A deconvolution method for force reconstruction in rods under axial impact

A deconvolution method to extract the force history exerted axially on one end of a rod using the responses recorded remotely from the impact location is presented in this paper. The traditional Green’s function is completely eliminated in the solution process. To apply the developed method, another set of force and response data, at the same locations as in the impact event in which the force is to be reconstructed, needs to be obtained either from measurement or from a theoretical/numerical solution. The latter was adopted in bar impact events due to the fact that the signals have very wide frequency bands, and the theoretical responses were calculated separately using the Love theory and the Pochhammer–Chree equation. Using optimization algorithms to search for the force from the input signals that were recorded by multiple gauges and were contaminated with noises, the method has been demonstrated to be robust. Further, to show that the developed method is general, an example for extracting the impact force exerted on a complicated sandwich structure using the recorded strain signals as the input data are also presented. This further demonstrates that the method can be applied to an impact event in which the Green’s function is very difficult to construct.