Reconstruction Of Distributed Dynamic Loads On Linear Elastic Systems-Theory And Methodology

This dissertation deals with the reconstruction of distributed dynamic loads on Euler-Bernoulli beam and elastic thin plate, to find simple but important properties or principles underlying the problem, and to propose new, concise and effective reconstruction theory.The finite element method cannot find its application in the situation, since the discrete data from engineering measurement is usually on only a small number of spatial points, which is much less than the data on time domain. However, the reconstruction of distributed dynamic loads on a linear elastic system is originally a problem involving infinite dimensions. Therefore, to approximately reconstruct the spatial distribution of the dynamic loads, both modal transformation and finite dimensional approximation are employed. Both Galerkin method and collocation method are applied together as projection methods to transform the original infinite dimensional problem into a finite dimensional one, and this coupling application is named approximate projection method.The reconstruction of distributed dynamic loads on a linear elastic system is an ill-posed problem, which always needs additional information due to lack of information. The authors believe that some important connection lies between the spatial data and the temporal data in the partial discrete response data. When an Euler-Bernoulli beam is excited by a harmonic load with single mode-shape distribution, the simple and important relationship finally emerges between the spatial data and the temporal data during the transformation from load to response, and the concept of scale factor is thus proposed.Animals'perceptual organs are naturally identification system, all of which are sensitive in finite but different bandwidth. Combing the naturally reasonable limit and the idea that important things will cause important effect, it is naturally to infer that finite reconstruction is also sensible. Based on the recognition and the concept of scale factor, a new reconstruction theory is found with the proposition of the mode selection method. The approximate projection method and the mode selection method are applied basically as physical regularization strategy to deal with the infinite-dimensional and ill-posed reconstruction problem, before applying other purely mathematical regularization methods.Load reconstruction near the fixed spatial boundaries is usually hard. The loads near the fixed spatial boundaries are impossible to be correctly reconstructed, if the natural modal functions or their modified forms are applied as base functions to express the spatial distribution of the load as generalized Fourier series. To tackle this problem, the concept of consistent spatial expression is proposed, and Legendre polynomials are applied as the consistent spatial base functions, which result in good effect in numerical simulations.Wavelet transform is not conveniently applied on the load reconstruction of a dynamic system, since it has no good and simple properties on the relationship between the input and output of a dynamic system, though it dose have profits on local analysis of signals. Nevertheless, the authors proposed the method of wavelet approximation to reconstruct the distributed dynamic loads on linear elastic system, and relatively good results are obtained. Meanwhile, as difficulties usually confront researchers identifying transient force from response with non-zero initial conditions, the method of fragment analysis is proposed to deal with this problem, and the method succeeds cooperating with the wavelet approximation method.Based on abovementioned methods and concepts, the reconstruction theories of distributed dynamic loads on both Euler-Bernoulli beam and elastic thin plate are proposed. The numerical simulations show good accordance with the theories, and many new phenomena are disclosed.