Fourier spectral element for simulation of vibro-acoustic modulation caused contact in the beam

The purpose of this research is to provide an efficient method for simulating the Vibro-acoustic modulation (VAM) effect in beam-type structures. Contact acoustic nonlinearity (CAN) can be induced by support loosening, which is a common defect in engineering systems. The appearance of sidebands caused by wave intermodulation is the basis of VAM based Structural Health Monitoring (SHM). The VAM simulation can be used for high level SHM, such as damage imaging, to provide some insights into the intermodulation mechanism and influencing factors. In this research, the Fourier spectral element method (FSEM) is used to simulate and investigate the VAM effect for the beam structures. The clamped support is represented by an elastic foundation that can be released by lowering its stiffness. The transducers, which contained three piezoelectric patches, two for high and low frequency actuation and one for sensing, were also incorporated in the numerical model. The Lagrange multiplier method and the node-to-node contact strategy were used to formulate the contact problem. The forward increment Lagrange multipliers approach was utilized for time integration. The results are consistent with the previous studies on beams with loosened supports. Furthermore, the FSEM results were compared to their FEM counterparts to assess the former's efficacy. The impact of loosening intensity on VAM signals and damage metrics was investigated using the FSEM model. According to the results, the FSEM has a high convergence rate and accuracy, making it a good choice for improving VAM-based damage identification.