Finite Element Dynamic Analysis of Laminated Viscoelastic Structures

This work is concerned with the dynamic behavior of laminated beam, plate and shell structures consisting of a viscoelastic damping layer constrained between two structural layers. Finite element models for modal, harmonic and transient analyses are developed. The dynamic interlaminar shear stresses are determined and presented under harmonic and transient loads. The effect of the damping ratio of the viscoelastic material is investigated. It is found that the viscoelastic material damping reduces the interlaminar stresses. The results also show the dependency of the viscoelastic material on frequency, hence, the effect of the viscoelastic material appears significantly under harmonic loading. In transient analysis, the importance of the viscoelastic material is observed in absorbing the impact and returning the structure to its original configuration.     

Control of mechanical deformation of a laminate by electrical load to piezoelectric actuator considering the effects of damping and transverse shear

In this paper, we treat the control of dynamic deformation of a laminate by applying electrical load to piezoelectric actuators. Dynamic behavior of the laminate is analyzed considering the effect of damping due to interlaminar shear and the effect of transverse shear. The analytical model is a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers. The model is assumed to be a symmetric cross-ply laminate with all edges simply supported and to be subjected to unavoidable mechanical load and to electrical loads to piezoelectric actuators. Behavior of the laminate is analyzed based on the first-order shear deformation theory. The effect of damping due to interlaminar shear is incorporated into our analysis by introducing the interlaminar shear stresses which satisfy the Newton’s law of viscosity. The following quantities are obtained: (1) natural frequencies of the laminate, (2) weight functions for the deflection and rotations and (3) transient deflection due to loads varying arbitrarily with time. Moreover, the methods to control the deflection due to mechanical load by applying electrical voltage to the piezoelectric actuator are shown.     

Dynamic stress concentration studies by boundary integrals and Laplace transform

The dynamic stress field and its concentrations around holes of arbitrary shape in infinitely extended bodies under plane stress or plane strain conditions are numerically determined. The material may be linear elastic or viscoelastic, while the dynamic load consists of plane compressional waves of harmonic or general transient nature. The method consists of applying the Laplace transform with respect to time to the governing equations of motion and formulating and solving the problem numerically in the transfomed domain by the boundary integral equation method. The stress field can then be obtaind by a numerical inversion of the trasformed solution. The correspondence principle is invoked for the case of viscoelastic material behavious. The method is simplified for the case of harmonic waves where no numerical inversion is involved.     

嵌入式高温共固化复合材料阻尼结构层间结合性能

使用正交实验法, 研制出满足嵌入式高温共固化复合材料阻尼结构制作工艺要求的黏弹性材料组分, 提出使用刷涂工艺代替压片工艺制备黏弹性材料薄膜, 并对两种工艺制备的碳纤维/双马来酰亚胺(T300/QY8911)复合材料试件进行层间剪切测试, 获得了薄膜厚度与层间最大剪切应力的变化关系, 实验数据表明: 刷涂工艺能提高嵌入式高温共固化复合材料阻尼结构层间结合性能10%以上, 而且阻尼层越薄, 提高幅度越大; 失效表面证明: 刷涂工艺所制得试件能在阻尼薄膜与复合材料界面间形成互穿网络结构。     

粘弹性阻尼隔振体的非线性振动分析

 研究了由基础振动激励、粘弹性材料隔离的被动隔振体的非线性动力响应.用变形的三次多项式函数表征隔振材料的非线性刚度,用分数阶算子表征阻尼,建立被动隔振体的分数阶非线性动力学方程.用谐波平衡法研究其非线性动力响应特性,得出频率响应方程和幅频曲线,分析了非线性因素对系统的影响.最后,用Floquet理论讨论了周期解的稳态性和稳定区间.分析结果表明,含分数阶算子的动力学模型能够准确地描述粘弹性材料隔振器的动态特性.忽略隔振材料的阻尼非线性、刚度非线性将导致隔振设计和隔振效果分析的明显误差.分析方法和结论为精确进行粘弹性材料的被动隔振设计和隔振效果评价提供理论参考.     

Winkler地基上黏弹性输流管的参数共振稳定性

本文研究了黏弹性输流管在Winkler地基上的横向振动。管道的黏弹性材料用Kelvin本构关系描述,在两端铰支边界条件下,对系统的控制方程应用直接多尺度法建立相应的可解性条件,得到了系统次谐波共振和组合共振的稳定性边界条件,考察了系统的各种参数如阻尼、脉动流速、质量比、弹性地基对稳定性边界条件的影响。     

嵌入式低温共固化高阻尼纤维/树脂基复合材料

通过正交试验新研制出一种可以与玻璃纤维/BA9913环氧树脂预浸料低温共固化的高阻尼黏弹性材料,提出使用四氢呋喃（THF）作为溶剂,将该高阻尼材料制成黏弹性材料溶液。采用双面刷涂工艺,将玻璃纤维/BA9913环氧树脂复合材料制成带阻尼薄膜的预浸料,按照设计的铺层根据热压罐固化工艺制成嵌入式低温共固化高阻尼复合材料试件。模态试验和层间剪切试验验证了本文所提出制作工艺和黏弹性材料组分的有效性,试件一阶模态损耗因子可达7.2%。为嵌入式低温共固化高阻尼复合材料的广泛使用奠定了基础。      

