薄壁圆锥壳畸变相似模型设计及几何区间确定方法

针对传统的相似模型设计方法、量纲分析法以及方程分析法在一些情况下使用的局限性，基于最小二乘法，通过过渡模型固有频率建立了薄壁圆锥壳的畸变相似关系式，并提出一种畸变模型适用区间确定的方法，基于模型与原型在固有特性相似(固有频率成比例映射关系，并且振型保持一致)时畸变模型尺寸适用区间的确定方法，利用多项式拟合，得到单一材料薄壁圆锥壳在不同阶次相似畸变模型几何结构适用区间的边界方程.最后通过试验验证，证明了推导畸变相似关系式的准确性，为薄壁圆锥壳结构试验模型动力学相似提供了理论依据.

Design of Distortion Similar Model for Thin-Walled Conical Shell and Method for Determining Geometric Interval

The distortion similarity relation of thin-walled conical shells was established by using the natural frequency of transition model based on least square method， aiming at the limitation of traditional similarity model design method， dimension analysis method and equation analysis method in some cases， a method for determining the applicable interval of distortion model was also proposed. The boundary equation of the applicable interval of geometric structure of a single material thin-walled conical shell with similar distortion model of different orders was obtained by polynomial fitting method， based on the method for determining the applicable interval of distortion model size when the model and prototype are similar in natural characteristics (natural frequencies are proportional mapping relationship， and mode shapes are consistent). The accuracy of derivation of distortion similarity relation is proved by experiment verification， which provides theoretical basis for dynamic similarity of thin-walled conical shell structure test model.