薄壁构件试验模型的动力学相似设计方法

针对由薄壁构件相似模型试验结果预测原型动力学特性的问题,建立了统一的数学模型,并基于方程分析法推导了动力学相似关系.通过对薄壳单元进行受力分析,推导得到薄壁构件的微分方程,并通过微分方程得到完全几何相似模型可准确预测原型动力学特性的相似关系.在建立薄壁构件结构参数对固有频率的敏感性与相似因子指数的比值关系基础上,提出薄壁构件不完全几何相似模型与原型的动力学相似关系(即畸变相似关系)的确定方法.最后给出基于敏感性分析的薄壁构件精确畸变相似关系设计流程,为薄壁构件相似试验模型的设计及动力学特性的预测提供参考.

Dynamic similitude design method of experimental models for thin walled structures

Aiming at the problem that experimental results of elastic thin walled structures similitude models predict dynamic characteristics of the prototype the unified mathematical model was established and dynamic scaling laws was proposed based on the equation analysis method. The unified governing equation of elastic thin walled structures was firstly obtained by the stress analysis of a shell element and the scaling law was deduced between the geometrically complete model and the prototype based on the unified governing equation. On the basis of establishing the ratio relationship between indexes of scaling factors and sensitivity results of structural parameters for the natural frequency and the method of determining the dynamic scaling law distorted scaling law was proposed between the geometrically partial similitude models and the prototype. Finally the design procedure of determining accurate distorted scaling laws was given out based on the sensitivity analysis which provided the design method of similitude models and the prediction of dynamic characteristics for elastic thin walled structures.