A Modified Trunction Method for Pressure Reconstruction in Case of Non Ponctual Impact on An Elastic Plate

Abstract eng:
This work deals with reconstruction of distributed force signal resulting from a non punctual object impacting perpendicularly an elastic homogeneous and isotropic rectangular plate. The impacting force is assumed to be uniformly distributed over a rectangular patch of the plate. The direct problem was solved by using modal decomposition method with explicit analytical modes. A discrete problem was written for that by sampling the obtained convolution integral. To extract the pressure signal by deconvolution of the dynamic response measured at a given point of the plate, solution of an inverse problem had been considered. Since this type of problem is known to be ill-posed due to bad conditioning of the involved Toeplitz like matrix, regularization is needed to obtain a physically meaningful solution. A new regularization technique based on truncation filtering was examined. This technique uses as a first step the generalized decomposition of Toeplitz matrix on singular values. Then, regularization of the decomposed form through a truncation filter is performed. The truncation consists in eliminating the first low index terms up to an optimal rank representing the contribution of low amplitude generalized singular values. If the impact force signal has a half sine like standard form, the index corresponding to time instant where the maximum displacement response is obtained was found to be the optimal order of truncation. This technique has proved to be effective in reconstruction of impact pressures through various cases of study and the computational cost was found to be much lower than that of the classical truncation method based on L-curve criterion.

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