Modeling of vibro-acoustic modulation induced by non-linear contact in the Euler-Bernoulli beam using the Fourier spectral element

Exploiting the nonlinear nature of structural damage through piezoelectric patches is one of the latest concepts of early detection of damage. Support loosening as one of the prevalent defects in engineering systems is a source of contact acoustic nonlinearity. Vibro-acoustic modulation has proven to be a promising method for revealing structural nonlinearity characteristics. Requiring a large number of cycles to be solved in the time domain to reach the steady-state before evaluating the results in the frequency domain, makes using existing computational methods such as finite element method to model this phenomenon very expensive. This paper is concerned with a novel numerical method called Fourier spectral element to investigate the vibro-acoustic modulation in the Euler-Bernoulli beam caused by contact nonlinearity. Three piezoelectrics were attached to the beam as the probe, pump and sensor. The numerical outcomes are compared against the experimental results to check the validity of the developed method. The results show that the Fourier spectral element not only provides a high convergence rate but is also capable of simulating the phenomenon of modulation with sufficient accuracy.