四边简支条件下正交各向异性蜂窝夹层板的固有特性分析

以四边简支正交各向异性矩形蜂窝夹层板为研究对象,应用Reissner-Mindlin夹层板剪切理论,在考虑横向剪切变形的基础上,给出了一种将夹层板弯曲控制方程组化为仅含一个位移函数的单一方程的方法,从而获得了四边简支条件下矩形蜂窝夹层板弯曲振动固有频率的精确解,理论结果与数值结果和实验结果取得很好的一致,验证了本文方法的合理性;在此基础上研究了面板、芯层的各项结构和材料设计参数对夹层板其固有频率的影响,并对各设计参数对夹层板固有频率的调控机理进行了分析。研究结果对蜂窝夹层板的结构设计和工程应用具有指导意义。     

钢板夹泡沫铝组合板抗爆性能研究

鉴于泡沫铝材料优异的吸能特性和夹层结构在强度、刚度上的优势,提出了分层结构为钢板-泡沫铝芯层-钢板的抗爆组合板。对厚度为10 cm、7 cm和5 cm的组合板进行了5组不同装药量的爆炸试验,考察了各板在不同装药量爆炸条件下的变形及破坏情况,并对变形破坏过程进行了理论分析。研究表明:组合板承受爆炸冲击荷载时,通过局部压缩变形和整体弯曲变形吸收能量。钢板相同时,适当增大泡沫铝芯层厚度,增强面板与芯层间连接,可提高该组合板的抗爆性能,防止组合板发生剥离,减小其承受爆炸冲击荷载时产生的变形。     

An analytical and experimental comparison of orthotropic sandwich panels using the Hydromat Test System

A new two-dimensional test system, called the Hydromat Test System, simulates the hydrostatic and hydrodynamic loading conditions which are often present in actual sandwich structures, such as marine hulls. The test fixture uses a square 24 inch×24 inch panel sample which is simply supported all around and has a distributed load provided by a water-filled bladder.

In this study, the Hydromat Test System has been used to obtain data on sandwich panels with orthotropic face sheets and isotropic cores. This data has been compared to analytical expressions for the deflection and the in-plane strains based on small deflection sandwich panel theory. The engineering constants needed for the analytical solution were obtained from characterization tests of the face sheet materials. Core shear properties were obtained experimentally using two different ASTM standards. Four panels, with two different core materials and two different face sheets, were tested. Face sheet properties varied from slightly orthotropic (plane weave) to highly orthotropic (unidirectional), with an axial to transverse tensile moduli ratio of 1.2 and 3.9, respectively. The cores were closed cell foams with both a low and a high shear stiffness.

The analytically obtained center panel deflection varied from 1 to 10% of that obtained by experiment. Most of the analytical tensile strains were less than 10% different from the measured ones. Both experimental deflection and strain data are in excellent agreement with the small deflection theory. It was concluded that the Hydromat Test System provides predictable and repeatable boundary conditions and loading mechanism and is a suitable method for testing soft cored, highly orthotropic sandwich panels.     

复合材料夹芯板低速冲击后弯曲及横向静压特性

对低速冲击后的复合材料Nomex 蜂窝夹芯板进行了纯弯曲和准静态横向压缩实验, 用X 光技术、热揭层技术和外观检测等对板内的损伤进行测量, 分析了被冲击面在受压情况下蜂窝夹芯板的弯曲破坏特点, 对比了横向静压与低速冲击所造成的板内损伤, 讨论了不同横向压缩速度时接触力P-压入位移$h 的变化规律和损伤情况。结果表明: 低速冲击可使蜂窝夹芯板的弯曲强度大幅度降低; Nomex 蜂窝夹芯板对低速冲击不敏感。      

考虑芯层横向变形的粘弹性复合材料夹层板结构的声振特性分析

夹层板结构具有很高的比强度和比刚度。若芯层采用粘弹性阻尼材料，夹层板结构还具有良好的隔振和隔声特性，因此在工程结构中得到广泛应用。以往的夹层板理论大多忽略了芯层的横向正应变和横向正应力，在分析芯层较厚的夹层板或者夹层结构的高频振动问题时由于不能体现芯层的横向压缩变形，往往显得不够合理。针对这一不足，构造了一个复合材料夹层板单元：夹层板的上下面板采用基于一阶剪切变形理论的Mindlin假定以及层合板理论进行分析；采用文献[6，7]中提出的Timoshenko层合厚梁理论构造了单元每边的转角和剪应变场，消除了Mindlin板单元当板厚变小时的剪切锁死问题；假定芯层的位移沿厚度方向线性变化，并用上下面板的自由度表示，最终形成以上下面板自由度表示的系统总的运动方程。该单元不仅考虑了芯层的横向剪切变形，还考虑了芯层的横向压缩变形。数值计算结果表明：无论对于静力问题、动力问题还是声辐射等问题，考虑芯层的横向压缩变形是合理的，也是有必要的。     

