| With the development of modern complicated machine and engineering structures, an even higher demand is posed to the optimal design. That is the dynamic optimal design which concerns comprehensively influencing factors about forced vibration, unacceptable frequency band, stiffness, intensity etc., based on the analytical model of FEM, to satisfy the needs of practical engineering. The crux of the matter at present is to study a new and utility dynamic optimal design method, which strives to reduce reanalysis and is easy for engineers to master and use and convenient for manmachine interaction. This is the most urgent task for the problems of practical engineering.There are two primary problems in dynamic optimal design: The unacceptable frequency bands(eigenvalue problems) and dynamic response(forced vibration). These two problems can be solved by 慸irect solution?method or be solved as inverse problems. The methods most in use to the solution of the problem with unacceptable frequency bands: one is a mathematical programming or optimum criterion method; the other is structure matrix perturbation. The former needs more structure reanalysis and more computational time, the later may reduce reanalysis to some extend, but the small-perturbed parameter s is hard to set. The problem with constraints of dynamic response amplitude hasn抰 been studied widely, because it is more complicated and more difficulty.The question studied in the dissertation is supported by National Natural Science Fund(N259675041): Theory and Method of Visual Inverse Perturbation Method. The purpose of the dissertation is to study and advance a new effective and practical dynamic optimal design method梚nverse perturbation method based on the analytical model of FEM. The work to solve the problems mentioned above by inverse perturbation method includes 3 aspects as follows:1 .The inverse perturbation method to the solution for the inverse problem of general eigenvalue: The problems with the constraints of unacceptable frequency bands are attributed to the solution of the inverse problem of general eignenvalue.Taking advantage of the theories of the inverse problem of general eigenvalue and the decomposition of finite element matrices, the explicit expressions of eigenvalue 2 and perturbed parameter e (correspondence with design variables) and the computation equations of ~ are derived. The s 憇 value is determined by the difference of the increment of 2, so in this way reanalysis can be avoided or reduced. The characteristic of the inverse problem of general eignenvalue is multi-value and indetermination. By solving this problem several methods to determine the value of the perturbed parameter e are described in the dissertation, such as sensitivity ratio analytical method based on average of probability.2.The inverse perturbation method to the solution for the inverse problem of dynamic response amplitude: According to the solution of inverse thought and the decomposition method of finite element stiffness and mass matrices, the explicit expressions of dynamic response amplitude and perturbed parameter s are also derived. The inverse perturbation method for the problem of dynamic response amplitude can be applied both for inverse and optimal problem of dynamic response amplitude.3.The application of inverse perturbation method for dynamic optimum design and its software: The optimum method with constraints of fractional optimum design and man-machine synergy is introduced in the dissertation. The software of the inverse perturbation method is programmed in MATLAB. It has been successfully applied to solve the problems of truss structure system, axial vibration system, rotor system and plane beam system etc.Illustrative examples demonstrate that the method is characterized in reducing reanalysis significantly, bears the merits in computing speed and precision. The inverse perturbation method can be as an approach for dynamic optimum design. Though illustrated with beam element system, in accordance with t...
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