Abstract
Abstract A model is proposed to investigate the contact kinematics of a frictional constraint experiencing two-dimensional relative motion. In this model, a contact plane is defined and its orientation is invariant. In addition, the contact normal load is assumed constant. In this study, analytical criteria are developed to determine the transitions between stick and slip which characterize how the friction force relates to the two-dimensional relative motion. Using the stick–slip transition criteria, a stick–slip diagram of elliptical motion is developed. This stick–slip diagram illustrates the fundamental characteristics of the two-dimensional contact kinematics when the relative motion has an elliptical trajectory. Fourier series expansion is employed to divide the induced periodic friction force into two components: non-linear spring resistance and friction damping. In this study, a set of non-linear functions that relate the non-linear spring resistance and friction damping to the elliptical motion are developed. It is shown that these non-linear functions can be analytically derived for the two extreme cases: circular motion and one-dimensional motion. The single-term harmonic balance scheme along with the non-linear spring resistance and friction damping of the frictional constraint are then used to calculate the resonant response of a frictionally constrained two-degree-of-freedom oscillator. The accuracy of the method is demonstrated by comparing the results with those of the direct time integration method.
Published Version
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