多翼型粘弹性阻尼层叶片的动态特性数值分析

采用有限元软件建立2MW风力机复合材料单翼型和多翼型叶片模型,将粘弹性阻尼层加入多翼型叶片中并进行额定风速载荷作用下的谐响应分析,探索单翼型和多翼型叶片的动态特性区别,并揭示粘弹性阻尼层层数和厚度变化对多翼型叶片动态特性的影响规律。研究结果表明,在高阶频率多翼型叶片的挥舞方向位移和应变能均远小于单翼型叶片的;粘弹性阻尼层对多翼型叶片的低阶频率的挥舞方向位移和应变能有很好的抑制效果。     

Effect of time-dependent material properties on dynamic response

By representing the time-dependent material properties by mechanical models, i.e. the generalized Maxwell and/or Voigt (or Kelvin) models, it is possible to formulate a consistent procedure to analyse the effect of material damping on dynamic response. As a continuation of the previous work which concerned the creep and relaxation of viscoelastic materials, the present paper applies this representation to the harmonic response analysis. The harmonic solution can be obtained by decomposing the relevant forces and displacements into real and imaginary parts and it is shown that the modal analysis by an appropriate eigensolution procedure is useful for obtaining the dependence of vibration amplitude on frequencies of sinusoidal external excitations.     

The modified couple stress model for bending of normal deformable viscoelastic nanobeams resting on visco-Pasternak foundations

ABSTRACT

The modified couple stress theory (MCST) is utilized to investigate the bending of viscoelastic nanobeams laying on visco-Pasternak elastic foundations based on a new shear and normal deformations beam theory. This model consists of the material length scale coefficient that captures the size impact on small-scale beams. The simply supported beam is made of viscoelastic material, subjected to time harmonic transverse load. The nanobeam is presumed to be laying on double layers of foundations. The first layer is modeled as Kelvin–Voigt viscoelastic model and the second is taken as a shear layer. Based on the proposed beam theory and MCST, the differential motion equations are deduced using Hamilton’s principle. To check the validity of the obtained formulations, the predicted results are compared with those available in the open literature. In addition, the influences of various parameters such as the material length scale parameter, length-to-depth ratio, viscoelastic damping structure, the stiffness and damping coefficients of the viscoelastic substrate, and shear and normal strains on the deflection and stresses are illustrated.     

Homogenised finite element for transient dynamic analysis of unconstrained layer damping beams involving fractional derivative models

This paper presents a homogenised finite element formulation for the transient dynamic analysis of asymmetric and symmetric unconstrained layer damping beams in which the viscoelastic material is characterised by a five-parameter fractional derivative model. This formulation is based on the weighted residual method (Galerkin’s approach) providing a fractional matrix equation of motion. The application of Grünwald-Letnikov’s definition of the fractional derivatives allows to solve numerically the fractional equation by means of two different implicit formulations. Numerical examples for a cantilever beam with viscoelastic treatment are presented comparing the response provided by the proposed homogenised formulation with that of Padovan, based on the principle of virtual work. Different damping levels and load cases are analysed, as well as the influence of the truncation and time-step. From the numerical applications it can be concluded that the presented formulation allows to reduce significantly the degrees of freedom and consequently the computational time and storage needs for the transient dynamic analysis of structural systems in which damping treatments have been applied by means of viscoelastic materials characterised by fractional derivative models.     

简谐激励下共固化复合材料粘弹阻尼结构的损耗因子研究

基于模态叠加法和模态应变能法,推导出在任意简谐激励下粘弹阻尼结构的损耗因子的计算方法,并采用这种方法分析了共固化复合材料粘弹阻尼结构在简谐激励下的损耗因子.分析结果与动态机械分析仪(DMA)实测结果基本吻合,从而验证了本文建立方法的有效性,对粘弹阻尼结构的损耗因子的分析以及共固化复合材料粘弹阻尼结构的设计和应用具有一定的参考价值.     

