Structural Dynamic Response Calculation Based On Responses Of Limited Test Freedom Degrees

Compared with the vibration test technology, the numerical calculation method has the advantages of quick sloving, low cost and being capable of calculating the responses of any position in the structure, and so on. The random excitations must be known if existing numerical calculation methods are applied to determine the structural dynamic responses under the random excitations, however, the random excitations are difficult to be measured directly in many practical situations recently. Moreover, the research on the random dynamic loading identification has rarely been seen in the literatures, which leads to the application of existing numerical calculation methods in many engineering being still limited. Therefore, it is expected in this dissertation that a numerical calculation method without determining the random excitations can also be applied to obtain the structural dynamic responses of all monitor positions, and calculation results can be in accordance with the test results. The specific work of this dissertation includes the following four parts:(1) Only first to obtain an accurate calculation model, calculation results can be in agreement with the test results. By combining the artificial fish swarm algorithm(AFSA) with crossover and Gauss mutation with the simulated annealing algorithm(SAA), a novel structural finite element model(FEM) updating method based on the hybrid artificial fish swarm algorithm(HAFSA) is presented, and a facile and convenient interface module is designed to deal with the difficulty that an external FEM updating program encounters when it is directly implanted to the Patran/Nastran software. An objective function is established by using the residuals between the measurement data vectors of the test model and the calculation value vectors of the FEM, and crossover and Gauss mutation operators are added to the original AFSA to increase the global optimization search velocity. The bulletin is refreshed by the optimization objective function value continuously, and SAA is applied to carry out local refined search to greatly improve the precision of the optimization solution. The optimization values of design variables are obtained after the algorithm end condition is satisfied. Fortran language is combined with Visual Basic language to compile the interface module. The Patran/Nastran software is transferred iteratively when the model updating program is run. Updating results of the GARTEUR aircraft model show that the FEM updating based on HAFSA is feasible and effective, and an accurate FEM can be obtained conveniently as well.(2) All monitor degrees of freedom of the test model are far fewer than the degrees of freedom of the FEM, and the amount of numerical calculation to solve the dynamic response can be greatly reduced by appling the condensed FEM. To the condensation of engineering structural FEM, the dynamic condensation method is an extremely efficient method, however, the calculation efficiency of many structural dynamic condensation methods need to be further enhanced. Combining the matrix power accelerated subspace iteration method with the shift technique, this dissertation presents a novel structural dynamic condensation method. Firstly, the structural initial FEM is condensed only once by carrying out the matrix power accelerated subspace iteration method, and the eigenvalues of the initial condensed FEM are calculated. Then, the shift place is determined by judging the convergence situation of low-order eigenvalues, and a new general eigen-equation with shift is built after a suited shift cost is chosen. Finally, the dynamic condensation matrix of the new general eigen-equation is calculated iteratively via the matrix power accelerated subspace iteration, and the accurate condensed FEM is obtained after the iteration convergence. The numerical examples show that the presented method is feasible and has the advantage of quicker convergence rate as well as high reduction accuracy.(3) Due to the extreme complexity of the random vibration problems, the stationary random vibration is applied most widely in engineering. Therefore, for the dynamic response problems of the linear time-invariant structure subjected to the stationary random excitation, combining the pseudo excitation method(PEM) with the matrix expansion technology, this dissertation presents a novel structural dynamic response calculation method to solve the structural dynamic response problem on the multi-point stationary random excitations. Without determining the specific values of the stationary random excitations, a stationary random vibration problem is transformed into one or several harmonic vibration problems by the spectral decomposition of the response power spectrum matrix of the limited test freedom degrees. One or several pseudo harmonic vibration equations are analyzed and the calculation model is condensed according to the scale of all monitor degrees of freedom of the test model. Based on the matrix expansion technology, all monitor degrees of freedom dynamic responses of the test model are obtained by the expansion of limited test degrees of freedom dynamic responses. The numerical examples show that calculation results agree well with the simulation test data, and the feasibility and the effectiveness of the presented calculation method are confirmed.(4) Finally, the presented methods are applied in the calculation of a satellite structure and a cable-stayed bridge, and the perfect results are obtained to further verify the applicability of the presented methods for the engineering complex structures.