Multiscale design of a rectangular sandwich plate with viscoelastic core and supported at extents by viscoelastic materials

This work presents a multiscale model of viscoelastic constrained layer damping treatments for vibrating plates/beams. The approach integrates a finite element (FE) model of macroscale vibrations and a micromechanical model to include effects of microscale structure and properties. The FE model captures the shear deformation of the viscoelastic core, rotary inertial effects of all layers, and viscoelastic boundaries of the plate. Comparison with analytical and FE results validates the proposed FE model. A self-consistent (SC) model makes the micro to macro scale transition to approximate the effective behavior a heterogeneous core. Modal damping resulting from the presence of voids and negative stiffness regions in the core material is modeled. Results show that negative stiffness regions in the viscoelastic core material, even at low volume fractions, yield superior macroscopic damping behavior. The coupled SC and FE models provide a powerful multiscale predictive design tool for sandwich beams and plates.     

梁模型三明治板的隔声预报

提出一种针对有限大三明治蜂窝板的隔声预报方法。在一定条件下,三明治蜂窝板被看成是正交各向异性的,通过对蜂窝板正交方向上切割下来梁的简单测 试,可以得到三明治蜂窝板的等效刚度,结合正交各向异性板的振动方程,把板的振动展开成模态叠加的形式并求解,最终可以得到一块有限大三明治蜂窝板的理论隔声公式,理论预报结果与实验室测量结果对比良好。     

复合材料面板对筒型基座整体抑振机制影响规律研究

提出一种新型复合材料筒型基座结构形式，其面板采用夹芯结构设计；通过系统阻抗特性分析理论预测面板结构及材料参数对基座减振性能的影响规律；针对夹芯面板开展静/动力学特性试验；以振级落差为减振效果评价指标，通过激振试验研究了面板结构参数对基座抑振机制的影响规律。研究结果表明：在频段 ，夹芯面板刚度能有效控制基座减振性能，随着频率的增加，面板刚度抑振机制减弱，阻尼高频损耗抑振机制增强；夹芯面板芯材厚度的增加对基座高频抑振性能优于表层厚度增加；面板对基座减振耗能贡献高于环壁间阻尼芯材。     

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).     

Torsion of carbon fiber composite pyramidal core sandwich plates

A combined theoretical, experimental and numerical investigation of carbon fiber composite pyramidal core sandwich plates subjected to torsion loading is conducted. Pyramidal core sandwich plates are made from carbon fiber composite material by a hot compression molding method. Based on the Classical Laminate Plate Theory and Shear Deformation Theory, the equivalent mechanical properties of laminated face-sheet are obtained; based on a homogenization concept combined with a mechanical of materials approach, the equivalent in-plane and out-of-plane shear moduli of pyramidal core are obtained. A torsion solution is derived with Prandtl stress function and can be used in the sandwich plate with orthotropic face-sheets and orthotropic core. The influences of material properties and geometrical parameters on the equivalent torsional stiffness are explored. In order to verify the accuracy of the analytical torsion solution, experimental tests of sandwich plate samples with different face-sheet thicknesses are conducted and two types of finite element models are developed. Good agreements among analytical predictions, finite element simulations and experimental evaluations are achieved, which prove the validity of the present derivation and simulation. The proposed method could also be applied in design applications and optimization of the pyramidal core sandwich structures.     

