Research On Stochastic Vibration Analysis And General Reliability Of Fuzzy, Fuzzy Stochastic Structures

Structures with fuzzy parameters or the first kind of fuzzy-random parameters are taken as research objects in this paper. Firstly, a novel two factors method is presented. The analytical modeling of structural static finite element is constructed and solved, and the structural sensitivity analysis based on the general reliability index is given; the structural dynamic characteristic based on the two factors method is then derived. When the applied forces are fuzzy excitation, fuzzy-random excitation or random process (stationary random process or non-stationary random process) excitation respectively, the structural dynamic response, the structural general dynamic reliability under stationary stochastic excitation and the effects of the uncertain structural parameters on the structural analytical results et al are studied systemically. The main research works can be described as follows:1. Considering the fuzziness or fuzzy-randomness of structural physical parameters and geometric dimensions simultaneously, a novel Two Factors Method is presented. The analytical modeling of structural static finite element is constructed and solved; for fuzzy-random truss structures, the fuzzy numeric characteristic of the fuzzy-random static response is developed. Via an example, the rationality and validity of the theory and method given here are verified, and the theoretical basis for the further dynamicanalysis of such kind of fuzzy or fuzzy-random structures is offered.2. The structural sensitivity analysis based on general reliability index is preceded. The sensitivity of general reliability index for design variables are derived. And the semi-analytical expressions for sensitivity are presented. Thus the sensitivity analysis based on general reliability is transformed into regular sensitivity analysis. The sensitivity analysis based on general reliability can be simplified greatly and it is the basis of optimization of such kind of structures.3. Considering the fuzziness or fuzzy-randomness of structural physical parameters and geometric dimensions of truss system simultaneously, the analytical modeling of structural dynamic characteristic is presented and solved based on Two Factors Method,and the fuzzy numeric characteristic of dynamic characteristic of fuzzy random truss system is derived. The feasibility and validity of the method given are verified through an example.4. Considering the fuzziness or fuzzy-randomness of structural physics parameters, geometric dimension and loads simultaneously, the dynamic responses of the fuzzy or fuzzy random truss system under fuzzy or fuzzy random forces are developed, and the fuzzy numerical characteristics of the dynamic response of fuzzy random truss are obtained. The validity of the theory and method given here is inspected by examples.5. After dynamic characteristics of fuzzy random truss system and fuzzy random frame system are analyzed by Two Factors Method, from the time domain analysis of structural random vibration, fuzzy or fuzzy random correlation function matrices of displacement response of fuzzy or fuzzy random structures under the stationary or non-stationary random excitation are derived respectively; from the frequency domain analysis of stochastic vibration, the mean square value of the structural displacement and stress response of fuzzy or fuzzy random system under the stationary random excitation or non- stationary random excitation are then developed respectively, and fuzzy numeric characteristics of dynamic response of fuzzy random system are obtained with the random variable's functional moment method and the algebra synthesis method. The feasibility and validity of the method given are inspected by several examples.6. For structures with fuzzy or fuzzy-random physical parameters and geometric dimensions simultaneously, the general dynamic reliability under stationary stochastic excitation is discussed, which is the important theoretical basis of structural dynamic optimization. The effects of fuzziness or fuzzy-randomness of structural parameters on structural general dynamic reliability are examined, and some instructive conclusions are obtained.