基于混合率模型的功能梯度材料火箭壳体振动特性分析

Vibration Analysis of Functionally Graded Material Rocket Shells Based on Rue-of-Mixture Model

关键词:  功能梯度材料  混合率  各向异性  火箭壳体  振动分析

Key words:  Functionally graded material  Rue-of-mixture  Anisotropy  Rocket shells  Vibration analysis

摘要:

为了研究功能梯度材料（Functionally graded material，FGM）火箭壳体的振动特性，发展了一种基于混合率模型的FGM材料性能计算方法。首先，对FGM壳体的材料分布特征进行了分析，建立了统一的材料公式模型，可表征材料性能沿厚度方向变化规律不同的多种FGM材料模型。其次，建立了FGM壳体材料的几何分层模型，基于混合率法则推导得到了宏观等效的正交各向异性材料性能参数表达式，并讨论了分层数对预测结果的影响。然后，将该方法用于矩形平板、带孔圆板、圆柱壳体、锥形壳体和球形壳体的振动分析，计算结果与相关文献结果具有较好的一致性，最大误差不超过2.33%，表明该方法具有较高的精度。最后，将该方法成功用于FGM火箭壳体的振动特性分析，针对材料性能沿厚度方向的几种不同分布模式，计算了FGM火箭壳体的前10阶固有频率和振动模态。

Abstract:

In order to study the vibration characteristics of functionally graded material （FGM） rocket shells， a method was developed in this work for calculating the FGM material properties based on the rue-of-mixture model. First， the material distributions of the FGM shell are analyzed and studied， and a unified material formula model is established， which can characterize a variety of FGM material models with different material distributions along the thickness direction. Secondly， the layered model is established for the FGM shell， and the macroscropic effective orthotropic material parameter expression is derived based on the rue-of-mixture， where the influence of the layered number on the prediction results is discussed. Then， the method is applied to the vibration analysis of rectangular plate， circular holed plate， cylindrical shells， conical shells and spherical shells. The calculated results are in good agreement with related literatures， with the maximum relative error within 2.33%， proving the high accuracy of the proposed method in this paper. Finally， the method is successfully applied to the vibration analysis of FGM rocket shells， where the first ten natural frequencies and vibration modes are calculated for several different through-the-thickness material distributions.