粘弹性夹芯层合旋转圆板的气动弹性动力稳定性分析

基于哈密尔顿原理,考虑作用于圆板上的空气动力载荷以及粘弹性复模量本构模型,本文建立了含有粘弹性夹芯层的旋转圆板的空气动力学模型,并给出了相应的稳定性的控制方程及边界条件。运用Galerkin方法,文中数值求解并给出了夹芯层合旋转圆板的动力学基本特征,以及结构几何参数、材料参数对于其前、后行波振动频率、阻尼和动力稳定性的影响。结果表明：通过优化合理选取粘弹性夹芯层合旋转圆板的几何参数和材料参数,可提高旋转圆板的临界转速和颤振速度,从而增强其稳定性。     

The buckled states of annular sandwich plates

In this paper, the axisymmetric buckled states of an annular sandwich plate (Reissner- type sandwich plate) with the clamped inner edge which is subjected to a uniform radial compressive thrust at the clamped outer edge are studied. Firstly, the basic equation of the buckled problem is derived. Secondly, the critical loads for some parameters are obtained by using the shooting method. Finally, we discuss the existence of the buckled states in the vicinity of the critical loads and obtain the asymptotic expansions of the buckled states.     

Aeroelastic dynamics stability of rotating sandwich annular plate with viscoelastic core layer

A dynamic model for a rotating sandwich annular plate with a viscoelastic core layer is developed. All fundamental equations and boundary conditions are established based on Hamilton’s principle, and the rotation effect and viscoelastic properties of the sandwich structure are taken into account. The aerodynamics force acting on the plate is described by a rotating damping model, and the constitutive behavior of the viscoelastic core layer is formulated by the frequency-dependent complex modulus. The effects of geometrical and material parameters on frequencies and damping of forward and backward traveling waves and the dynamic stability for the rotating sandwich plate are numerically analyzed by means of Galerkin’s method. The results show that the critical and flutter speeds of the rotating plate can be increased at some certain parameters of the viscoelastic core layer.     

多孔金属夹层板在冲击载荷作用下的动态响应

借助两种有限元软件ABAQUS和LS_DYNA, 模拟和分析了两种厚度不同的泡沫铝合金夹层板(三明治板)、方孔蜂窝形夹层板和波纹形夹层板在冲击载荷下的动态响应. 4种夹层板的单位面积密度相同,冲击载荷分别用泡沫铝子弹与不锈钢子弹模拟. 讨论了泡沫金属夹层板和格构式夹层板在不同冲击载荷作用下的变形机制,重点在于对夹层板的吸能特性及板内各部分吸能变化规律的探讨.研究结果表明: 在泡沫子弹冲击下,夹层板主要是通过自身变形来消耗子弹动能,并转化为自身内能. 厚度为22\,mm的泡沫金属夹层板吸收能量最多,底面变形最小,是结构性能最优的夹层板;在刚性子弹高速冲击穿透过程中,格构式夹层板的吸能性能比单位面积密度相同的泡沫金属夹层板的吸能性能更好. 波纹形夹层板的能量吸收能力在4种板中最高.      

Numerical solution to the buckling problem for a sandwich plate under uniaxial compression

A thin rectangular sandwich plate with isotropic linear elastic layers is considered. The plate is in a plane-strain state under uniaxial compression. An exact statement of the buckling problem is given. Its approximate solution is found by the finite-difference method. The concept of base scheme is used to formulate discrete problems in explicit and compact form. As an example, the critical parameters of the plate are calculated using a computation optimization procedure. Its efficiency is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 98–105, September 2006.     

具有填充材料的金属格栅夹层板在高速冲击下动态响应的数值分析

利用大型非线性有限元程序ABAQUS和LS-DYNA,对具有填充材料的金属格栅结构的冲击问题进行数值模拟.研究了不同的填充材料(金属泡沫和陶瓷)分别填充到不同的格栅构型(波纹型、蜂窝型和加强六边形)夹层板后,各类夹层板受到金属泡沫子弹和不锈钢子弹冲击时变形与能量吸收特性,探讨了夹层板上下面层板、支撑格栅及填充材料等各部分的吸能比率.研究结果表明,泡沫填充夹层板在缓冲吸能方面具有优势,陶瓷填充夹层板则在抵抗冲击穿透方面更具有优势,不同构型的夹层板,性能略有不同.     

静载荷对夹层圆板超谐波共振的影响

研究静载荷作用下夹层圆板的超谐波共振问题.基于Hoff型夹层板理论,给出了静载荷作用下夹层圆板的非线性动力学方程.应用Galerkin法推导了静载荷作用下夹层圆板的轴对称非线性振动方程.运用多尺度法分别对系统的三次超谐波问题和二次超谐波问题进行了求解,并依据Lyapunov稳定性理论得到了系统稳态运动的稳定性判据.通过...     

