【作者】 苏荣华；

【导师】 梁冰；

【作者基本信息】 辽宁工程技术大学 ， 工程力学， 2005， 博士

【摘要】 发展随机参数结构模态分析理论和技术,对结构动态性能评价、结构动态设计、故障诊断及状态监测等有着十分重要的意义。本文针对线性随机参数结构的模态分析开展工作,研究实际结构中随机因素引起的结构振动模态参数及其动力传递的变异规律。主要工作如下: 1.用Monte-Carlo 随机模拟方法研究随机参数结构模态参数模型的变异规律。首次提出相对均差系数概念,定量描述了随机参数系统模态参数均值相对均值参数系统模态参数的变异性。本文采用相对均差系数与变异系数两个无量纲量,从两个不同的角度较为全面研究了随机参数结构模态参数模型的变异规律。无论是质量还是刚度变异系数的增大,都会引起单自由度随机参数系统的谐振频率(固有频率、阻尼固有频率、位移谐振频率)均值相对均值参数系统的谐振频率偏离的增加。结构参数(质量、刚度、阻尼系数)同时存在随机变异时,随着结构参数变异性增大(δ=1%～30%),多自由度随机参数系统的高阶模态频率均值单调增大,低阶模态频率均值单调减小,模态密集度降低;各阶模态阻尼比均值都单调增大;模态振型变异比较敏感,变异规律较为复杂,但是总的说来,低阶模态的峰值增大,高阶模态的峰值趋于平缓。2.随机参数结构模态频率与随机结构参数的相关分析。结果表明:互相关系数随着结构参数的变异性的增大发生变化,但相关程度分布格局不发生变化,只是对各结构参数的相关程度趋于均匀化。3.对单自由度随机参数系统的频率响应函数(包括幅频特性、相频特性、实频特性、相频特性)的变异规律的研究。质量和刚度的随机会削弱频响函数的峰值,增加半功率带宽;阻尼系数的随机会引起频响函数峰值的增大,但对频响函数的影响远小于随机质量和刚度的影响。实频与虚频特性对随机结构参数变异的敏感度高于幅频与相频特性。文中采用相对均差函数和变异函数定量描述当质量、刚度、阻尼系数按正态分布和均匀分布随机变异时系统的幅频特性、相频特性、实频特性、相频特性曲线的变异规律。4.对单自由度随机参数系统在随机激励下的动力响应谱的变异规律分析。研究质量、刚度、阻尼系数按正态分布随机变异时随机系统在随机激励下动力响更多还原

【Abstract】 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更多还原