Periodic forced response of structures having three-dimensional frictional constraints

Many mechanical systems have moving components that are mutually constrained through frictional contacts. When subjected to cyclic excitations, a contact interface may undergo constant changes among sticks, slips and separations, which leads to very complex contact kinematics. In this paper, a 3-D friction contact model is employed to predict the periodic forced response of structures having 3-D frictional constraints. Analytical criteria based on this friction contact model are used to determine the transitions among sticks, slips and separations of the friction contact, and subsequently the constrained force which consists of the induced stick-slip friction force on the contact plane and the contact normal load. The resulting constrained force is often a periodic function and can be considered as a feedback force that influences the response of the constrained structures. By using the Multi-Harmonic Balance Method along with Fast Fourier Transform, the constrained force can be integrated with the receptance of the structures so as to calculate the forced response of the constrained structures. It results in a set of non-linear algebraic equations that can be solved iteratively to yield the relative motion as well as the constrained force at the friction contact. This method is used to predict the periodic response of a frictionally constrained 3-d.o.f. oscillator. The predicted results are compared with those of the direct time integration method so as to validate the proposed method. In addition, the effect of super-harmonic components on the resonant response and jump phenomenon is examined.