A layerwise finite element formulation for vibration and damping analysis of sandwich plate with moderately thick viscoelastic core

Abstract

Most previous studies of viscoelastic sandwich plates were based on the assumption that damping was only resulting from shear deformation in the viscoelastic core. However, extensive and compressive deformations in the viscoelastic core should also be considered especially for sandwich plates with moderately thick viscoelastic core. This paper presents a finite element formulation for vibration and damping analysis of sandwich plates with moderately thick viscoelastic core based on a mixed layerwise theory. The face layers satisfy the Kirchhoff theory while the viscoelastic core meets a general high-order deformation theory. The viscoelastic core is modeled as a quasi-three-dimensional solid where other types of deformation such as longitudinal extension and transverse compression are also considered. To better describe the distribution of the displacement fields, auxiliary points located across the depth of the sandwich plate are introduced. And based on the auxiliary points, the longitudinal and transverse displacements of the viscoelastic core are interpolated independently by Lagrange interpolation functions. Quadrilateral finite elements are developed and dynamic equations are derived by Hamilton’s principle in the variation form. Allowing for the frequency-dependent characteristics of the viscoelastic material, an iterative procedure is introduced to solve the nonlinear eigenvalue problem. The comparison with results in the open literature validates the remarkable accuracy of the present model for sandwich plates with moderately thick viscoelastic core, and demonstrates the importance of the higher-order variation of the transverse displacement along the thickness of the viscoelastic core for the improvement of the analysis accuracy. Moreover, the influence of the thickness and stiffness ratios of the viscoelastic core to the face layers on the damping characteristics of the viscoelastic sandwich plate is discussed.     

Sound radiation of orthogonally rib-stiffened sandwich structures with cavity absorption

A comprehensive theoretical model is developed for the radiation of sound from an infinite orthogonally rib-stiffened sandwich structure filled with fibrous sound absorptive material in the partitioned cavity, when excited by a time-harmonic point force. The vibrations of the rib-stiffeners are accounted for by considering all possible motions. Built upon the concepts of dynamic density and bulk modulus, both frequency dependent, an equivalent fluid model is employed to characterize the absorption of sound in the fibrous material. Given the periodicity of the sandwich structure, Fourier transform technique is employed to solve the series of panel vibration equations and acoustic equations. In the absence of fibrous sound absorptive material, the model can be favorably degraded to the case of an infinite rib-stiffened structure with air or vacuum cavity. Validation of the model is performed by comparing the present model predictions with previously published data, excellent agreements are achieved. The influences of air–structure coupling effect and cavity-filling fibrous material on the sound radiation are systematically examined. The physical features associated with sound penetration across these sandwich structures are interpreted by considering the combined effects of fiberglass stiffness and damping, the balance of which is significantly affected by stiffener separation. The proposed model provides a convenient and efficient tool for the factual engineering design of this kind of sandwich structures.     

波纹夹层板线性弯曲分析的无网格伽辽金法

提出了一种求解波纹夹层板结构线性弯曲问题的无网格模型。将波纹夹层板看成两侧平板和中间波纹板核的复合结构,用正交各向异性板等效近似波纹板核。先基于一阶剪切变形理论,由无网格伽辽金法建立各板的刚度方程,再通过位移协调条件将各板刚度方程叠加,以得到整体刚度方程。采用全转换法处理位移边界。算例表明：该文所提出的无网格模型分析波...     

橡胶芯夹层板隔声特性研究

基于夹层板的Hoff理论和声学反射、透射和辐射机理，建立了声振理论模型，结合模态函数的正交性及流-固耦合边界条件求解了声振耦合系统方程。再根据声场的特性，建立了混合声场下夹层板的隔声量表达式。最后，用数值方法研究了芯层的损耗因子、厚度、弹性模量，以及平面尺寸对夹层板隔声量的影响，对工程应用有一定的参考价值。     

Core material effect on wave number and vibrational damping characteristics in carbon fiber sandwich composites

