Vibration source identification using corrected finite difference schemes

This paper addresses the problem of the location and identification of vibration excitations from the measurement of the displacement field of a vibrating structure. It constitutes an improvement of the force analysis technique published several years ago. The development is based on the use of the motion equation which is discretized by finite difference schemes approximating spatial derivatives of the displacement. In a first instance, the error due to this approximation is analytically calculated in the case of beams and the low-pass filtering effect of the finite difference schemes in the wavenumber domain is shown. This filter also contains singularities implying bias errors, especially if the spacing between sensors is chosen in order to regularize the problem. In a second instance, a corrected value is applied to the classic schemes used in the force analysis technique, which suppresses completely the singularities of the filter. After the complete description of the corrected force analysis technique on beams, the extension to plates is described, where simulations with noisy data show the very good accuracy one can obtain without the requirement of an added regularization for the excitation identification.