附加阻尼結(jié)構(gòu)的理論分析與設(shè)計方法

1、1附加阻尼處理結(jié)構(gòu)的理論分析與設(shè)計附加阻尼處理結(jié)構(gòu)的理論分析與設(shè)計方法方法呂毅寧（）附加阻尼處理結(jié)構(gòu)的理論分析與設(shè)計方法附加阻尼處理結(jié)構(gòu)的理論分析與設(shè)計方法.11概述.12基本理論.23阻尼材料及其特性.34分析方法.34.1復(fù)剛度法.44.2變形能法.44.3模態(tài)分析法和有限元法.44.3.1粘彈性結(jié)構(gòu)的有限元建模方法及比較.54.3.2粘彈性結(jié)構(gòu)動力問題的有限元分析概述.64.3.3彈性粘彈性復(fù)合結(jié)構(gòu)的有限元模型和動力學(xué)方程.124.3.4復(fù)合結(jié)構(gòu)的有限元動力方程的求解方法穩(wěn)態(tài)、瞬態(tài).174.4粘彈性材料本構(gòu)模型.184.5表面阻尼處理簡單結(jié)構(gòu)元件的分析方法.204.6表面阻尼處理復(fù)雜結(jié)構(gòu)

2、的分析方法.205自由阻尼結(jié)構(gòu)的設(shè)計.205.1參數(shù)優(yōu)化設(shè)計.205.2拓?fù)洌ú贾茫﹥?yōu)化設(shè)計.216粘彈性阻尼在汽車中的應(yīng)用.216.1概述.216.2約束阻尼層新技術(shù)2conformal constrained layer damping.236.3自由阻尼層新技術(shù).236.4約束阻尼層新技術(shù)2laminated vibration damped steel .236.5車身底板的阻尼處理技術(shù).246.6其它結(jié)構(gòu)阻尼處理技術(shù).307表面阻尼處理材料和結(jié)構(gòu)產(chǎn)品供應(yīng)商.327.1表面阻尼處理材料.327.2約束阻尼處理結(jié)構(gòu).341 概述概述表面阻尼處理是提高結(jié)構(gòu)阻尼、抑制共振、改善結(jié)構(gòu)抗振降噪性

3、能的有效方法之一。這種技術(shù)已經(jīng)廣泛應(yīng)用于航空航天、交通運輸、輕工紡織等行業(yè)。表面阻尼處理主要應(yīng)用于以彎曲振動為主的薄壁零件，例如梁類、板類、管殼類結(jié)構(gòu)件等。表面阻尼處理方法包括兩類，即自由阻尼處理和約束2阻尼處理。自由阻尼結(jié)構(gòu)的理論分析方法有復(fù)剛度法、變形能法、模態(tài)分析法和有限元法。通過分析主要是得到結(jié)構(gòu)損耗因子。由于約束阻尼結(jié)構(gòu)的耗能效率較高，因此目前該領(lǐng)域的研究工作主要集中在約束阻尼結(jié)構(gòu)的建模、分析和優(yōu)化設(shè)計上。采用的主要的建模分析方法是有限元法。采用的有限元軟件主要是NASTRAN。滿足特殊需要而自主開發(fā)有限元軟件的情況很多，主要是為了計算結(jié)構(gòu)的損耗因子。求解阻尼結(jié)構(gòu)的振動問題的有限元方

4、法主要包括三種，即復(fù)特征值方法、模態(tài)應(yīng)變能方法和直接頻率響應(yīng)方法。2 基本理論基本理論表面阻尼處理方法包括兩類，即自由阻尼處理（Unconstrained-Layer Treatment）和約束阻尼處理（Constrained-Layer Treatment） ，基本結(jié)構(gòu)如圖 1 所示。自由阻尼處理結(jié)構(gòu)中，當(dāng)自由阻尼層（Free Damping Layer）隨著基本結(jié)構(gòu)一起彎曲振動時，主要通過拉、壓變形而損耗能量，故也被稱為拉伸型阻尼處理（Extensional Damping Treatment） ；而約束阻尼層（Constrained Damping Layer）隨結(jié)構(gòu)一起彎曲振動時，由于

5、約束層（Constrained Layer）的限制，主要發(fā)生剪切變形而損耗能量，所以又被稱為剪切型阻尼處理（Shear Damping Treatment） 。通常拉伸阻尼耗能遠(yuǎn)遠(yuǎn)小于剪切耗能，因此約束阻尼處理的效果要優(yōu)于自由阻尼處理，但是自由阻尼處理的工藝較簡單、成本較低。因此，在實際工程應(yīng)用中，兩種方法都很普遍。a) 自由阻尼處理結(jié)構(gòu)b) 約束阻尼處理結(jié)構(gòu)圖 1 表面阻尼處理結(jié)構(gòu)示意圖表 1 自由阻尼處理和約束阻尼處理方法的比較自由阻尼處理自由阻尼處理約束阻尼處理約束阻尼處理結(jié)構(gòu)組成結(jié)構(gòu)組成薄壁結(jié)構(gòu)件自由阻尼層薄壁結(jié)構(gòu)件約束阻尼層約束層（薄鐵皮或者鋁片）耗能機(jī)理耗能機(jī)理阻尼層的拉壓變形阻尼

