The nonlinear vibration and stability of a non-uniform continuous spindle system with nonlinear and nonsmooth boundaries

Abstract

In this paper, the vibrations of a non-uniform continuous Timoshenko beam model for spindle system with nonlinear and nonsmooth boundaries are analyzed. The Galerkin method is used to discretize the governing nonlinear partial differential equations. Then, the averaging technique is applied to obtain the modulation equations. The frequency response curves are presented and variations of the curves with respect to the bearing interference fit value are discussed. As the interference fit value increases, the nonlinearity of system decreases. All curves are found converge asymptotically to the same dimensionless frequency value as the vibration amplitudes increase. Fixed points are also observed near the natural frequencies in the response curves. These above results provide theoretical foundations for further nonlinear dynamic analysis and design of the spindle bearing systems.