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.     

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.     

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.     

压电复合材料悬臂板1∶3内共振的非线性动力学分析

本文以飞行器机翼为工程背景,将机翼简化为悬臂板模型,在应用经典板理论和Hamilton原理建立横向和面内激励共同作用下压电复合材料悬臂板的无量纲非线性偏微分方程的基础上,利用Galerkin方法将系统离散为两自由度的非线性常微分方程.然后考虑主参数共振-1∶3内共振,运用多尺度法将两自由度的系统控制方程进行摄动分析,推导出四维平均方程.基于四阶Runge-Kutta法,使用MATLAB软件研究了横向外激励幅值和压电参数项对压电复合材料悬臂板非线性动力学行为的影响.结果表明,系统存在周期和混沌运动,所得结论对实际工程具有指导意义.     

变流速输液管的周期和混沌振动

研究了参数激励和外激励联合作用下输流管道的非线性振动问题．只考虑管道变形的几何非线性因素,利用Hamilton原理得到单侧受简谐均布载荷作用下输液管的非线性动力学方程,对系统运动偏微分方程综合运用多尺度法和Galerkin离散方法,得到了主参数共振-1／2亚谐共振和1：2内共振情况下的平均方程．数值模拟结果表明参数激励和外激励联合作用下的悬臂输液管呈现周期运动、多倍周期运动和混沌运动的变化规律．     

环形天线结构的复杂动力学研究

部分改进高维系统的广义Melnikov方法研究含参非线性动力系统的混沌问题,并应用于研究环形天线结构的混沌运动等复杂非线性动力学行为.通过定义恰当的横截面,发展适用于研究五维含参非线性动力系统的Melnikov方法,获得系统发生Smale马蹄意义下混沌运动区域及判定定理.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环形天线结构的混沌运动,得到系统发生混沌运动的不稳定区域及相应的参数控制条件.探讨阻尼系数、参数激励对系统动力学行为的影响,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.     

受电压激励的复合材料悬臂板的分叉分析

以飞行器机翼作为工程背景,将机翼简化为悬臂板模型,研究了受横向电压激励、基础激励、面内激励联合作用下复合材料层合悬臂板的非线性动力学问题.首先建立其动力学模型,考虑冯-卡门大变形理论,利用Hamilton原理建立复合材料层合悬臂板的非线性动力学方程;选择符合边界条件的模态函数,利用Galerkin方法对系统进行四阶离散,得到四自由度非线性常微分方程;代入系统实际物理参数,应用MATLAB软件数值模拟得到系统振动幅值随电压激励变化的分叉图,由图可知,电压激励使系统从混沌运动变为倍周期运动,降低了系统振幅,保持系统的稳定.     

1:2内共振条件下蜂窝夹芯板的两倍周期运动研究

主要利用推广的四维次谐Melnikov方法研究一类面内载荷与横向载荷联合作用下四边简支矩形蜂窝夹芯板的周期运动.首先,通过引入周期变换和相应的Poincaré映射,获得一个四维次谐Melnikov向量函数,通过对该向量函数简单零点的研究,得到一类四维非线性非自治系统周期运动的存在性判定定理.然后,利用推广的四维次谐Melnikov方法研究了1∶2内共振情况下蜂窝夹芯板的周期运动,获得了系统存在两倍周期运动的参数域.最后,对系统进行数值模拟,验证了理论分析的正确性.     

基于Kelvin模型的粘弹性浅拱的动力稳定性

研究了外激励作用下非线性粘弹性浅拱的动力行为．通过达朗贝尔原理和欧拉一贝努利假定建立了浅拱的动力学控制方程,其中采用Kelvin模型来表示非线性粘弹性材料的本构关系,并利用Galerkin法将方程简化用于数值分析．分析了粘弹性材料参数、浅拱矢高、外激励幅值和频率对系统分岔和混沌等非线性动力学行为的影响,结果表明各种参数条件下系统的非线性动力特性十分复杂,周期运动、准周期运动和混沌运动窗口在一定条件下交替出现．     

压电纤维复合材料层合壳的非线性动力学研究

本文对横向激励作用下的1-3型压电纤维复合材料层合壳进行了非线性动力学分析,并研究了压电特性对结构振动响应的影响.首先建立了压电纤维复合材料层合壳的非线性动力学方程,并且在已知的几何结构和材料特性基础上考虑了电场属性.然后根据位移边界条件,选择合适的振型函数,通过Galerkin方法将运动控制方程转化成两自由度的非线性常微分方程.通过数值模拟方法分析了横向激励和压电系数对压电纤维复合材料层合壳非线性振动特性的影响.通过波形图、三维相图、庞加莱图和分叉图等来研究壳体不同类型的周期和混沌运动.结果表明,外激励作用下结构存在复杂的非线性振动响应,同时压电参数对层合壳结构振动响应具有很强的调节作用.     

