Geometrically nonlinear forced vibrations of the symmetric rectangular honeycomb sandwich panels with completed clamped supported boundaries

Geometrically nonlinear forced vibrations of symmetric rectangular honeycomb sandwich panels with clamped supported boundaries at the four edges are investigated using the homotopy analysis method (HAM). The honeycomb core of hexagonal cells is modeled as a thick layer of orthotropic material whose parameters of physical and mechanical properties are calculated by the corrected Gibson’s formula. The basic formulation of nonlinear forced vibrations has been developed based on the classical plate theory (CPT) and the nonlinear strain–displacement relation. The equilibrium equations have been obtained using Hamilton’s principle. Effects of axial half-waves, height and height ratio on the nonlinear free vibration response have been investigated for honeycomb sandwich panels.     

Geometrically nonlinear forced vibrations of the symmetric honeycomb sandwich panels affected by the water

Geometrically nonlinear forced vibrations of the symmetric rectangular honeycomb sandwich panels with the four edges simply supported and one surface affected by the water are investigated in this paper using the homotopy analysis method (HAM). The honeycomb core of hexagonal cells is modeled as a thick layer of orthotropic material whose physical and mechanical properties are determined using the Gibson correlations. The effect of water acting on honeycomb panels can be described as added mass, additional damping and additional stiffness coefficients which are obtained by the semi-analytical fluid pressures. The basic formulation of nonlinear forced vibrations has been developed base on the third-order shear deformation plate theory and Green Lagrange nonlinear strain–displacement relation. The equilibrium equations have been obtained using the Hamilton’s principle. Effects of water velocity, height and height ratio on the nonlinear forced vibration response have been studied for the honeycomb sandwich panels.     

四边固支对称蜂窝夹层板主共振非线性动力学计算

应用同伦分析方法(HAM)研究了四边固支对称蜂窝夹层板主共振情况下的非线性动力学特性。将铝基蜂窝芯层等效为一正交异性层, 等效弹性参数由修正后的Gibson方程得出。基于经典叠层板理论(CPT)和几何大变形理论建立了四边固支蜂窝夹层板受横向激振力作用下的受迫振动微分方程, 通过振型正交化将蜂窝夹层板受迫振动微分方程简化成双模态下的动力学控制方程, 得到了主共振情况下的平均方程, 研究了不同结构参数对动力学特性的影响。计算结果表明, 蜂窝夹层板的幅频特性曲线类似单自由度Duffing方程响应曲线, 随着结构参数的增大, 硬特性明显加大并且振幅的峰值明显减小, 所得结论可为蜂窝夹层板的设计和实际应用提供理论依据。     

Failure mode maps for honeycomb sandwich panels

Failure modes for sandwich beams of GFRP laminate skins and Nomex honeycomb core are investigated. Theoretical models using honeycomb mechanics and classical beam theory are described. A failure mode map for loading under 3-point bending is constructed, showing the dependence of failure mode and load on the ratio of skin thickness to span length and honeycomb relative density. Beam specimens are tested in 3-point bending. The experimental data agree satisfactorily with the theoretical predictions. The effect of honeycomb direction is also examined. The concept of a failure mode map is extended to give a useful design tool for sandwich panels manufacturers and their customers.     

Impact behavior and energy absorption of paper honeycomb sandwich panels

Dynamic cushioning tests were conducted by free drop and shock absorption principle. The effect of paper honeycomb structure factors on the impact behavior was analyzed. Results of many experiments show that the dynamic impact curve of paper honeycomb sandwich panel is concave and upward; the thickness and length of honeycomb cell-wall have a great effect on its cushioning properties; increasing the relative density of paper honeycomb can improve the energy absorption ability of the sandwich panels; the thickness of paper honeycomb core has an up and down fluctuant effect on the cushioning properties; with the increase of the thickness of paper honeycomb core, the effect dies down; flexible corrugated paperboard as liners can improve the compression resistance and cushioning properties of paper honeycombs. The research results can be used to optimize the structure design of paper honeycomb sandwich panel and material selection for packaging design.     

