Reconstruction of a distributed force applied on a thin cylindrical shell by an inverse method and spatial filtering

The localization and the magnitude of acting steady-states forces resulting from the dynamic response of a cylindrical shell are investigated. The derivatives present in the equation of motion are expressed in terms of displacements using finite-difference schemes. Displacements of the structure are introduced into the equation of motion in order to calculate the distribution of these forces. Numerical simulations show that when the force distribution is calculated using well-defined displacements, the exact position of the force is easily determined. However, when the displacements are mixed with uncertainties, noise appears and the real force is relatively inaccurate. In order to handle this instability in the inverse problem, a regularization method based on signal processing techniques such as windowing and filtering in the spatial wavenumber domain should be performed. Numerical examples that illustrate the regularization process show that when the local filtering is applied to the force distribution, calculated from noisy data, reasonable results are obtained. Experiments are performed on a cylindrical shell in order to measure its velocities. Unfortunately, using the displacements derived from measured velocities, high sensitivity to the noise in the measurements is observed. Overall, the experimental identification gives also good results when the same technique of filtering is applied to the force distribution.