含空腔点阵增强夹芯结构的固有振动分析方法

Analysis on natural vibration of lattice reinforced sandwich structure with cavities

[目的]为研究芯层含多种组分的含空腔点阵增强夹芯结构的固有振动特性,探讨此夹芯结构的固有振动分析方法,[方法]首先,通过体积平均,将圆台形空腔近似视为圆柱形空腔来处理,采用多层次均匀化的思路,将含增强柱和空腔的复杂芯层等效为正交各向异性材料,并利用Mori-Tanaka方法进行2次单相夹杂处理,获取芯层的等效弹性模量。然后,基于一阶剪切变形理论建立运动学方程,进一步利用芯层等效弹性模量的计算值,采用双三角级数求解四边简支含空腔点阵增强夹芯结构的固有频率。最后,在此基础上,分别探讨芯材面板模量比、点阵增强柱体积比和空腔体积比对含空腔点阵增强夹芯结构固有频率的影响规律。[结果]与有限元计算结果的对比显示,固有频率的相对误差不超过3%,验证了该方法的正确性。[结论]所提方法可快速、准确地计算含空腔点阵增强夹芯结构的中、低频固有频率,且数理模型清晰,公式简单,易于对其规律进行研究。

[Objectives]In order to study the natural vibration characteristics of the lattice reinforced sandwich structure with cavities,whose core layer contains multiple components,an analysis method for the natural vibration of the sandwich structure is discussed here.[Methods]Firstly,frustum cone-like cavities are approximated as cylinder-like ones in the principle of volume average.the multi-level homogenization is adopted,the complex core layer of the sandwich structure is taken as orthotropic material,and the single-phase inclusions are performed twice by using Mori-Tanaka method to obtain the equivalent elastic modulus of the core layer.Then the equation of motion is established based on first-order shear deformation theory,and then combined with the resultant equivalent elastic modulus of the core layer so as to figure out the natural frequency of the four-sided simply supported lattice reinforced sandwich structure with cavities by using double Fourier series.On this basis,the influences of core panel modulus ratio,lattice-enhanced cylinder volume ratio and cavity volume ratio on the natural frequency of the lattice reinforced sandwich structure with cavities are discussed.[Results]By comparing with the finite element calculation results,the relative error of the natural frequency is less than 3%,and the correctness of this method is verified.[Conclusions]The method discussed in this paper can calculate the natural vibration characteristics at medium and low frequencies of the lattice reinforced sandwich structure with cavities accurately and quickly by using clear mathematical models and simple formulas,which helps to study the law of the natural vibration characteristics easily.