悬臂式蜂窝夹层板的非线性动力学建模及分析

蜂窝夹层结构因其良好的力学特性,在众多工程领域具有非常广泛的应用.本文建立了悬臂边界条件下,蜂窝夹层板的动力学模型并研究其非线性动力学行为.选取文献中更加接近实体有限元解的等效弹性参数公式对蜂窝芯层进行等效简化,得到六角形蜂窝芯的等效弹性参数.基于Reddy高阶剪切变形理论,应用Hamilton原理建立悬臂式蜂窝夹层板在受到面内激励和横向激励联合作用下的偏微分运动方程.然后利用Galerkin方法得到两自由度非自治常微分形式运动方程.在此基础上,通过对悬臂式蜂窝夹层板进行数值模拟分析系统的非线性动力学.结果表明面内激励和横向激励对系统的动力学特性有着重要影响,在不同激励作用下系统会出现周期运动、概周期运动以及混沌运动等复杂的非线性动力学响应.     

受面内激励和横向外激励联合作用下蜂窝夹层板的双Hopf分叉

随着航空航天事业的发展,对各种材料性能的要求也越来越高.而蜂窝夹层板在结构和性能上具有许多优点,已在航空航天等领域应用广泛,并在一些重要结构中充当承力部件,但由于其特殊的蜂窝结构,相对于一般的板,在受力时会发生比较大的变形,所以用非线性理论研究蜂窝夹层板结构,并考察不同参数对非线性振动特性的影响,具有重要的理论和实际意义.如今,蜂窝夹层板的几何非线性问题已引起更多学者的关注.在一般均质理论的假设下,一些学者已经研究了各向同性蜂窝夹层板板的非线性动力学特性.本文研究了一类受面内激励和横向外激励联合作用下的四边简支蜂窝夹层板在主参数共振-1:2内共振时的双Hopf分叉问题.首先利用多尺度法得到系统的平均方程,然后结合分叉理论得到了系统的分叉响应方程,根据对分叉响应方程的分析,得到了六种不同的分叉响应曲线并给出了系统产生双Hopf分叉的条件.利用数值方法得到系统在参数平面的分叉集,通过对不同分叉区域的分析发现,随着参数的变化系统平衡点会分叉为两类周期解,随后周期解会通过广义静态分叉为准周期解,或者通过广义Hopf分叉为3D环面.     

带飞行因子的粒子群算法的铝蜂窝夹层板模型修正

蜂窝板结构具有较高的比强度、比刚度和良好的隔热隔振、耐冲击等优点,在航空航天领域得到了广泛应用。根据等效板理论将蜂窝夹层板等效为壳单元,以试验测得的前五阶模态频率为基础,用带飞行因子的粒子群算法对其材料等效密度和刚度参数进行模型修正,修正后模型计算频率与试验值误差较原误差有了明显减小,与标准粒子群算法相比,带飞行因子粒子群算法修正后的模型能更好地逼近原结构,模型质量有了改善。证实了带飞行因子粒子群算法在模型修正过程中的可行性和有效性。     

蜂窝结构等效电磁模型的比较与改进

蜂窝结构是吸波材料中广泛使用的一种结构,但其复杂的几何结构给其电磁特性分析与设计带来了一定的困难.采用强扰动理论和变分法的两种等效模型与实验结果进行对比,分析了两种模型中横向等效电磁参数的对称性与实验结果中的非对称性方面存在的显著差异,并通过引入代表蜂窝结构横向非对称性参数的方法对等效电磁模型进行了改进.数值仿真表明,在使用等效电磁模型来描述蜂窝结构时,变分模型要优于强扰动模型,而改进模型不仅使得两种等效电磁模型都能够反映出蜂窝结构横向电磁参数的非对称性,而且能够在一定程度上提高等效电磁模型的准确性.     

基于神经网络的蜂窝夹芯等效弹性参数的预测

针对Gibson公式计算蜂窝夹芯面内等效弹性参数的不足,通过考虑蜂窝夹芯宏观尺度对等效弹性参数的影响,利用贝叶斯正则化神经网络,并结合正交试验和有限元方法,建立了4个主要影响因素与蜂窝夹芯等效弹性参数之间非线性映射关系的神经网络模型,采用BP神经网络成功实现了对蜂窝夹芯等效弹性参数的预测.对于无限宽度蜂窝夹芯,仿真结果与Gibson公式计算结果一致,而对于有限宽度蜂窝夹芯,通过与铝质蜂窝夹芯压缩实验结果进行比较,采用神经网络方法得到的结果与实测结果吻合更好,证实了该方法的有效性和准确性.     

