Reconstruction Of Distributed Random Dynamic Loads

The identification (or reconstruction) of dynamic load is the second kind of the inverse problem in structural dynamic analysis, which is a process of reconstructing loads applied to structure in case of structural dynamic model and information of structural response. When it is difficult to measure the loads applied to the structure with acquisition equipment, the identification technology of dynamic loads makes it possible for obtaining external loads, so its researches have an important theoretical value and practical prospects. Present researches focus on identification of deterministic dynamic loads, and become more and more fruitful. However, rare research pays attention to identify random loads, let alone distributed random loads. The dissertation presents identification technology of stationary random dynamic loads, for multi-degree-of-freedom systems, Bernoulli-Euler beam and elastic thin plate, based on linear elastic theory.Different from deterministic dynamic loads, random dynamic loads have to take effects of relationship between loads and randomness of time history, hence, its researches become more challenging and involve more computation. From simplicity to complexity and small to large scale, beginning with the forward problem of structural dynamics, the studies presented in the dissertation include the identification of random dynamic loads of multi-degree-of-freedom systems, Bernoulli-Euler beam and elastic thin plate respectively, with the help of inverse problem simulation. The dissertation begins with a brief survey on the reconstruction technology of dynamic loads in the Chapter 1. There follows main bodies of the dissertation, from Chapter 2 to 5. It ends with a few concluding remarks in Chapter6. The main contents of the dissertation are as follows:1). Ill-posedness is revealed in the inverse problem, whose reasons and countermeasure are discussed. The regularization method is proposed to improve the ill-posed problem. In addition, in order to transform infinite dimensions problem into finite dimension parameters, Legendre orthogonal polynomial is employed as base functions for Generalization Fourier Expansion. Fast dichotomy search and frequency domain ways are proposed for order determination. At last, projection method is used to establish the relationship between the continuous input function and limited output information. All of these provide basic theory for the research of load identification.2). Discussed in detail the relationship between relevant feature of multi-point random dynamic load and characteristic of power spectrum matrix, the conclusion can be obtained that the power spectrum has non-negative matrix properties. By spectral decomposition formula, the arbitrary correlated power spectrum matrix is decomposed into the complete-correlated power spectrum matrices, and then the calculation of structural dynamic response under random load will be achieved by calculation of structural dynamic response under deterministic force. The identification methods of arbitrary correlated random dynamic load can be obtained after the establishment the inverse model of forward problem. Then the chapter reveals the reasons that caused instability in solution, and tries to use Tikhonov regularization method to improve the accuracy of recognition results. Finally it explores the various factors on the recognition result.3).Based on orthogonal projection, pseudo-excitation method for one-dimensional distributed random loads is proposed: cross-power function of one-dimensional distributed random dynamic loads is expanded by two-dimensional Legendre orthogonal polynomials series, with limited parameters information indicating the distribution of infinite information. The calculation of structural dynamic response under distributed random load will be achieved by calculation of structural dynamic response under distributed deterministic force. The power spectrum of response is calculated by vector multiplication for each frequency. Thus fast and accurate algorithm is established for response calculation under one-dimensional distributed random dynamic loads. Compared with CQC and SRSS, the proposed method is more accurate and efficient.4). Linear relationship between response and excite is obtained in light of the inverse process of pseudo-excitation method for one-dimensional distributed random load. The identification of distributed random dynamic loads is realized by the identification of the orthogonal base function coefficients. Thus, general distributed random dynamic load identification theory is complete,and simple algorithm is also provided for typical models of distributed random dynamic load. Tikhonov regularization algorithm is applied to improving the accuracy of recognition results, with the help of regularization parameter set by L-curve method.5). Distribution area of random dynamic load will be extended to elastic thin plate, and pseudo-excitation method for two-dimensional distributed random loads is proposed: cross-power function of two-dimensional distributed random dynamic load is expanded by four-dimensional Legendre orthogonal polynomials series. The calculation of structural dynamic response under distributed random load will be achieved by calculation of structural dynamic response under distributed deterministic force. The power spectrum of response is calculated by vector multiplication for each frequency. Thus fast and accurate algorithm is established for response calculation under one-dimensional distributed random dynamic loads. The method is compared with CQC and SRSS to verify its precision and efficiency. 6). Identification of two-dimensional distributed random dynamic loads is carried out by the inverse process of pseudo-excitation method for two-dimensional distributed random dynamic loads. Typical models of distributed load are also reconstructed by simple algorithm. Tikhonov regularization algorithm is also applied to improving the accuracy of recognition results.7). Above-mentioned methods are checked by a lot of simulation examples, in a addition, experiments designed for multi-point random loads reconstruction and two-dimensional distributed random loads reconstruction further assess the feasibility of engineering applications.