Fundamental frequency and design of the CFCF composite sandwich plate

The design efficiency of sandwich panels is often associated with the value of fundamental frequency. This paper investigates the free vibrations of rectangular sandwich plates having two adjacent edges fully clamped and the remaining two edges free (CFCF). The vibration analysis is performed by applying Hamilton’s principle in conjunction with the first-order shear deformation theory. The analytical solution determining the fundamental frequency of the plate is obtained using the generalised Galerkin method and verified by comparison with the results of finite element modal analysis. The approach developed in the paper and equations obtained are applied to the design of sandwich plates having composite facings and orthotropic core. Design charts representing the effects of the thickness of the facings and core on the mass of composite sandwich panel for a given value of the fundamental frequency are obtained.     

轴向运动软夹层梁横向振动分析

针对传统夹层梁沿厚度方向不可压缩缺点,以上下约束层与夹心层中面横向位移为独立变量,提出全新的夹层梁理论。将夹层内任意点横向位移假设沿厚度方向变化的二次待定多项式,利用界面位移协调条件,获得以夹心层中面、上下约束层中面横向位移表示的夹心层横向位移模式,由此获得厚度方向正应变及相应剪应变。基于Hamilton原理,建立轴向运动软夹层梁横向振动控制方程组,用Galerkin法求解控制方程。研究表明,软夹层梁一阶模态为上下约束层与夹层一起作横向运动,两层之间无相对变形,与传统夹层梁理论一致;软夹层梁二阶模态为上下约束层向两相反方向运动,软夹层中面相对上下约束层不动,夹层处于上下拉伸或压缩状态;软夹层梁三阶模态为上下约束层向同一方向运动,夹心层中面向相反方向运动,夹心层上下处于不同变形状态（拉或压）。通过对振型、模态函数、自由振动响应、轴向运动速度对频率影响等因素分析表明,传统夹层梁模型为夹层梁模型的特殊形式。     

Dynamic response of clamped sandwich beam with aluminium alloy foam core subjected to impact loading

The dynamic response of clamped sandwich beam with aluminium alloy open-cell foam core subjected to impact loading is investigated in the paper. The face sheet and the core of the sandwich beam have the different thickness. And the sandwich beam is impacted by a steel projectile in the mid-span. The impact force is recorded by using accelerometer. The results show that tensile crack and core shear are the dominant failure modes. And the impact velocity and the thickness of the face sheet and the foam core have a significant influence on the failure modes and the impact forces. Combining with the inertia effect and experimental results, the failure mechanisms of the sandwich beams are discussed. The thickness of the foam core plays an important role in the failure mechanism of the sandwich beam. In present paper, the failure of the sandwich beam with a thin core is dominated by the bending moment, while the sandwich beam with a thick core fails by bending deformation in the front face sheet and the bottom face sheet in opposite direction due to the plastic hinges in the front face sheet.     

Free vibration analysis of simply supported sandwich beams with lattice truss core

Free vibration of AISI 304 stainless steel sandwich beams with pyramidal truss core is investigated in the present paper. The lattice truss core is transformed to a continuous homogeneous material. Considering the deformation characteristics of the sandwich beam, the following assumptions are made: (1) the thickness of the sandwich beam remains constant during deformation; (2) for the thin face sheets, only bending deformation is considered, neglecting the effect of transverse shear deformation; (3) for the core, only shear deformation is considered as the core is too weak to provide a significant contribution to the bending stiffness of the sandwich beam. The shear stress is assumed to be constant along the thickness of the core. The governing equation of free vibration is derived from Hamilton's principle, and the natural frequencies are calculated under simply supported boundary conditions. Finally, numerical simulation is carried out to get the mode shapes and natural frequencies. Our results show that the theoretical solutions agree well with the numerical results. It indicates the present method would be useful for free vibration analysis of sandwich beams with lattice truss core.     

Deformation and failure of clamped shallow sandwich arches with foam core subjected to projectile impact

The dynamic response of clamped shallow sandwich arches with core of aluminum foam has been experimentally studied by impacting the arches at mid-span with metal foam projectiles. The resistance to shock loading is measured by the permanent transverse deflection at mid-span of the arches. The deformation mechanisms of shallow sandwich arches were investigated. In addition, the deformation/failure modes of the shallow sandwich arch were classified and analyzed systematically. The effects of initial projectile momentum, face sheet thickness, core thickness and radius of curvature on the structural response were obtained. The results indicated that permanent deflection at mid-span can be efficiently controlled by increasing face sheet thickness, core thickness or appropriately increasing curvature. Meanwhile, shock resistance of the shallow sandwich arch can also be improved. The experimental results are useful in the optimum design of cellular metallic sandwich structures.     