格栅夹层板抑振性能研究

为了有效降低铺板与圆柱壳体耦合结构中因铺板振动而引起的壳体振动,提出了以格栅夹层板作为一种铺板结构.以格栅夹层板安装于带有端板的圆柱壳体上作为研究模型,采用有限元软件对格栅夹层板的抑振性能展开了仿真分析,讨论了格栅结构参数对其抑振效果的影响,并实验验证了格栅夹层板的抑振效果.仿真和实验结果一致表明：格栅夹层板能有效降低圆柱壳体的振动响应,尤其是在中高频段抑振效果显著；格栅的结构参数对抑振效果影响规律比较复杂,格栅夹层的上层面板采用阻尼较大的材料利于提高其抑振效果.     

粘弹性夹层圆板自由振动的理论解

研究了粘弹性夹层圆板的自由振动特性.基于经典弹性薄板理论和Kelvin-Voigt粘弹性本构方程,建立了粘弹性夹层圆板振动控制方程.采用分离变量法导出了粘弹性夹层圆板的自然频率及振型解析表达式,计算了固支和简支粘弹性夹层圆板的自然频率,并与有限元计算结果进行比较;讨论了粘弹性夹层圆板的夹心层比率对自然频率及衰减系数的影响.研究表明：（1）随着夹心层厚度的增大,系统频率先增大后减小,高阶时该趋势表现更为明显;（2）随着夹心层厚度的增大,衰减系数一直增大,高阶时该趋势表现更为明显.     

折叠式夹层结构压皱性能数值仿真

为研究网格尺寸、加载速率及仿真试件的单元数和单元长度等对夹层板压皱性能的影响,用Abaqus对U-I形折叠式夹层板的压皱性能进行数值仿真,提出精度高、效率高的数值仿真模型化技术,分析不同变形模式和夹层结构尺寸对压皱性能的影响.结果表明:变形模式是决定夹层板压皱性能的关键因素;不同的结构参数组合会形成不同的变形模式,进而影响结构的压皱载荷和吸能特性;存在较优的夹芯壁厚、高度、间距和夹角的尺寸组合使夹层结构的吸能效率较优.     

负泊松比蜂窝夹层板的多周期运动研究

发展高维Melnikov方法研究含参非线性动力系统的多周期解分岔问题,并应用于研究负泊松比蜂窝夹层板的多周期运动等复杂非线性动力学行为.通过建立曲线坐标与Poincaré映射,发展适用于四维含参非线性动力系统的Melnikov函数,获得系统多周期解的存在性及个数判定定理.将所得理论结果应用于研究面内激励与横向激励共同作用下负泊松比蜂窝夹层板的多周期运动,获得系统周期轨道的存在性、个数及相应的参数控制条件.探讨横向激励系数对系统动力学行为的影响,得到在一定参数条件下,系统最多存在4个周期轨道,并利用数值模拟方法给出其相图构型,验证理论结果的正确性.     

基于 MCM 噪声参数测量不确定度评定的方法研究磁

开展了基于蒙特卡洛法（MCM ）的噪声参数测量不确定度评定工作,以等效噪声参数方程作为不确定度评定的测量模型,利用从测量系统获得的物理量求解函数方程,得到反映等效噪声参数分布情况的数据,并从等效噪声参数导出噪声参数及其概率分布,最后得到噪声参数测量的不确定度。该方法有效地结合了数学随机仿真、物理测量边界判据,实现了噪声参数测量结果的不确定度评定,该方法符合国际标准,可应用的测量系统种类多,普适性高。最后通过实验数据验证,证明了评定方法的有效性,不确定度评定数据的真实性和可靠性。     

高速列车浮式地板振动响应有限元分析

针对采用试验方法开发高速列车浮式地板耗时耗力,且试验规模小,不能反映整车的振动效果的问题,基于有限元法进行高速列车振动响应分析.对三明治夹芯理论、蜂窝板理论和等效板理论进行比较,确定采用等效板理论数值模拟某浮式地板中的蜂窝板;利用橡胶材料的超弹性理论拟合橡胶材料参数;建立完整模型模拟实际工况下浮式地板的振动响应,得到浮式地板的隔振效果.结果表明此浮式地板的隔振效果约为90%,满足设计要求.     