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。     

Generation of transient vibrations on aluminum honeycomb sandwich panels subjected to hypervelocity impacts

This paper presents the results of a set of experiments aimed at discovering the main features of impact-induced vibrations on all-aluminum honeycomb sandwich panels, representative of the GOCE satellite's top floor, which is exposed to the orbital debris environment. The activity focused on the characterization of the vibrations induced in the vicinity of internal payloads by hypervelocity impacts occurring on the vehicle's external shell. More than 30 tests were realized by launching 0.8–2.3 mm aluminum projectiles in the velocity range 4–5.5 km/s on targets with tri-axial accelerometer assemblies mounted on both the front and rear face of the panel, at a nominal distance of 150 mm from the impact point. It was found that a hypervelocity impact produces in both the front and rear side of the sandwich panel a vibration environment which can be described through the shock response spectrum (SRS) of three different types of waves that can be distinguished on the basis of the acceleration direction: out-of-plane, in-plane longitudinal and in-plane shear. The influence of projectile mass and velocity on SRS appeared to vary with frequency, with the most significant difference in the range between ∼10³ and ∼10⁴ Hz. The results of whole experimental set were used to derive an interpolation law through standard techniques of nonlinear fit. The empirical equation obtained makes it possible to predict the near-field vibration environment produced by hypervelocity impacts with debris having given size and velocity, reproducing all the test data with an average uncertainty of ±6 dB.     

四边简支双曲率蜂窝夹层薄壳自由振动分析

基于Reddy三阶剪切理论,研究了四边简支双曲率蜂窝夹层薄壳的自由振动,以及结构参数对蜂窝夹层薄壳固有频率的影响.将由六边形胞元组成的蜂窝芯层等效为一正交异性层,其等效弹性参数由修正后的Gibson公式得到,应用Reddy三阶剪切理论和Hamilton变分原理推导出四边简支条件下双曲率蜂窝夹层薄壳的频率方程.具体算例表明,采用Reddy三阶剪切理论计算的固有频率精度较高;双曲率蜂窝夹层薄壳的曲率、厚度比及胞元角度对蜂窝夹层壳固有频率有不同程度的影响,其中蜂窝夹层薄壳的固有频率随曲率的增大而增大,随厚度比的增大呈波动变化,随胞元角度的增大而减小.     

简支边界条件下超椭圆蜂窝夹芯板的自由振动

基于Reddy三阶剪切板理论,将铝基蜂窝芯层等效为一正交异性层,等效弹性参数由修正后的Gibson公式得出,对简支边界条件下超椭圆蜂窝夹芯板弯曲振动的固有频率进行了理论推导,应用具体算例与实验值和有限元计算结果进行了验证,结果表明本文方法具有较高的计算精度。研究了板宽、板厚和芯层胞元结构参数对简支边界条件下超椭圆蜂窝夹芯板固有频率的影响,并绘出相应的曲线图,该曲线图对超椭圆蜂窝夹芯板的工程应用具有指导意义。     

蜂窝金属夹芯板重复冲击动态响应研究

蜂窝金属及其夹芯结构是一种物理功能与结构一体化的新型轻质高强结构,广泛应用于结构轻量化与碰撞冲击防护领域.采用ABAQUS非线性有限元软件建立了蜂窝金属夹芯板(honeycomb sandwich panel,HSP)结构动态冲击数值仿真模型,数值仿真计算结果与文献实验结果吻合较好,验证了数值仿真模型的正确性.在此基础...     

Dynamic response of aluminum honeycomb sandwich panels under foam projectile impact

The dynamic response of honeycomb sandwich panels under aluminum foam projectile impact was investigated. The different configurations of panels were tested, and deformation/failure modes were obtained. Corresponding numerical simulations were also presented to investigate the energy absorption and deformation mechanism of sandwich panels. Results showed that the deformation/failure modes of sandwich panels were sensitive to the impact velocity and density of aluminum foam. When the panel was impacted by the aluminum foam projectile with the back mass of nylon, the “accelerating impact” stage can be produced and may lead to further compression and damage of the sandwich structures.     

Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

In this paper, nonlinear static and free vibration analysis of functionally graded piezoelectric plates has been carried out using finite element method under different sets of mechanical and electrical loadings. The plate with functionally graded piezoelectric material (FGPM) is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. Only the geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the FGPM plate thickness. The governing equations are obtained using potential energy and Hamilton’s principle that includes elastic and piezoelectric effects. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. Results are presented for two constituent FGPM plate under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.     