Buckling,collapse and failure analysis of FRP sandwich panels

Rectangular orthotropic fiber-reinforced plastic (FRP) sandwich panels were tested for buckling in uni-axial compression. The panels, with 0.32 cm (0.125 in.) face sheets and a 1.27 cm (0.5 in.) core of either balsa or linear poly(vinyl chloride) (PVC) foam, were tested in two sizes: 154×77 cm² (72×36 in.²) and 102×77 cm² (48×36 in.²). The sandwich panels were fabricated using the vacuum-assisted resin transfer molding process. The two short edges of the sandwich panels were clamped, while the two long edges were simply supported for testing. The clamped panel ends were potted into a steel frame. The experimental elastic buckling loads were then measured using strain gauges fixed to both sides of the panels. A total of 12 panels were tested under uni-axial compression. Bifurcation in the load versus engineering strain curve was noted in all cases. For all six sandwich panels tested using balsa core, the type of failure was easily identified as face sheet delamination followed by core shear failure. For all six PVC foam core sandwich panels tested, the type of failure consisted of core shear failure with little or no face sheet delamination. In the failed balsa core panels there was little or no evidence of balsa remaining on the FRP face sheet, however, in the PVC foam core panels there were ample amounts of foam left on the FRP face sheet. It was concluded that although the buckling loads for the foam core panels were not as high as those for the balsa core panels, PVC foam core bonding to the FRP face sheets was superior to balsa core bonding.     

Effect of core thickness on wave number and damping properties in sandwich composites

Due to their higher strength-to-weight and stiffness-to-weight ratios compared to metals, fiber reinforced composite materials are a great alternative for use in many structural applications. However these properties lead to poor acoustic performance as composite materials are excellent noise radiators. This is particularly true for sandwich composite structures. Therefore the focus of this study is to investigate the effect of a core thickness change on the vibrational properties of Rohacell foam/carbon-fiber face sheet sandwich composite beams. Four different foam core thicknesses were explored, using a combination of experimental and analytical methods to characterize sound and vibrational properties of the sandwich beams. First, the wave number responses of the beams were obtained, from which coincidence frequencies were identified. Second, from the frequency response functions the structural damping loss factor, η, was determined using the half-power bandwidth method. Experimental and analytical results show that the relationship between core thickness and coincidence frequency is non-linear. A drastic increase in coincidence frequency was observed for the sandwich beam with the thinnest core thickness due to the low bending stiffness. Moreover this low bending stiffness results in low damping values, and consequently high wave number amplitude responses at low frequency ranges (<1000 Hz).     

Compressive and shear buckling analysis of metal matrix composite sandwich panels under different thermal environments

Combined inplane compressive and shear buckling analysis was conducted on flat rectangular sandwich panels using the Rayleigh-Ritz minium energy method with a consideration of transverse shear effect of the sandwich core. The sandwich panels were fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that slightly slender (along the unidirectional compressive loading axis) rectangular sandwich panels have the most desirable stiffness-to-weight ratios for aerospace structural applications; the degradation of buckling strength sandwich panels with rising temperature is faster in shear than in compression; and the fiber orientation of the face sheets for optimum combined-load buckling strength of sandwich panels is a strong function of both loading condition and panel aspect ratio. Under the same specific weight and panel aspect ratio, a sandwich panel with metal matrix composite face sheets has a much higher buckling strength than one having monolithic face sheets.     

A triangular plate element for thermo‐elastic analysis of sandwich panels with a functionally graded core

A sandwich construction is commonly composed of a single soft isotropic core with relatively stiff orthotropic face sheets. The stiffness of the core may be functionally graded through the thickness in order to reduce the interfacial shear stresses. In analysing sandwich panels with a functionally gradient core, the three‐dimensional conventional finite elements or elements based on the layerwise (zig‐zag) theory can be used. Although these elements accurately model a sandwich panel, they are computationally costly when the core is modelled as composed of several layers due to its grading material properties. An alternative to these elements is an element based on a single‐layer plate theory in which the weighted‐average field variablescapture the panel deformation in the thickness direction. This study presents a new triangular finite element based on {3,2}‐order single‐layer theory for modelling thick sandwich panels with or without a functionally graded core subjected to thermo‐mechanical loading. A hybrid energy functional is employed in the derivation of the element because of a C¹ interelement continuity requirement. The variations of temperature and distributed loading acting on the top and bottom surfaces are non‐uniform. The temperature also varies arbitrarily through the thickness. Copyright © 2006 John Wiley & Sons, Ltd.     

Buckling Analysis of Composite Sandwich Plates with Flexible Core Using Improved High-Order Theory

A new improved high-order theory is presented for global and local buckling analysis of sandwich plates with soft orthotropic core. Continuity conditions for transverse shear stresses at the interfaces as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of plate are satisfied. Overall buckling loads, as well as wrinkling loads, are obtained for various sandwich plates. Effect of geometrical parameters and material properties of face sheets and core are studied on the overall buckling and face wrinkling of sandwich plates.     