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.     

复合边界条件下功能梯度板1:1内共振的周期与混沌运动

以两对边简支另两对边自由的功能梯度材料板为研究对象,首先建立了考虑材料物性参数与温度相关的、在热/机械载荷共同作用下的几何非线性动力学方程,采用渐进摄动法对系统在1:1内共振-主参数共振-1/2亚谐共振情况下的非线性动力学行为进行了摄动分析,得到系统的四自由度平均方程,并对平均方程进行数值计算,分析外激励对系统非线性动...     

多夹心层蜂窝板动力学特性分析与仿真

蜂窝夹层板广泛的应用在航空航天领域，蜂窝夹层板的动力学特性分析是一重要的课题。由于蜂窝板是一种结构型材料，无法直接给定其物理参数，因此该文首先研究了蜂窝板的三明治等效模型，应用该等效模型对蜂窝板夹芯进等效计算，得到了等效物理参数。利用这些参数建立了多夹心层蜂窝板的有限元模型，完成了不同算例在不同边界条件下的振动仿真，得到了各阶模态频率和振型的可视化仿真结果。将仿真结果与解析解对比说明，等效模型是合理的，且能很方便地处理多夹心层蜂窝板，可进一步推广至其他多夹心层蜂窝板结构的分析当中。     

Optimum design of honeycomb sandwich constructions with buckling constraints

Optimum design of honeycomb sandwich constructions with buckling constraints is treated in this paper. Four modes of instability for honeycomb sandwich structures are considered in buckling constraints, including overall buckling, core shear instability, face wrinkling, and monocell buckling. The face thicknesses, core depth, cell wall thickness, and diameter of an inscribed circle in a honeycomb cell are taken as design variables. Eight-nodal quadrilateral honeycomb sandwich isoparametric shell elements and hybrid approximation techniques in combination with the dual solution are used. Some comparisons are also made between the cases with and without buckling constraints. Numerical results are given for four examples.     

Complex modes based numerical analysis of viscoelastic sandwich plates vibrations

In this paper, a numerical method for linear and nonlinear vibrations analysis of viscoelastic sandwich beams and plates is developed with finite element based solution. This method couples the harmonic balance technique to complex mode Galerkin’s procedure. This results in a scalar nonlinear complex amplitude–frequency relationship involving numerical computation of three coefficients. A general formulation taking into account the frequency dependence of the viscoelastic behaviour allowing to intoduce any viscoelastic law is given. Complex eigenmodes are numerically computed in a general procedure and used as Galerkin’s basis. The free and steady-state vibrations analyses of viscoelastic sandwich beams and plates are investigated for constant and frequency dependent viscoelastic laws and for various boundary conditions. The equivalent frequencies and loss factors as well as forced harmonic response and phase curves are performed. The obtained results show the efficiency of the present approach to large amplitudes vibrations of viscoelastic sandwich structures with nonlinear frequency dependence.     

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.     

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.     

Process for design optimization of honeycomb core sandwich panels for blast load mitigation

A general process for optimization of a sandwich panel to minimize the effects of air blast loading is presented here. The panel geometry consists of two metal face plates with a crushable honeycomb or other type of core. Optimization is necessary as there is strong coupling between the several variables and the physics, which makes parametric studies relatively ineffective. Virtual testing is used to develop a homogenized model for the stress–strain curve of the honeycomb core, which can be readily applied to other types of cellular core. The homogenized model has been validated by comparison to existing results as well as to results from detailed finite element (FE) models. A design of experiments (DOE) based response surface optimization method in combination with LS-DYNA is used to minimize dynamic deflection or acceleration of the back face plate. Constraints on total mass and on plastic strain in the face plates are imposed. The mechanism of lowering the backface deflection is by increasing front face plate thickness which effectively distributes the blast load to a larger area of the core and avoids local concave deformation of the front face plate. Further, core depth is increased which increases panel stiffness. For acceleration minimization, results again produce a stiffer front face plate, but accompanied by a sufficiently soft core. The mechanism of lowering the backface acceleration is by absorbing energy with low transmitted stress. A clear cut comparison between monolithic metal plates and sandwich plates, for the same loading and failure criteria, is presented here.