梯度铝蜂窝夹芯板的力学行为

梯度分层铝合金蜂窝板是一种有效的吸能结构,本工作在梯度铝蜂窝结构的基础上根据梯度率的概念,通过改变蜂窝芯层的胞壁长度,设计了4种质量相同、梯度率不同的铝蜂窝夹芯结构。通过准静态压缩实验,并结合非线性有限元模拟准静态及冲击态下梯度铝蜂窝夹芯结构的变形情况及其力学性能,分析对比了相同质量下梯度铝蜂窝夹芯结构在准静态下的变形模式以及冲击载荷下分层均质蜂窝结构和不同梯度率的分层梯度蜂窝结构的动态响应和能量吸收特性。结果表明:在准静态压缩过程中,铝蜂窝梯度夹芯板的变形具有明显的局部化特征,蜂窝芯的变形为低密度优先变形直至密实,层级之间的密实化应变差随芯层密度的增大而逐渐减小;在高速冲击下,梯度蜂窝板并非严格按照准静态过程中逐级变形直至密实,而是在锤头冲击惯性及芯层密度的相互作用下整体发生的线弹性变形、弹性屈曲、塑性坍塌及密实化;另外,在本工作所设计的梯度率中,当梯度率为γ₁=0.0276时,梯度蜂窝夹芯板的吸能性达到最好,相较于同等质量下的均质蜂窝夹芯板,能量吸收提高了10.63%。     

四边简支新型类方形蜂窝夹层结构振动特性研究

新型类方形蜂窝是六边形蜂窝的一种过渡形式,对其等效弹性参数和振动特性的研究具有重要意义。采用改进的Gibson公式对比分析了双壁厚与等壁厚类方形蜂窝夹芯的面内等效弹性参数的差异,并应用经典层合板理论分析了不同等效弹性参数下2种壁厚类型的四边简支类方形蜂窝夹层结构的振动特性,基于有限元仿真技术分析了不同壁厚类方形蜂窝夹层结构的振动特性,并与理论分析结果进行对比。结果表明等效弹性参数的数值模拟结果与理论值基本吻合。在蜂窝基本结构参数相同的条件下,双壁厚类方形蜂窝夹芯的面内等效剪切模量、面外刚度和等效密度均比等壁厚类方形蜂窝夹芯大;在低阶振动模态下,双壁厚类方形蜂窝夹层结构的固有频率比等壁厚类方形蜂窝夹层结构的低,在高阶振动模态下,双壁厚类方形蜂窝夹层结构的固有频率比等壁厚类方形蜂窝夹层结构的高;影响夹层结构固有频率的3个主要因素所占权重由大到小依次为蜂窝夹芯yoz面等效剪切模量、蜂窝夹芯等效密度,蜂窝夹芯壁厚。研究结果表明采用经典层结构理论计算得到类方形蜂窝夹层结构的固有频率与数值仿真结果的一致性较好,这进一步证明了采用改进Gibson公式得到的类方形蜂窝夹芯等效弹性参数的正确性,同时证明了将该振动理论运用到一般蜂窝夹层结构研究的可行性,为扩展研究其他类型蜂窝夹层结构振动特性奠定了基础。     

Failure initiation and propagation characteristics of honeycomb sandwich composites

The energy absorbed during the failure of a variety of structural shapes is influenced by material, geometry and the failure mode. Failure initiation and propagation of the honeycomb sandwich under loading involves not only non-linear behavior of the constituent materials, but also complex interactions between various failure mechanisms. Therefore, there is a need for an improved understanding of the material characteristics and energy absorption modes to facilitate the design of sandwich performance. In the present study, failure initiation and propagation characteristics of sandwich beams and panels subjected to quasi-static and impact loadings were investigated. Experimental studies involved a series of penetration and perforation tests on 2D beam and 3D panel configurations using a truncated cone impactor with impact velocities up to 10 m/s. Preliminary tests were also performed on the sandwich beams subjected to the three-point bending. Load-carrying, energy-absorbing characteristics and failure mechanisms under quasi-static and impact loading were determined. Dominant deformation modes involved upper skin compression failure in the vicinity of the indenter, core crushing and lower skin tensile failure.     

Three-dimensional exact solutions for free vibrations of simply supported magneto-electro-elastic cylindrical panels

This work investigates the free vibrations of magneto-electro-elastic cylindrical panels based on three-dimensional theory. Firstly, the general solutions for transversely isotropic magneto-electro-elastic materials are introduced and the displacement functions in the general solutions are expanded in trigonometric functions along the circumferential and axial directions. Then an ordinary differential equation of the displacement functions in radial direction is derived and solved. As a result, the frequency equations are obtained through the traction-free conditions on the cylindrical surfaces of the panel as well as the electric and magnetic conditions. For the torsion and thickness-shear modes, the frequency equations in simpler forms are presented. It is found that the magneto-electro-elastic coupling effects disappeared in torsion vibration. Meanwhile, the frequencies of pure elastic materials and magneto-electro-elastic materials have an explicit relation for the thickness-shear modes. The aforementioned solutions satisfy all the governing equations and boundary conditions point by point and they are three-dimensionally exact. Finally the numerical example demonstrates the present method and is compared with those from finite element method. Parametric investigation is also conducted to show the behavior of free vibrations of cylindrical panels.     