An equivalent layer sandwich panel model

An equivalent layer method for modeling sandwich panels with thin laminated composite facings and honeycomb cores is presented. It avoids the need for separate face sheet and core representations. The equivalent layer is given Mindlin plate behavior and it reproduces the face sheet midsurface strains and displacements, while matching the strain energy and work of external loads. The equivalent layer also matches the eight resultants of stress in the sandwich panel. This article starts with a derivation of the sandwich panel strain energy and the inherent bending, stretching, and transverse shearing stiffnesses. It is then shown that the available equivalent layer stiffness parameters can be used for exact matching if the sandwich has a special neutral surface. Therefore, the equivalent layer can be used for linear or geometrically nonlinear analyses for in-plane and out-of-plane loads. Examples are given illustrating two general types of sandwich panels for which exact equivalence is possible. Included are equivalent layer linear response calculations using finite element computer code ADINA.     

Optimal design of sandwich and laminated composite plates based on the planning of experiments

Optimal design problems of sandwich plates with soft core and laminated composite face layers, and multilayered composite plates are investigated. The optimal design problems are solved by using the method of the planning of experiments. The optimization procedure is divided into the following stages: choice of control parameters and establishment of the domain of search, elaboration of plans of experiment for the chosen number of reference points, execution of the experiment, determination of simple mathematical models from the experimental data, design of the structure on the basis of the mathematical models discovered, and finally verification experiments at the point of the optimal solution. Vibration and damping analysis is performed by using a sandwich plate finite elements based on a broken line model. Damping properties of the core and face layers of the plate are taken into account in the optimal design. Modal loss factors are computed using the method of complex eigenvalues or the energy method. Frequencies and modal loss factors of the plate are constraints in the optimal design problem. There are also constraints on geometrical parameters and the bending stiffness of the plate. The mass of the plate is the objective function. Design parameters are the thickness of the plate layers. In the points of experiments computer simulation using FEM is carried out. Using this information, simple mathematical models for frequencies and modal loss factors for the plate are determined. These simple mathematical functions are used as constraints in the nonlinear programming problem, which is solved by random search and the penalty function method. Numerical examples of the optimal design of clamped sandwich and simply supported laminated composite plates are presented. A significant improvement of damping properties of a sandwich plate is observed in comparison with a simple plate of equal natural frequencies.     

Finite element model updating of honeycomb sandwich plates using a response surface model and global optimization technique

Honeycomb sandwich plates are used widely in the aerospace industry. Building accurate finite element models of honeycomb sandwich plates is necessary for analyzing and optimizing the microvibration that occurs in spacecraft. This study investigated two types of finite element dynamic models of honeycomb plates: a sandwich shell model and a shell-volume-shell model. Two response surface model-based optimization methods and a particle swarm optimization method were compared for updating the finite element models. Finally, we validated the accuracy of the two optimized honeycomb sandwich plate finite element dynamic models by comparing the results obtained by the frequency response functions with experimental data.     

基于等效模型的冷板热仿真

为解决冷板翅片在ICEPAK热设计仿真中网格数目多的问题,提出根据冷板热特性规律曲线,在ICEPAK中寻找简单模型代替冷板进行热分析的冷板等效模型方法.仿真计算结果表明：当等效模型输入通过冷板实体模型仿真计算得出热阻和流阻特性曲线后,计算得出的表面温度与冷板实体模型最为相近,误差在合理的范围内,计算时间也减少.该方法可节省计算资源,具有一定的实用性.     

Axisymmetric bending of circular and annular sandwich plates with nonlinear elastic core material

This paper compares the analytical model of the axisymmetric bending of a circular sandwich plate with the finite element method (FEM) based numerical model. The differential equations of the bending of circular symmetrical sandwich plates with isotropic face sheets and a nonlinear elastic core material are obtained. The perturbation method of a small parameter is used to represent the nonlinear differential equations as a sequence of linear equations specifying each other. The linear differential equations are solved by reducing them to the Bessel equation. The results of the calculations with the use of the analytical and FEM models are compared with the results obtained by other authors by the example of the following problems: (1) axisymmetric transverse bending of a circular sandwich plate; (2) axisymmetric transverse bending of an annular sandwich plate. The effect of the nonlinear elasticity of the core material on the strained state of the sandwich plate is described.