弹性空腔声振耦合试验相似动力学特性分析

针对典型弹性空腔声振耦合高速风洞试验问题，基于风洞试验相似原理，以典型弹性空腔为实例，采用量纲分析法建立了完全几何相似模型固有频率和频率响应的相似关系；结合结构有限元理论，通过引入完全几何相似模型作为过渡模型，建立了厚度畸变缩比模型固有频率和频率响应的相似关系；开展了缩比弹性空腔模型的固有频率及动力学响应的数值仿真。根据缩比模型的计算结果，利用已建立的相似关系对全尺寸模型的动力学响应进行预测，结果表明:预测响应曲线与实际计算结果曲线基本重合，验证了提出的缩比空腔模型固有频率及频响相似关系的可行性，为基于动力学相似的缩比弹性空腔风洞试验模型设计和声振耦合试验提供理论指导，且该相似关系的分析方法可推广应用于复杂外形薄壁结构的动力学相似关系建立中。 

Analysis of similar dynamic characteristics of vibro-acoustic experiment for elastic cavity

In allusion to the vibro-acoustic experiments of cavity in wind tunnel, taking typical elastic cavity as the research object, dimensional analysis was adopted to establish the similitude relations of structural natural frequencies and dynamics for complete geometric similarity model. Combining the structural finite element theory, the similitude relations of structural natural frequencies and dynamics for incomplete geometric similarity model were established by introducing the complete geometric similarity model as intermediate model. Numerical simulations of natural frequencies and dynamics of scale-down elastic cavity model were carried out. According to the numerical results of scale-down model, the dynamic response results of full-scale model were predicted by the proposed similitude relations. Results showed that the predicted dynamic response curves were in coincidence with the actual numerical results, which verified the feasibility of the proposed similitude relations and also provided a theoretic guidance for structural design and vibro-acoustic experiments of scaled down elastic cavity model with similar dynamics. The analysis method of the established similitude relations can be applied to complex thin-wall structures.