含不确定参数的复合材料壁板热颤振分析

研究了含有不确定结构参数的壁板颤振问题,利用vonKarman大变形应变-位移关系、气动力活塞理论和准定常热应力理论建立了复合材料壁板颤振的气动弹性力学模型,考虑在壁板颤振分析模型中存在的不确定参数,将其用区间向量定量化,基于区间扩张理论和Taylor级数展开,并结合有限元计算方法,提出了区间分析的方法来估计含有不确定参数的壁板结构颤振临界风速的区间,以及发生极限环振动时振幅的变化区间。通过数值算例,将本文提出的壁板颤振的区间有限元模型与随机有限元模型进行了比较,显示了本文方法的有效性和可行性。这种方法的优点是只需要知道不确定参数的所在范围界限,为解决含有不确定参数的壁板颤振这类复杂的气动弹性动力学问题提供了一个途径。

Thermal Flutter Analysis of Composite Panel with Uncertain Parameters

The panel flutter with uncertain structural parameters is studied in this article. Based on von Karman's large deflection plate theory, piston theory aerodynamics and quasi-steady thermal stress theory, an aeroelastic model of a composite panel is established. The uncertainties in structural parameters are considered and described by interval numbers on the basis of a deterministic panel flutter analysis model. By virtue of interval extension and Taylor series expansion combined with the application of the finite element method, an interval analysis method is presented to estimate the intervals of flutter critical wind speed and amplitudes of limit cycle oscillations. The proposed interval finite element model and the stochastic finite element model for panel flutter analysis are compared by numerical examples, and the results show the efficiency and feasibility of the method presented. The advantage of this method is that only the intervals of uncertainties are required, and it provides a way to solve complex aeroelastic dynamic problems such as panel flutter with uncertain parameters.