Harmonic Balance of Bouc-Wen Model to Identify Hysteresis Effects in Bolted Joints

This chapter presents a new methodology through a harmonic balance method to identify the parameters to describe the hysteresis effect in bolted joints using the Bouc-Wen model. The main idea is to adopt a priori smoothing procedure in the restoring force that divides it into smooth polynomial intervals that describe, separately, the loading and unloading hysteresis cycles. This previous step allows us to obtain a closed-form analytical solution through the harmonic balance method to a nonlinear system with a weak hysteretic restoring force based on its parameters. The methodology is illustrated on the BERT benchmark, that consists of a cantilever aluminum beam with a bolted joint connection at its middle. The experimental displacement amplitudes are used as input of an inverse problem in which the output is the parameters obtained through an optimization procedure. The advantage of this approach is the direct use of the harmonic balance equations on the objective function. The results show that the identified Bouc-Wen model can adequately describe the hysteresis effect of the bolted joint.