Stick-slip vibration of a cantilever beam subjected to harmonic base excitation

Stick-slip vibration of a cantilever beam subjected to harmonic base excitation is analyzed in this paper. To model the stick-slip vibration, considering nonlinearity and discontinuity of the friction force, two kinds of equations of motion are used: one for motion in the stick state and the other for motion in the slip state. Using the finite element method, dynamic responses of stick-slip vibration are calculated by iteratively solving the equations and connecting the stick- and slip-state motions; such calculations are conducted for various excitation conditions. The dynamic responses show that the occurrence of stick-slip vibration depends on excitation amplitude and frequency, and an occurrence of stick-slip vibration is associated with the modal characteristic of a beam. Furthermore, to formulate an analytical expression for the criterion of stick-slip occurrence, the static friction force caused by the base excitation is determined analytically. Finally, excitation conditions for stick-slip occurrence are obtained and validated in a parametric plane of the excitation amplitude and frequency, and design guidelines for avoiding stick-slip occurrence are presented.