对边简支负泊松比蜂窝夹层板的弯曲自由振动

负泊松比蜂窝夹层板作为一种特殊的复合材料结构,目前对其动态行为尚缺乏认识。应用Reddy剪切板理论分析了对边简支负泊松比蜂窝夹层板的弯曲振动。将内凹六边形胞元的蜂窝芯层等效为一正交异性层,芯层的等效弹性参数由修正后的Gibson公式得出。由具体算例可知经典叠层板理论和一阶剪切板理论不适合用于蜂窝夹层板的振动分析。应用Reddy剪切板理论研究了蜂窝夹层板板厚比、芯层板厚及胞元角度对弯曲振动频率的影响,并绘出相应的曲线图。结果表明:对于对边简支负泊松比蜂窝夹层板,当板厚比小于某一值时,固有频率参数随板厚比的增加而增加;但当板厚比大于该值时,固有频率参数随板厚比的增加呈现复杂的变化形式。本文得到的结果为蜂窝夹层板的设计和实际应用提供了理论依据和数值参考。      

On the elastic stability of simply supported anisotropic sandwich panels

Here, the elastic stability behavior of simply supported anisotropic sandwich flat panels subjected to mechanical in-plane loads is investigated using an analytical approach. The formulation is based on first-order shear deformation theory and the shear correction factors employed are based on energy consideration that depends on the lay-up as well as material properties. The governing equations are obtained using the Raleigh–Ritz method assuming a combination of sine and cosine functions in the form of double Fourier series for the displacement fields. The effectiveness of the integrated formulation is tested for global characteristics considering examples related to multi-layered laminates and sandwich panels for which solutions are available.     

Prediction of inter-laminar stresses in composite honeycomb sandwich panels under mechanical loading using Variational Asymptotic Method

This work focuses on the formulation of an asymptotically correct theory for symmetric composite honeycomb sandwich plate structures. In these panels, transverse stresses tremendously influence design. The conventional 2-D finite elements cannot predict the thickness-wise distributions of transverse shear or normal stresses and 3-D displacements. Unfortunately, the use of the more accurate three-dimensional finite elements is computationally prohibitive. The development of the present theory is based on the Variational Asymptotic Method (VAM). Its unique features are the identification and utilization of additional small parameters associated with the anisotropy and non-homogeneity of composite sandwich plate structures. These parameters are ratios of smallness of the thickness of both facial layers to that of the core and smallness of 3-D stiffness coefficients of the core to that of the face sheets. Finally, anisotropy in the core and face sheets is addressed by the small parameters within the 3-D stiffness matrices. Numerical results are illustrated for several sample problems. The 3-D responses recovered using VAM-based model are obtained in a much more computationally efficient manner than, and are in agreement with, those of available 3-D elasticity solutions and 3-D FE solutions of MSC NASTRAN.     

Insight into the shear behaviour of composite sandwich panels with foam core

While sandwich construction offers well-known advantages for high stiffness with light weight, the problem of designing the sandwich structure to withstand shear loading remains an important problem. This problem is more difficult with lower stiffness foam cores under high shear loading because the core is typically the weakest component of the structure and is the first one to fail in shear under the assuming of perfect contact between the skin and the foam core. In the present study, the shear response of the composite sandwich panels with Polyvinylchloride (PVC) foam core was investigated. The PVC H100 foam core is sandwiched between Glass Fiber Reinforced Polymer (GFRP) skins using epoxy resin to build a high performance sandwich panel to be investigated. Experiments have been carried out to characterise the mechanical response of the constituent materials under tension, compression and shear loading. Static shear tests for the sandwich panel reveal that the main failure mode is the delamination between the skin and the core rather than shearing the core itself due to the considerable value of the shear strength of the PVC foam. The Finite Element Analysis (FEA) of the sandwich structure shows that shear response and failure mode can be predicted, but that accurate predictions require a consideration of the non-linear response of the foam core. The results have a direct application in predicting the ability of the sandwich structure to withstand the shear loading.