zhang Yuhuan. Nonlinear free vibration and stability of a rotating composite shaft with internal damping[J]. Journal of Vibration and Shock, 2018, 37(1): 117-127

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