Extension of the Harmonic Balance Method for dynamic systems with Iwan joints

Abstract

In many applications it would be advantageous to be able to compute the nonlinear Frequency Response Functions (FRF) of structures containing bolted interfaces, but to do this with time integration is expensive so more efficient methods are desired. Harmonic Balance methods are typically more efficient, yet they are difficult to apply to systems with joints because one must track the state of many points on a surface and their highly nonlinear evolution from stick to slip in each cycle of vibration. This paper proposes an adaptation of the alternating frequency time harmonic balance method that is able to compute the steady-state response and consequently the nonlinear FRFs of systems with Iwan elements in an accurate and efficient manner. Rather than including the state of all of the sliders in the state vector, the points at which the displacement across the joint reverses are identified and used as a surrogate, greatly reducing the number of state variables and making the state variables more continuous. Furthermore, the nonlinear force and the Jacobian only need to be computed for the degrees of the freedom related to the joints, improving the efficiency of the approach. While the damping in the hysteretic system is not velocity dependent, an effective damping is introduced and added to the Jacobian to improve convergence of the Newton–Raphson algorithm for frequencies near the resonance. The proposed method, dubbed as “Hysteresis Identification via Reversal Points or (HIRP)”, is tested on various models with multiple DOF and Iwan elements, including a relatively high order model of two beams with two bolted joints. The results obtained show the capability of the proposed method and its efficiency and accuracy for realistic, industrially relevant models.