Response of metallic pyramidal lattice core sandwich panels to high intensity impulsive loading in air

Small scale explosive loading of sandwich panels with low relative density pyramidal lattice cores has been used to study the large scale bending and fracture response of a model sandwich panel system in which the core has little stretch resistance. The panels were made from a ductile stainless steel and the practical consequence of reducing the sandwich panel face sheet thickness to induce a recently predicted beneficial fluid-structure interaction (FSI) effect was investigated. The panel responses are compared to those of monolithic solid plates of equivalent areal density. The impulse imparted to the panels was varied from 1.5 to 7.6 kPa s by changing the standoff distance between the center of a spherical explosive charge and the front face of the panels. A decoupled finite element model has been used to computationally investigate the dynamic response of the panels. It predicts panel deformations well and is used to identify the deformation time sequence and the face sheet and core failure mechanisms. The study shows that efforts to use thin face sheets to exploit FSI benefits are constrained by dynamic fracture of the front face and that this failure mode is in part a consequence of the high strength of the inertially stabilized trusses. Even though the pyramidal lattice core offers little in-plane stretch resistance, and the FSI effect is negligible during loading by air, the sandwich panels are found to suffer slightly smaller back face deflections and transmit smaller vertical component forces to the supports compared to equivalent monolithic plates.     

单向加筋双层板隔声性能的有限元分析

为考察筋板声学透明假设理论对于加筋双层板隔声计算的适用性，对典型波纹芯体加筋双层板在简谐平面声波正入射和斜入射激励下的声透射损失（STL）进行有限元分析。分别建立筋板声学透明声腔和结构-声学全耦合加筋双层板的有限元模型，计算得到结构具有不同芯体构型和腔内声学介质时的STL曲线。结果表明，筋板“声学透明”假设模型带给加筋双层板STL计算误差取决于筋板结构阻抗和筋板间腔内介质声阻抗相对大小。因此，加筋双层板结构STL的准确预测需考虑筋板与腔内介质间与的结构-声学耦合作用。     

Experiments on curved sandwich panels under blast loading

In this paper curved sandwich panels with two aluminium face sheets and an aluminium foam core under air blast loadings were investigated experimentally. Specimens with two values of radius of curvature and different core/face sheet configurations were tested for three blast intensities. All the four edges of the panels were fully clamped. The experiments were carried out by a four-cable ballistic pendulum with corresponding sensors. Impulse acting on the front face of the assembly, deflection history at the centre of back face sheet, and strain history at some characteristic points on the back face were obtained. Then the deformation/failure modes of specimens were classified and analysed systematically. The experimental data show that the initial curvature of a curved sandwich panel may change the deformation/collapse mode with an extended range for bending dominated deformation, which suggests that the performance of the sandwich shell structures may exceed that of both their equivalent solid counterpart and a flat sandwich plate.     

Sandwich shell finite element for dynamic explicit analysis

The contribution of this paper consists of new development of transverse shear stresses through the thickness and finding an expression for the critical time step for explicit time integration of layered shells. This work presents the finite element (FE) formulation and implementation of a higher‐order shear deformable shell element for dynamic explicit analysis of composite and sandwich shells. The formulation is developed using a displacement‐based third‐order shear deformation shell theory. Using the differential equilibrium equations and the interlayer requirements, special treatment is developed for the transverse shear, resulting in a continuous, piecewise quartic distribution of the transverse shear stresses through the shell thickness. Expressions are developed for the critical time step of the explicit time integration for orthotropic homogeneous and layered shells based on the developed third‐order formulation. To assess the performance of the present shell element, it is implemented in the general non‐linear explicit dynamic FE code DYNA3D. Several problems are solved and results are presented and compared to other theoretical and numerical results. Copyright © 2002 John Wiley & Sons, Ltd.     

Dynamic models for low-velocity impact damage of composite sandwich panels – Part B: Damage initiation

Equivalent single and multi degree-of-freedom systems are used to predict low-velocity impact damage of composite sandwich panels by rigid projectiles. The composite sandwich panels are symmetric and consist of orthotropic laminate facesheets and a core with constant crushing resistance. The transient deformation response of the sandwich panels subjected to impact were predicted in a previous paper, and analytical solutions for the impact force and velocity at damage initiation in sandwich panels are presented in this second paper. Several damage initiation modes are considered, including tensile and shear fracture of the top facesheet, core shear failure, and tensile failure of back facesheet. The impact failure modes are similar to static indentation failure modes, but inertial resistance and high strain rate material properties of the facesheets and core influence impact damage loads. Predicted damage initiation loads and impact velocities compare well with experimental results.