Research On Modal Analysis And Its Application Of Stochastic Parameter Structure

Developing modal analysis theory and technology of stochastic parameter structure is very important in evaluation of structure dynamic performance, structural dynamic design, fault diagnose and state monitoring, etc. In this thesis, research work on modal analysis of linear stochastic parameter structure is opened, the variation rules of structure vibrating modal parameters and dynamic force transfer caused by stochastic factor in reality structure are studied. The main results are listed as follows: 1. Using Monte-Carlo stochastic simulation method to study the variation rules of stochastic parameters structure modal parameters model. The conception of relative mean value deviation factor is first given. Comparing with mean parameters system, the variability of modal parameters of stochastic parameter system is quantitatively described. Relative mean value deviation factor and variation factor, from two different points of view, are used for analyzing the variation rules of modal parameter model quantitatively in stochastic structure vibration system. Either of the increase of mass or stiffness variant coefficient will cause the deviation increasing of the mean value, the deviation is between SDOF stochastic parameter system harmonic vibration frequency (natural frequency, damping natural frequency, resonance frequency) and harmonic vibration frequency of equalizing value parameter system. When the structural parameters (mass, stiffness, damp coefficient) have simultaneous random variation, as the variability of structural parameter increase(s δ=1%~30%), the high-order modal frequency mean value of MDOF stochastic parameter system is monotone increasing, the mean value of low-order modal frequency is monotone decreasing, modal intensity is decreasing, the mean value of every order modal damping ratio is monotone increasing. The variability of modes has higher sensitivity, and its variant regularity is more complex. However, in a word, the peak value of low-order mode is increasing and the peak value of high-order mode tends to be flat. 2. Correlation analysis between the stochastic parameter structure's modal frequency and stochastic structure parameters. The results indicate: cross-correlation coefficient changes as the variability of structure parameters increase, however, distributing pattern of cross correlation degree is invariant. Only these cross correlation coefficients tend to uniform. 3. The research about variant regularity of SDOF stochastic parameter structure's frequency response function. The randomness of mass and rigidity can considerably weaken the peak of frequency response function, increase half-power bandwidth; the randomness of damp coefficient can considerably increase frequency response function's peak, but this influence to frequency response function is smaller than the influence of uncertain mass and rigidity. The variation degree of real frequency and imaginary frequency characteristics caused by stochastic structure parameters is higher than of amplitude frequency and phase-frequency characteristics. This thesis uses relative mean value deviation function and variation function to describe the variant regularity of the characteristic curve of amplitude frequency, phase-frequency, real frequency and imaginary frequency. 4. Analysis to the variation rules of SDOF stochastic parameter system's dynamics response spectrum when excitation is random. Do the research about the variant regularity of dynamics response mean value, self-power density spectrum, cross-power density spectrum and root-mean-square value when excitation is random, while mass, rigidity, damp coefficient is stochastic variant according to Gaussian. Researches indicate: it is closely correlated between variation of vibration response characteristic measures of SDOF linear random system when random excitation and variation of frequency response function. So, the research to variant regularity of frequency response function is important content of the stochastic parameter structure modal analysis theory. In order to quantitatively describe the variant regularity between the reacting characteristic measures of mean parameter system and the reacting characteristic measure mean of stochastic parameter system, this text offers the definite formula of characteristic measure's relative mean value deviation factor (or function), as a result, the research to variant regularity becomes more complete and profound. 5. The stochastic parameter structural combined random vibration response analysis. The author studies mathematic description of stochastic parameter structure vibration, deduces the combined random vibration dynamics transmission's theoretical formula of stochastic parameter structure on the basis of pioneers'researches. This text presents response mean's amplified dynamics coefficient, response self-power spectrum density function's amplified multiple, response cross-power spectrum density function's amplified multiple, the concept of stochastic...