证据和随机混合不确定声固耦合系统的数值分析方法研究

发布时间：2018-03-17 16:15

本文选题：声固耦合系统　切入点：有限元法　出处：《湖南大学》2016年硕士论文　论文类型：学位论文

【摘要】：一直以来,国内外学者对声固耦合系统问题进行研究时,一般都是基于确定性分析方法。然而,实际工程中的声固耦合系统往往在部件材料属性、外部载荷和边界条件等方面都存在一定的不确定性。一般情况下,单一的不确定因素在数值上可能比较小,但是当多个不确定因素相互耦合时,就有可能导致声固耦合系统响应产生很大的偏差。为了研究各类不确定因素对声固耦合系统响应的影响,本文开展随机不确定、证据不确定和随机与证据混合不确定三类不确定声固耦合系统的分析研究。在随机、证据及其混合模型的基础上构建声固耦合系统的不确定数值分析模型,并研究相应的不确定数值分析算法,以更加深入地研究不确定性声固耦合系统问题。本文开展并完成的主要研究工作包括:(1)研究了随机摄动有限元法,以预测随机声固耦合系统响应结果的期望和方差。该方法首先构造随机声固耦合系统的随机FEM/FEM模型;然后进行随机声固耦合系统响应的随机摄动分析;最后求解得到随机声固耦合系统响应结果的期望和方差。用随机摄动有限元法对某壳结构声固耦合系统进行了数值分析,结果表明:随机摄动有限元法能有效预测随机声固耦合系统响应结果的期望和方差。(2)研究了证据理论有限元法,以预测证据不确定声固耦合系统响应期望和方差范围。该方法首先运用区间摄动分析法构造证据子区间不确定声固耦合模型,进而求得子区间对应系统响应的变化范围;然后,采用证据理论期望和方差求解方法得到证据不确定声固耦合系统响应期望和方差的变化范围。用证据理论有限元法对某壳结构声固耦合系统进行了数值分析,结果表明:证据理论有限元法能有效预测证据不确定声固耦合系统响应期望和方差范围。(3)研究了混合证据和随机有限元分析方法,以预测证据和随机混合不确定声固耦合系统响应期望和方差范围。该方法首先将混合摄动分析法应用到构造证据子区间与随机混合不确定声固耦合模型;然后,采用随机矩法计算子区间与随机混合系统近似响应的期望和方差;再根据系统响应期望和方差与子区间变量间的线性关系,采用顶点法计算系统响应期望和方差变化范围的上下界;最后,对每个由随机向量和联合焦元构成的子区间组成的混合不确定组合重复计算上述过程即得到证据与随机混合系统响应期望和方差的变化范围。用混合证据和随机有限元法对某壳结构声固耦合系统进行了数值分析,结果表明:混合证据和随机有限元法能有效预测证据不确定声固耦合系统响应期望和方差范围。
[Abstract]:For a long time, scholars at home and abroad have been studying the problem of acousto-solid coupling system, which is usually based on deterministic analysis method. However, in practical engineering, the acousto-solid coupling system is usually based on the material properties of components. There are some uncertainties in external loads and boundary conditions. In general, a single uncertainty may be relatively small numerically, but when multiple uncertainties are coupled with each other, In order to study the influence of all kinds of uncertain factors on the response of acousto-solid coupling system, random uncertainty is carried out in this paper. Analysis and Research on three kinds of uncertain Acousto-Structure Coupling Systems of evidence uncertainty and Stochastic and mixed uncertainty. On the basis of stochastic, evidential and mixed models, the uncertain numerical analysis model of acousto-solid coupling system is constructed. The corresponding uncertain numerical analysis algorithm is studied to study the problem of acousto-solid coupling system with uncertainty more deeply. The main research work done in this paper includes: 1) the stochastic perturbed finite element method is studied. In order to predict the expectation and variance of the response results of the stochastic acousto-solid coupling system, the stochastic FEM/FEM model of the stochastic acousto-solid coupling system is constructed firstly, and then the random perturbation analysis of the response of the stochastic acousto-solid coupling system is carried out. Finally, the expectation and variance of the response results of the stochastic acousto-solid coupling system are obtained. The numerical analysis of the acousto-solid coupling system of a shell structure is carried out by using the stochastic perturbation finite element method. The results show that the stochastic perturbation finite element method can effectively predict the expected and variance of the response results of stochastic acousto-solid coupling systems. In order to predict the expected and variance range of acousto-solid coupling system response with uncertain evidence, the method first constructs the acousto-solid coupling model with interval perturbation analysis method, and then obtains the variation range of the system response corresponding to the subinterval. The variation range of response expectation and variance of acousto-solid coupling system with uncertain evidence is obtained by using the method of expectation and variance of evidence theory. The finite element method of evidence theory is used to analyze the acousto-solid coupling system of a shell structure. The results show that the evidence theory finite element method can effectively predict the response expectation and variance range of acousto-solid coupling systems with uncertain evidence. Based on predictive evidence and random mixed uncertain acousto-solid coupling system response expectation and variance range, the mixed perturbation analysis method is first applied to construct the acousto-solid coupling model with evidence subinterval and random mixing uncertainty. The stochastic moment method is used to calculate the expectation and variance of approximate response of subinterval and stochastic mixed system, and then according to the linear relation between system expectation and variance and subinterval variable, The vertex method is used to calculate the upper and lower bounds of the variation range of system response expectation and variance. For each mixed uncertain combination consisting of a random vector and a joint focal element, the above process is calculated repeatedly to obtain the range of variation of the expected and variance of the evidence and the response of the stochastic mixed system. The mixed evidence and the random are used to calculate the variation range of the expected and variance of the response of the stochastic mixed system. The finite element method is used to analyze the acousto-solid coupling system of a shell structure. The results show that the mixed evidence and stochastic finite element method can effectively predict the expected response and variance range of the acousto-solid coupling system.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TB115

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