轻质金属泡沫夹芯曲板的抗爆炸冲击响应研究

夹芯结构具有高比强度、高比刚度和优异的吸能能力,已经被广泛应用于工程结构用来抵御高强度的爆炸冲击载荷。本文采用有限元数值模拟方法研究了爆炸载荷作用下四边固支夹芯曲板的动力响应。比较了同等质量下夹芯曲板、夹芯平板、实体曲板和实体平板四种结构的抗爆炸冲击性能,讨论了不同曲率和非对称因子对结构动力响应的影响,得到了使得夹芯曲板抗爆炸性能最佳的非对称因子。研究结果表明：夹芯曲板的抗爆炸冲击性能优于等质量的夹芯平板、实体曲板和实体平板结构,增大夹芯曲板的曲率能够提高结构的抗爆炸冲击性能。     

泡沫铝子弹高速撞击下铝基复合泡沫夹层板的动态响应

应用一级轻气炮驱动泡沫铝弹丸高速撞击加载技术,对实心钢板以及前/后面板为Q235钢板、芯层分别为铝基复合泡沫和普通泡沫铝的夹层板结构,在脉冲载荷作用下的动态力学响应进行实验研究。结果表明:泡沫铝子弹高速撞击靶板可近似模拟爆炸载荷效果;铝基复合泡沫夹层板的变形分为芯层压缩和整体变形两个阶段;与其他靶板相比,铝基复合泡沫夹层板的抗冲击性能最优。基于实验研究,应用LS-DYNA非线性动力有限元软件,对泡沫铝夹层板的动态响应进行数值模拟。结果表明:泡沫铝子弹的长度和初始速度对子弹与夹层板之间的接触作用力影响显著,并且呈线性关系。泡沫芯层强度对等质量及等厚度夹层板的抗冲击性能均有显著影响,夹层板中心挠度对前、后面板的厚度匹配较为敏感,在临界范围内,若背板厚度大于面板厚度,可减小夹层板的最终挠度。夹层板面板宜采用刚度较低、延性好、拉伸破坏应变较大的金属材料。     

层级褶皱结构夹层板的等效弹性常数

针对二级层级褶皱结构夹层板,通过变形协调研究了其等效弹性常数。首先对一级层级褶皱结构进行正交各向异性等效,得到一级等效弹性常数;将二级层级褶皱结构看成是由正交各向异性材料组成的三角形桁架夹心,将二级层级褶皱结构等效为均匀连续正交各向异性板,依据夹层板面板与夹心变形协调特点得到夹层板整体等效弹性常数。结合结构几何参数对等效公式的误差进行了讨论,并对等效公式做出修正。通过与数值分析结果对比,表明本文提出的等效公式具有较高精度。     

A comprehensive analysis of functionally graded sandwich plates: Part 1—Deflection and stresses

A two-dimensional solution is presented for bending analysis of simply supported functionally graded ceramic–metal sandwich plates. The sandwich plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity and Poisson’s ratio of the faces are assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. Several kinds of sandwich plates are used taking into account the symmetry of the plate and the thickness of each layer. We derive field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. Numerical results of the sinusoidal, third-order, first-order and classical theories are presented to show the effect of material distribution on the deflections and stresses.     

Resonant effects of local loads on circular sandwich plates on an elastic foundation

The axisymmetric forced vibrations of a circular sandwich plate on an elastic foundation are studied. The plate is subjected to axisymmetric surface and mechanical loads with frequency equal to one of the natural frequencies of the plate. The foundation reaction is described by the Winkler model. To describe the kinematics of an asymmetric sandwich, the hypothesis of broken normal is used. The core is assumed to be light. The analytical solution of the problem is obtained and numerical results are analyzed     

黏弹夹芯板的有限元建模及实验研究

从有限元分析和数值模拟及实验验证的角度研究了黏弹夹芯板的频率依赖振动特性。夹芯板中间层为黏弹性材料,其刚度和阻尼的频率依赖性行为直接影响系统的模态频率和阻尼,并导致振动模式求解的复杂化。采用三阶七参数Biot模型描述黏弹性材料频率相关的黏弹性行为。开发了三层四节点28自由度的夹芯板单元,基于经典板理论和哈密顿原理建立了黏弹夹芯板的有限元动力学方程。通过引入辅助耗散坐标,将Biot模型和黏弹夹芯板的有限元动力学模型结合起来,并将其转化为常规二阶线性系统形式,极大简化了求解非线性振动特性的过程。对一边固定、另三边自由的黏弹夹芯板进行了前三阶固有频率和损耗因子的预测,并与实验结果对比。数值模拟结果和实验结果吻合良好,说明所提有限元方法是正确有效的。     