A sandwich composite is typically designed to possess high bending stiffness and low density and consists of two thin and stiff skin sheets and a lightweight core. Due to the high stiffness-to-weight and strength-to-weight ratios, sandwich composite materials are widely used in various structural applications including aircraft, spacecraft, automotive, wind-turbine blades and so on. However, sandwich composite structures used in such applications often suffer from poor acoustic performance. Ironically, these superior mechanical properties make the sandwich composites “excellent” noise radiators. There is a growing interest in optimizing and developing a new sandwich composite which will meet the high stiffness-to-weight ratio and offer improved acoustic performance. The focus of this study is to investigate the structural–vibrational performance of carbon-fiber face sheet sandwich composite beams with varying core materials and properties. Core materials utilized in this study included Nomex and Kevlar Honeycomb cores, and Rohacell foam cores with different densities and shear moduli. The structural–vibrational performance including acoustic and vibrational damping properties was experimentally characterized by analyzing the wave number response, and structural damping loss factor (η) from the frequency response functions, respectively. It was observed that the relationship between the slopes of the wave number data for frequencies above 1000 Hz is inversely proportional to the core material’s specific modulus (G/ρ). The analysis also showed the importance of using a honeycomb core’s effective properties for equal comparison to foam-cored sandwich structures. Utilizing analytical modeling, the loss factors of the core materials (β) was determined based upon the measured structural loss factors (η) for a frequency range up to 4000 Hz. It was determined that low shear modulus cores have similar material damping values to structural damping values. However as the core’s shear modulus increases, the percent difference between these values is found to increase linearly. It was also observed that high structural damping values correlated to low wave number amplitudes, which correspond to reductions in the level of noise radiation from the structure.     

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。     

Buckling and postbuckling of soft-core sandwich plates with composite facesheets

Finite element analysis is conducted to investigate the effect of coupling between the stiff facesheets and the flexible core on the stability of sandwich plates. The facesheets and the core are treated separately as three-dimensional solids. Initially, linear buckling analysis was carried out to determine the buckling loads for a wide range of the facesheet stiffness and core stiffness. Numerical results indicate that, for sandwich plates with a soft core such as PVC foam, the model that smears the facesheets and core overestimates the initial buckling load, demonstrating the importance of treating the facesheets and the core separately. Subsequently, postbuckling analysis was carried out. Numerical results show that, for sandwich plates with a soft core, the postbuckling behavior is unstable in that static equilibrium cannot be maintained once the buckling initiates. Received 20 August 1999     

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。     

夹层结构主动温控变阻尼振动控制技术

为提高夹层结构的抑振特性,开展了基于主动温控变阻尼技术的夹层结构振动控制方法研究。基于高分子聚合材料在玻璃化转变区的高阻尼特性,提出了一种针对夹层结构高分子聚合芯材进行温度控制,增大其损耗因子以提高结构阻尼的技术途径。根据此技术途径设计了以聚氨酯改性环氧材料为芯材,中间铺设加热膜的温控夹层梁。开展了不同控制温度下夹层梁的振动响应试验研究并探讨了温度对夹层梁弯曲刚度的影响规律,试验结果表明,当将夹层梁温度控制在玻璃化转变温度(Tg)左侧附近时,夹层梁的振动响应可较常温状态下降低8.85 dB,证明了所提出的主动温控变阻尼技术具有良好的抑振效果。     

基于夹层板理论的圆形孔蜂窝结构隔声量研究

蜂窝夹层结构广泛应用于航空航天、船舶、高速列车等交通工具领域。基于三明治等效理论建立了圆形蜂窝结构层芯的等效剪切参数,从而得到简支边界条件下的圆形孔蜂窝夹层板的声振耦合振动模型及传声损失,并在仿真中数值验证了理论模型的正确性。同时基于理论计算,分析了圆形孔蜂窝结构中的层芯胞元半径、层芯壁厚和结构材料对隔声量的影响。由分析可知:层芯半径小、壁厚薄的钢材圆形蜂窝结构具有更好的隔声性能。     

敷设阻尼加筋外地板结构振动声辐射特性研究

结合声学分析软件建立高速列车加筋外地板结构有限元模型,研究阻尼材料对加筋外地板声辐射特性的影响,并探究面板厚度、结构阻尼系数和阻尼材料对外地板隔声量的影响。研究结果表明:敷设阻尼层能够有效抑制外地板的声辐射,但不是越厚越好;增加面板厚度及结构阻尼系数能够提高外地板的隔声量;阻尼层厚度存在临界值,此时外地板隔声量最大。加筋外地板敷设树脂类阻尼且增大结构阻尼系数,声学性能较理想。     

