Dynamic response predictions of frictionally constrained lap joints subjected to cyclic loading

We consider a simple frictionally constrained lap joint. Two identical beams were joined by a constant normal load. A periodic bending moment was applied on each beam to investigate the contact tractions at the joint interface. Predicting the dynamic behaviors of a frictionally constrained lap joint under periodic loading is challenging owing to the inherent nonlinearity of the behaviors. A dynamic response analysis of nonlinear systems is generally conducted via numerical integration in the time domain. However, owing to the nonlinear nature, time-domain analyses are computationally expensive. To address this issue, efficient reduced-order modeling (ROMs) was proposed in this paper. The proposed technique is based on the interpretation of the nonlinear characteristics of the friction force as relevant damping and stiffness terms. To increase the computation speed, the proposed method allows for the precalculation of the equivalent terms and employs response-dependent equivalent parameters in iterative solution methods. For validation, steady-state responses due to periodic bending were examined. The results obtained from the ROMs agree well with those of the time-domain analysis conducted using the full finite-element model. This study demonstrates that the equivalent expression of the nonlinear friction force can be defined by equating the energy loss or store per cycle in a hysteretic system to the energy loss or store per cycle in the corresponding amplitude. The proposed technique permits accurate predictions of the steady-state response of resonant vibrations in a primarily nonlinear hysteretic system.