附加阻尼结构的理论分析与设计方法

附加阻尼处理结构的理论分析与设计方法吕毅宁（lvyining@）附加阻尼处理结构的理论分析与设计方法 (1)1概述 (1)2基本理论 (2)3阻尼材料及其特性 (3)4分析方法 (3)4.1复刚度法 (4)4.2变形能法 (4)4.3模态分析法和有限元法 (4)4.3.1粘弹性结构的有限元建模方法及比较 (5)4.3.2粘弹性结构动力问题的有限元分析概述 (7)4.3.3弹性—粘弹性复合结构的有限元模型和动力学方程 (11)4.3.4复合结构的有限元动力方程的求解方法——稳态、瞬态 (17)4.4粘弹性材料本构模型 (18)4.5表面阻尼处理简单结构元件的分析方法 (20)4.6表面阻尼处理复杂结构的分析方法 (20)5自由阻尼结构的设计 (20)5.1参数优化设计 (20)5.2拓扑（布置）优化设计 (21)6粘弹性阻尼在汽车中的应用 (21)6.1概述 (21)6.2约束阻尼层新技术2—conformal constrained layer damping (23)6.3自由阻尼层新技术 (23)6.4约束阻尼层新技术2—laminated vibration damped steel (23)6.5车身底板的阻尼处理技术 (24)6.6其它结构阻尼处理技术 (30)7表面阻尼处理材料和结构产品供应商 (32)7.1表面阻尼处理材料 (32)7.2约束阻尼处理结构 (34)1 概述表面阻尼处理是提高结构阻尼、抑制共振、改善结构抗振降噪性能的有效方法之一。

这种技术已经广泛应用于航空航天、交通运输、轻工纺织等行业。

表面阻尼处理主要应用于以弯曲振动为主的薄壁零件，例如梁类、板类、管壳类结构件等。

表面阻尼处理方法包括两类，即自由阻尼处理和约束阻尼处理。

自由阻尼结构的理论分析方法有复刚度法、变形能法、模态分析法和有限元法。

通过分析主要是得到结构损耗因子。

由于约束阻尼结构的耗能效率较高，因此目前该领域的研究工作主要集中在约束阻尼结构的建模、分析和优化设计上。

采用的主要的建模分析方法是有限元法。

采用的有限元软件主要是NASTRAN。

满足特殊需要而自主开发有限元软件的情况很多，主要是为了计算结构的损耗因子。

求解阻尼结构的振动问题的有限元方法主要包括三种，即复特征值方法、模态应变能方法和直接频率响应方法。

2 基本理论表面阻尼处理方法包括两类，即自由阻尼处理（Unconstrained-Layer Treatment）和约束阻尼处理（Constrained-Layer Treatment），基本结构如图1所示。

自由阻尼处理结构中，当自由阻尼层（Free Damping Layer）随着基本结构一起弯曲振动时，主要通过拉、压变形而损耗能量，故也被称为拉伸型阻尼处理（Extensional Damping Treatment）；而约束阻尼层（Constrained Damping Layer）随结构一起弯曲振动时，由于约束层（Constrained Layer）的限制，主要发生剪切变形而损耗能量，所以又被称为剪切型阻尼处理（Shear Damping Treatment）。

通常拉伸阻尼耗能远远小于剪切耗能，因此约束阻尼处理的效果要优于自由阻尼处理，但是自由阻尼处理的工艺较简单、成本较低。

因此，在实际工程应用中，两种方法都很普遍。

a) 自由阻尼处理结构b) 约束阻尼处理结构图1 表面阻尼处理结构示意图表1 自由阻尼处理和约束阻尼处理方法的比较3. Damping treatmentsViscoelastic materials have been used to enhance the damping in a structure in three different ways: free-layer damping treatment, constrained-layer or sandwich-layer damping treatment and tunedviscoelastic damper. Although these designs have been around for over 40 years, recent improvements in the understanding and application of the damping principles, together with advances in materials science and manufacturing have led to many successful applications. The key point in any design is to recognize that the damping material must be applied in such a way that it is significantly strained whenever the structure is deformed in the vibration mode under investigation.3.1. Free-layer damping (FLD)Fig. 2 illustrates a portion of a structure with a free-layer or sometimes called extensional type damping treatment. The damping material is either sprayed on the structure or bonded using a pressure-sensitive adhesive. Examples include undercoating of an automobile and application of mastics（乳香，胶合铺料）to body and floor panels to provide damping. When the base structure is deflected in bending, the viscoelastic material deforms primarily in extension and compression in planes parallel to the base structure. The hysteresis loop of the cyclic stress and strain dissipates the energy. The degree of damping is limited by thickness and weight restrictions. The vibration analysis of a beam with a viscoelastic layer was first conducted by Kerwin and colleagues [10,11]. The viscoelastic characteristic of the material was modelled using the complex modulus approach. The system loss factor in a free-layer system increases with the thickness, storage modulus, and loss factor of the viscoelastic layer. Another interesting feature of the free layer treatment is that the damping performance is independent of the mode shape of vibration for full coverage by the viscoelastic layer. It is however, possible to optimize partial coverage for a particular mode or a limited number of modes [12,13].3 阻尼材料及其特性附加阻尼处理中采用的阻尼材料通常为粘弹性阻尼材料。