冲击波与破片对波纹杂交夹层板的联合毁伤数值研究

通过有限元软件LS-DYNA模拟了波纹杂交夹层板在冲击波与破片联合作用下的响应过程,研究了炸药当量、载荷类型和填充方式对波纹杂交夹层板变形与失效模式的影响,并与实体板、间隔板和波纹夹层板的抗联合毁伤性能进行了对比,讨论了波纹杂交夹层板的能量吸收特性。数值计算结果表明:与冲击波单独作用相比,破片群单独作用和冲击波与破片联合作用对结构造成的毁伤更为严重;当药量较小时,波纹夹层板和波纹杂交夹层板的抗联合毁伤性能优于实体板与间隔板,波纹杂交夹层板的抗联合毁伤性能从全填充、迎爆面填充到背爆面填充逐渐降低;当药量较大时,所有结构均产生破口失效;在能量耗散方面,冲击波单独作用时以波纹芯层吸能为主,破片群单独作用和冲击波与破片联合作用时以上面板吸能为主。     

Metal sandwich plates subject to intense air shocks

Recent results on fluid–structure interaction for plates subject to high intensity air shocks are employed to assess the performance of all-metal sandwich plates compared to monolithic solid plates of the same material and mass per area. For a planar shock wave striking the plate, the new results enable the structural analysis to be decoupled from an analysis of shock propagation in the air. The study complements prior work on the role of fluid–structure interaction in the design and assessment of sandwich plates subject to water shocks. Square honeycomb and folded plate core topologies are considered. Fluid–structure interaction enhances the performance of sandwich plates relative to solid plates under intense air shocks, but not as significantly as for water blasts. The paper investigates two methods for applying the loading to the sandwich plate—responses are contrasted for loads applied as a time-dependent pressure history versus imposition of an initial velocity.     

Optimal design of minimax deflection of an annular plate

The optimal design of minimax deflection of an annular plate is studied in this paper. The annular plate is subjected to an arbitrary axisymmetric loading. The problem can be posed as a standard nonlinear programming problem with equality constraints by means of the stepped reduction method. Some examples are also given to illustrate the method which has many advantages.Project Supported by the Science Fund of the National. Education Committee.     

One-dimensional response of sandwich plates to underwater shock loading

The one-dimensional shock response of sandwich plates is investigated for the case of identical face sheets separated by a compressible foam core. The dynamic response of the sandwich plates is analysed for front face impulsive loading, and the effect of strain hardening of the core material is determined. For realistic ratios of core mass to face sheet mass, it is found that the strain hardening capacity of the core has a negligible effect upon the average through-thickness compressive strain developed within the core. Consequently, it suffices to model the core as an ideally plastic-locking solid. The one-dimensional response of sandwich plates subjected to an underwater pressure pulse is investigated by both a lumped parameter model and a finite element (FE) model. Unlike the monolithic plate case, cavitation does not occur at the fluid-structure interface, and the sandwich plates remain loaded by fluid until the end of the core compression phase. The momentum transmitted to the sandwich plate increases with increasing core strength, suggesting that weak sandwich cores may enhance the underwater shock resistance of sandwich plates.     

网架结构拟夹层板法的有限元验证

用拟夹层板法和有限元法对网架结构进行分析,对三类屋面网架（正放四角锥网架、两向正交正放网架和正放抽空四角锥网架）进行了均布荷载、局部荷载（半跨均布荷载）作用下的静力分析以及固有振动分析,对三类竖向承重网架墙体进行了稳定性分析。通过与有限元法分析结果的对比,表明了拟夹层板法作为一种简化的计算方法,其精度是比较高的,绝大多数的误差都小于5％,是可以直接用于工程结构设计的一种有效方法。此外,拟夹层板法还可作为一种在宏观上检验有限元建模正确与否的实用方法。     

Thermoelastic bending of a sandwich ring plate on an elastic foundation

The thermomechanical bending of an elastic sandwich ring plate with light core on an elastic foundation is considered. To describe the kinematics of the plate that is asymmetric across the thickness, broken-normal hypotheses are accepted. The foundation reaction is described by Winkler's model. A system of equilibrium equations is derived and solved for displacements. Numerical results for a sandwich ring plate in a temperature field are presented Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 94–103, September 2008.     

Interior formulation of axisymmetric Levinson plate theory

In this study, we show that the axisymmetric Levinson plate theory is exclusively an interior theory and we provide a consistent variational formulation for it. First, we discuss an annular Levinson plate according to a vectorial formulation. The boundary layer of the plate is not modeled and, thus, the interior stresses acting as surface tractions do work on the lateral edges of the plate. This feature is confirmed energetically by the Clapeyron's theorem. The variational formulation is carried out for the annular Levinson plate by employing the principle of virtual displacements. As a novel contribution, the formulation includes the external virtual work done by the tractions based on the interior stresses on the inner and outer lateral edges of the Levinson plate. The obtained plate equations are consistent with the vectorially derived Levinson equations. Finally, we develop an exact plate finite element both by a force-based method and from the total potential energy of the Levinson plate.