具有分数导数本构关系的粘弹性浅拱的非线性动力学行为

利用分数导数本构模型描述材料的粘弹性特性,建立了粘弹性浅拱在横向荷载作用下的动力学方程。利用Galerkin截断法并结合边界条件分别得到了一阶和二阶Galerkin系统的控制微分方程。通过数值计算,分析了简谐激励下一阶Galerkin系统的非线动力学行为。研究表明:随着外激励幅值的变化,粘弹性浅拱系统可以通过倍周期分岔或阵发性两条路径进入混沌;固定外激励幅值、频率以及阻尼系数等状态参数,不同初始条件下,系统可以出现多周期解共存、周期解与混沌解共存的现象。     

Mechanics based model for predicting structure-induced rolling resistance (SRR) of the tire-pavement system

The structure-induced rolling resistance of pavements, and its impact on vehicle fuel consumption, is investigated in this study. The structural response of pavement causes additional rolling resistance and fuel consumption of vehicles through deformation of pavement and various dissipation mechanisms associated with inelastic material properties and damping. Accurate and computationally efficient models are required to capture these mechanisms and obtain realistic estimates of changes in vehicle fuel consumption. Two mechanistic-based approaches are currently used to calculate vehicle fuel consumption as related to structural rolling resistance: dissipation-induced and deflection-induced methods. The deflection-induced approach is adopted in this study, and realistic representation of pavement–vehicle interactions (PVIs) is incorporated. In addition to considering viscoelastic behavior of asphalt concrete layers, the realistic representation of PVIs in this study includes non-uniform three-dimensional tire contact stresses and dynamic analysis in pavement simulations. The effects of analysis type, tire contact stresses, pavement viscoelastic properties, pavement damping coefficients, vehicle speed, and pavement temperature are then investigated.     

基于混合分层理论的粘弹层合圆柱壳的阻尼振动和层间应力研究

应用混合分层理论,并在壳厚方向采用位移和应力插值函数推导出粘弹层合圆柱壳的动力学方程。计算了两层粘弹层合圆柱壳的振动频率和结构损耗因子,与Okazaki A的结果吻合良好。针对不同模量和厚度的粘弹性材料,计算出层合圆柱壳的层间横向应力的幅值。结果表明:过大的层间法向正应力是导致自由阻尼层合壳脱层破坏的主要因素,采用环向加强的粘弹性材料将有效地降低层间法向正应力的幅值。     

Harmonic wave propagation in viscoelastic heterogeneous materials Part I: Dispersion and damping relations

An analytico-numerical method is presented to study the propagation of plane harmonic waves in infinite periodic linear viscoelastic media. Part I considers only the dispersion and attenuation of acoustical longitudinal and shear waves. To show the accuracy of the method, examples of plane harmonic wave propagation in an infinite homogeneous medium and in a periodic layered viscoelastic medium are presented. The method is then used to calculate the damping and dispersion relations for a fibre-reinforced viscoelastic composite material. The results show clearly the influence of materials' viscoelastic properties and heterogeneities on the propagation of plane harmonic waves through the media.     

阻尼材料对环肋柱壳稳态响应影响的分析

利用Ｆｌｕｇｇｅ壳体理论，讨论了敷设自由层粘弹性阻尼材料的环肋柱壳受周期性径向激励的稳态响应，用复模量形式计及基壳和粘弹性阻尼材料的损耗因子，并计入流固耦合作用，讨论了粘弹性阻尼材料的物理参数和厚度对其稳态响应的影响。     

Probabilistic analysis of delamination onset in linear anisotropic elastic and viscoelastic composite columns

Previously developed deterministic and stochastic combined load invariant failure criteria are used to determine the onset of delamination in elastic and viscoelastic columns. The analysis includes the effects of initial imperfections as well as offset column loads and transverse shear contributions. The delamination predictions are found to be sensitive to the magnitude of applied loads and of initial imperfections. Illustrative numerical examples are presented for elastic and viscoelastic columns with random combined failure stresses in bending, shear, compression and with normal interlaminar stresses. Probabilities of delamination onset are established for various axial loads and initial imperfections and in the viscoelastic columns additionally as a function of lifetime. Since the failure theories consider the combined effects of bending, shear, compression and normal interlaminar stresses, delamination onset is predicted at smaller axial loads than the critical buckling loads in the elastic case and at shorter viscoelastic lifetimes compared to equivalent columns with no delamination effects.     

纤维增强复合材料身管阻尼特性分析

针对火炮发射时纤维增强复合材料身管的阻尼效应,根据粘弹性材料动态特性,给出了纤维增强复合材料能量耗散公式,采用基于有限元技术的模态应变能分析方法,对某口径复合材料身管进行了阻尼特性分析,获得了该复合材料身管在各阶固有频率下的应变能和阻尼损耗因子,为复合材料身管的动态特性分析提供了阻尼特性参数.     

空间桁架结构采用黏弹性阻尼的振动控制技术

航天器空间桁架结构在太空特殊物理环境下的振动控制问题是航天技术中的一大难题,为探讨阻尼被动控制技术的有效程度。首先从理论上分析黏弹性材料（VEM）的阻尼作用机理,由此设计一种双夹层圆柱式黏弹性阻尼器（VED）,研究VED阻尼杆在桁架中的最佳位置配置问题,并推导阻尼桁架结构的动力学方程,结合VEM的阻尼特性分析结构的动态品质。最后以一字型桁架为例,对VED阻尼被动控制效果进行仿真分析,结果显示在共振区内桁架的振幅衰减达35 %,可取得良好的控制效果。