Reconstruction of distributed dynamic loads on a thin plate via mode-selection and consistent spatial expression

This paper presents a convenient and efficient approach to reconstruct two-dimensional distributed dynamic loads on a damped thin elastic plate from its steady-state dynamic response. The approach is based on a mode-selection method which comes from an idea that an optimal range of frequency and mode exists for dynamic load reconstruction, as well as on the consistent spatial expression of the distributed dynamic loads. The criterion for mode selection is derived theoretically. A comparison between the method of truncated singular value decomposition (TSVD) and the method of mode selection demonstrates that the former is unstable while the latter is not only stable, but robust. With the proposed criterion, the method of mode selection enables one to find an optimal range for load reconstruction provided that the error bounds of both parameters and objective are given or estimated, and hence to make a balance between the reconstruction range and the error control.