An original differentiation tool for identification on continuous structures

The present contribution is dedicated to the identification of mechanical parameters, especially distributed parameters for continuous structures. In the following, the continuous time identification method is adapted and improved. Firstly an original expansion method using Gauss-points is presented. A novel differentiation method is then developed and compared to a classical one. These improvements are tested numerically and experimentally. This general method can be applied to system identification, structure identification, damage detection, etc. The main advantage of it is its high order differentiation capability. Therefore, this method is applied to structure monitoring on a cantilever beam in flexural motion (which involves a fourth derivative). In the treated example, the parameter ρ S / EI and the fourth derivative ∂ 4 v / ∂ x 4 are computed. The parameter ρ S / EI is accurately reconstructed for the whole beam, using different sensor patch lengths and the identification method is shown to be a precise tool for damage location. The computed fourth derivative emphasizes the discontinuity due to the crack. Using only the discontinuity property of a crack, no assumption is needed about crack behaviour. This novel differentiation technique makes it possible to compute changes and is of great interest for damage location.