A novel approach for distributed dynamic load reconstruction by space-time domain decoupling

A novel inverse approach based on Green's function method and orthogonal polynomial fitting technique is presented in this paper to reconstruct the distributed dynamic load acting on a structure. This approach enables one to identify the time history and reconstruct the spatial distribution function separately. It is first assumed in this paper that the distribution function and the time history of the distributed dynamic load are separable. Modal analysis proves the sameness of the form between the modal loads and the actual time history. With the knowledge of corresponding Green's functions and modal responses, the modal loads are identified later. Approximating the spatial distribution function by a set of Chebyshev orthogonal polynomials, new distributed dynamic loads are constructed with each orthogonal polynomial performing as the spatial distribution function and the previously identified modal load acting as the time history. Fitting the modal loads, the coefficients of each orthogonal polynomial are achieved and then the spatial distribution function recovered. To overcome the intrinsic ill-conditioned characteristic, appropriate regularization methods are adopted in both the modal load identification and the distribution function reconstruction. Numerical examples demonstrate the validity and accuracy of the proposed method.