Reconstruction of distributed dynamic loads on an Euler beam via mode-selection and consistent spatial expression

The paper presents a new approach to reconstruct the distributed dynamic loads on an Euler beam from the beam response. The approach is based on a mode-selection method and an idea of consistent spatial expression for the distributed dynamic loads, and is supported by error estimation. The idea of the optimal range of frequency and spatial modes for load reconstruction is proposed and verified by numerical simulations. To cope with the tough problem of identifying the dynamic loads near a fixed boundary, the concept of consistent spatial expression for the dynamic loads is put forward, and the Legendre polynomials are used as the consistent orthogonal base functions to describe the distributed dynamic loads. The numerical simulations show that the reconstruction accuracy near the fixed boundaries can be greatly enhanced.