粘弹性阻尼材料兼有粘性和弹性两方面的特性。

阻尼材料的温频相关性。

阻尼材料的温频叠加原理。

阻尼材料的数学模型表示。

阻尼材料动态性能的测定。

4 分析方法自由阻尼结构的理论分析：复刚度法、变形能法、模态分析法和有限元法。

4.1 复刚度法表面阻尼处理结构主要是指表面阻尼处理的弯曲振动的结构。

复刚度法假设表面阻尼处理结构满足如下变形假设：1、 阻尼层与弹性层在弯曲振动时具有相同曲率（直平面/直法线假设）；2、 各层具有相同的振动模态，忽略振动过程中各层厚度的变化； 基于以上假设，对于梁、板类结构，其复弯曲刚度为)1()()()(*ηj EI EI j EI B +'=''+'=)()('''=EI EI η称为损耗因子，反映了结构振动时能量损耗能力的大小。

4.2 变形能法结构振动时，各个子结构的最大变形能分别为i W ，在一个振动周期内的阻尼耗能分别为i s D )(，则结构的损耗因子定义为∑∑=iiiis WD πη2)(如果已经知道各个子结构的损耗因子分别为i η，则：1、 各个子结构在一个振动周期内的阻尼耗能分别为i i i s W D πη2)(=2、 整体结构的损耗因子为∑∑=ii iii WW ηη4.3 模态分析法和有限元法模态分析法和有限元法适用于各种复杂结构。

1、 利用有限元法分析计算结构的刚度矩阵和质量矩阵2、 利用模态参数计算结构的模态变形能3、 利用能量法计算各阶模态的损耗因子（模态阻尼比）用有限元法分析阻尼结构有两种建模方法：一种是分层划分单元，将上下表面金属层和阻尼层分别划为板壳单元和体单元，层与层之间只在节点处协调，优点是可用现成的商用软件MSC/NASTRAN、SAP等求解，缺点是单元自由度高，求解费时。

二是整体划分单元，把约束层、阻尼层、基体层看成一个整体，这能更好地体现出阻尼结构各层之间协调关系，并有自由度少、运算省时、精度高等优点。

文献[杨莉、孙庆鸿，2004]采用整体划分单元法建立了自由阻尼板的有限元模型，并在用有限元法进行结构动态特性分析的基础上，预测了结构的声辐射。

4.3.1 粘弹性结构的有限元建模方法及比较方法1：Finite element representation of laminated metal. Steel laminate skins are modeled with offset shell elements. Adhesive laminate core is modeled with solid elements.方法2：Rigid links between the shell nodes and the volume element are used instead of defining offsets for shell elements.方法3：用梁单元建立粘弹性阻尼层的等效模型，可以提高模拟精度（JSV_1984，1992）4.3.2 粘弹性结构动力问题的有限元分析概述（瞬态响应分析、稳态响应分析）4.3.3 弹性—粘弹性复合结构的有限元模型和动力学方程【引用】4.3.4 复合结构的有限元动力方程的求解方法——稳态、瞬态【引用】4.4粘弹性材料本构模型Basic viscoelastic conceptsViscoelasticity may be defined as material response that exhibits characteristics of both a viscous fluid and an elastic solid. An elastic material such as a spring retracts to its original position when stretched and released, whereas a viscous fluid such as putty retains its extended shape when pulled. A viscoelastic material (VEM) combines these two properties—it returns to its original shape after being stressed, but does it slowly enough to oppose the next cycle of vibration.The degree to which a material behaves either viscously or elastically depends mainly on temperature and rate of loading (frequency). Many polymeric materials (plastics, rubbers, acrylics, silicones, vinyls, adhesives, urathanes, and epoxies, etc.) having long -chain molecules exhibit viscoelastic behavior. The dynamic properties (shear modulus, extensional modulus, etc.) of linear viscoelastic materials can be represented by the complex modulus approach. The introduction of complex modulus brings about a lot of convenience in studying the material properties of viscoelastic materials. The material properties of viscoelastic materials depend significantly on environmental conditions such as environmental temperature, vibration frequency, pre-load, dynamic load, environmental humidity and so on. Therefore, a good understanding of such effects, both separately and collectively, on the variation of the damping properties is necessary in order to tailor these materials for specific applications.1. Effects of temperatureThe temperature is perhaps the most important environmental factor affecting the dynamic properties of damping materials. This effect is shown in Fig. 1 for a typical polymeric material having four distinct regions. The first region is the glassy state where the material has very large storage modulus (dynamic stiffness) but very low damping. The storage modulus in this region changes slowly with temperature, while the loss factor changes significantly with increasing temperature. In the transition region where the material changes from a glassy state to a rubbery state, the material modulus decreases rapidly with increasing temperature because of softening of the material that increases loss factor. The damping usually peaks at or around the glass transition temperature of the material. Some polymers can be made to have more than one transition region by changing the polymeric structure and composition to take advantage of the peak damping capacity in this region. In the rubbery state both modulus and loss factor take somewhat low values and vary very slowly with temperature. The flow region is typical for a few damping materials such as vitreous enamels and thermoplastics, where the material continue to soften as temperature increases while loss factor reaches very high values.2. Effects of frequencyExperiments have shown that vibration frequency or the rate of loading has significant effect on the damping and dynamic modulus of viscoelastic materials. The variation of the modulus and loss factor of a typical high damping material with frequency over a range of three to five decades shows that for a material without the flow region, the effect of increasing temperature on the storage modulus is similar to the effect of reducing frequency. This behavior provides the basis for the temperature–frequency superposition principle that is used to transform material properties from the frequency domain to temperature domain, and vice versa [9].4.5表面阻尼处理简单结构元件的分析方法简单结构元件（Structural Elements）是指形状规则的简单结构，如均匀直梁、圆环、圆柱壳等结构。