Identification of the viscoelastic boundary conditions of Euler-Bernoulli beams using transmissibility

A new method to identify the viscoelastic boundary conditions of Euler-Bernoulli beams under forced response is here presented. The boundary conditions and transmissibility function with viscoelastic expressions in terms of the Green function are introduced in the identification process. Two distinct identification methods are proposed: the least squares method with singular value decomposition; and the pattern search optimization method. Three examples are reported to demonstrate the efficacy of the proposed methods. The results from the least squares method to provide accurate solutions under noise-free conditions, but poorly perform with the addition of 1% noise. Conversely, the pattern search optimization method integrates the solutions from different frequencies and provides promising solutions, even with 50% noise. The capability of identifying complex boundary conditions under high levels of noise might open the door for the proposed method to be considered in real-life applications of structural health monitoring and model updating with boundary conditions of beam-like structures such as bridges.