缝合泡沫夹芯复合材料低速冲击的多尺度数值方法

为了发展缝合泡沫夹芯复合材料低速冲击损伤的多尺度分析方法, 建立了缝合泡沫简化力学模型, 将缝合泡沫等效为缝线树脂柱增强的正交各向异性芯材, 其材料参数由各组分性能及所占体积分数根据均一化理论计算得出; 同时, 建立冲击试验有限元模型, 通过界面元模拟面板与芯材之间的层间分层。采用GENOA渐进损伤分析模块对缝合结构冲击动态响应过程进行数值模拟, 并将计算结果与试验记录进行对比分析。结果表明: 缝合可以减小面板破坏面积, 抑制面板与泡沫分层的扩展; 但缝纫会对结构造成初始损伤, 较高的缝合密度使芯材刚度增加, 不利于泡沫结构的缓冲吸能。数值模拟结果与试验记录吻合良好, 验证了多尺度分析方法的正确性。     

In-plane effective elastic properties of a novel cellular core for sandwich structures

Within this paper an analytical model is presented for the calculation of the in-plane effective elastic properties E_x and E_y of a novel cellular structure which is proposed to be used as a core in sandwich structures. The proposed cellular core may represent a less expensive and easily to produce alternative to the already known cellular structures used for the construction of sandwich structures. The developed analytical model is validated through experimental tests. The results obtained by analyzing the theoretical model show a good agreement with the tests. The structure topology is studied using a parameterized unit cell and it is shown the way in which the in-plane stiffness depends on the geometric parameters and relative density of the core.     

含界面脱粘及表板基体开裂损伤的复合材料夹层板非线性稳定性的研究

本文作者基于"zig-zag"模型和Mindlin一阶剪切变形板理论,推导了复合材料夹层板屈曲分析的有限元列式,在该列式中考虑了面板的横向剪切变形和芯体的面内刚度对夹层板力学性能的影响。针对具有面板和芯体间界面脱粘和纤维增强树脂基体微裂纹损伤的夹层板损伤特征,分别提出了分层模型和多标量损伤模型,并推导了多标量形式的损伤本构关系。采用修正的 Newton-Raphson迭代格式求解含损复合材料夹层板的非线性稳定性性状。通过算例研究了脱粘面积、基体的损伤演化、表板的铺设方式及载荷形式对复合材料夹层板屈曲性态的影响。本文作者给出的有限元模型和结论,对复合材料夹层板结构设计的损伤容限的制定具有一定的参考价值。     

高速列车夹芯地板结构隔声特性研究

采用传递矩阵法,建立高速列车内地板的声学特性分析模型,探索不同三明治夹芯板材料和结构对高速列车内地板隔声特性的影响,并根据内地板结构的传递损失评价具有不同参数的三明治夹芯板的隔声性能。通过不同的表层材质（木材、铝材、钢材）、厚度和蜂窝夹层密度,进行了内地板隔声量变化规律的分析和比较。探寻拟定隔声性能优越的三明治夹芯板材料类型和结构型式。结果表明,（1）表层夹板厚度一定,钢材作为表层材料,内地板隔声量最好,其次是铝材,最后是木材;（2）表层厚度影响,木材夹层板,厚度每增加1 mm,各个频段隔声量增加1 dB ～1.5 dB。铝材夹层板,厚度每增加1 mm,各个频段隔声量增加1 dB ～3 dB。钢材夹层板,厚度每增加1 mm,各个频段隔声量增加1 dB ～5 dB;（3）蜂窝板密度降低一半,内地板隔声量有增加趋势,但影响较小。