6、層的剪切和拉壓變形優(yōu)點優(yōu)點工藝較簡單、成本較低耗能效果好缺點缺點耗能效果較差3. Damping treatmentsViscoelastic materials have been used to enhance the damping in a structure in three different ways: free-3layer damping treatment, constrained-layer or sandwich-layer damping treatment and tuned viscoelastic damper. Although these designs h

7、ave 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

8、 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 materia

9、l 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，膠合鋪料） to body and floor panels to provide damping. When the base structure is deflected in bending, the viscoelastic material deforms prima

10、rily 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

11、 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

12、 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 阻尼材料及其特性阻尼材料及其特性附加阻尼處理中采用的阻尼材料通常為粘彈性阻尼材料。粘彈

13、性阻尼材料兼有粘性和彈性兩方面的特性。阻尼材料的溫頻相關(guān)性。阻尼材料的溫頻疊加原理。阻尼材料的數(shù)學(xué)模型表示。阻尼材料動態(tài)性能的測定。4 分析方法分析方法自由阻尼結(jié)構(gòu)的理論分析：復(fù)剛度法、變形能法、模態(tài)分析法和有限元法。44.1復(fù)剛度法復(fù)剛度法表面阻尼處理結(jié)構(gòu)主要是指表面阻尼處理的彎曲振動的結(jié)構(gòu)。復(fù)剛度法假設(shè)表面阻尼處理結(jié)構(gòu)滿足如下變形假設(shè)：1、 阻尼層與彈性層在彎曲振動時具有相同曲率（直平面/直法線假設(shè)） ；2、 各層具有相同的振動模態(tài)，忽略振動過程中各層厚度的變化；基于以上假設(shè)，對于梁、板類結(jié)構(gòu)，其復(fù)彎曲剛度為)1 ()()()(*jEIEIjEIB 稱為損耗因子，反映了結(jié)構(gòu)振動時能量損耗能

14、力的大小。)()( EIEI4.2變形能法變形能法結(jié)構(gòu)振動時，各個子結(jié)構(gòu)的最大變形能分別為，在一個振動周期內(nèi)的阻尼耗能分別為，則iWisD )(結(jié)構(gòu)的損耗因子定義為iiiisWD2)(如果已經(jīng)知道各個子結(jié)構(gòu)的損耗因子分別為，則：i1、 各個子結(jié)構(gòu)在一個振動周期內(nèi)的阻尼耗能分別為iiisWD2)(2、 整體結(jié)構(gòu)的損耗因子為iiiiiWW4.3模態(tài)分析法和有限元法模態(tài)分析法和有限元法模態(tài)分析法和有限元法適用于各種復(fù)雜結(jié)構(gòu)。1、 利用有限元法分析計算結(jié)構(gòu)的剛度矩陣和質(zhì)量矩陣2、 利用模態(tài)參數(shù)計算結(jié)構(gòu)的模態(tài)變形能3、 利用能量法計算各階模態(tài)的損耗因子（模態(tài)阻尼比）5用有限元法分析阻尼結(jié)構(gòu)有兩種建模方法

15、：一種是分層劃分單元，將上下表面金屬層和阻尼層分別劃為板殼單元和體單元，層與層之間只在節(jié)點處協(xié)調(diào)，優(yōu)點是可用現(xiàn)成的商用軟件MSC/NASTRAN、SAP 等求解，缺點是單元自由度高，求解費時。二是整體劃分單元，把約束層、阻尼層、基體層看成一個整體，這能更好地體現(xiàn)出阻尼結(jié)構(gòu)各層之間協(xié)調(diào)關(guān)系，并有自由度少、運算省時、精度高等優(yōu)點。文獻(xiàn)楊莉、孫慶鴻，2004采用整體劃分單元法建立了自由阻尼板的有限元模型，并在用有限元法進(jìn)行結(jié)構(gòu)動態(tài)特性分析的基礎(chǔ)上，預(yù)測了結(jié)構(gòu)的聲輻射。4.3.1粘彈性結(jié)構(gòu)的有限元建模方法及比較粘彈性結(jié)構(gòu)的有限元建模方法及比較方法 1：Finite element representa

16、tion of laminated metal. Steel laminate skins are modeled with offset shell elements. Adhesive laminate core is modeled with solid elements.6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：用梁單元建立粘彈性阻尼層的等效模型，可以提高模擬精度（JSV_198

17、4，1992）74.3.2粘彈性結(jié)構(gòu)動力問題的有限元分析概述粘彈性結(jié)構(gòu)動力問題的有限元分析概述8910（瞬態(tài)響應(yīng)分析、穩(wěn)態(tài)響應(yīng)分析）114.3.3彈性彈性粘彈性復(fù)合結(jié)構(gòu)的有限元模型和動力學(xué)方程粘彈性復(fù)合結(jié)構(gòu)的有限元模型和動力學(xué)方程【引用】1213141516174.3.4復(fù)合結(jié)構(gòu)的有限元動力方程的求解方法復(fù)合結(jié)構(gòu)的有限元動力方程的求解方法穩(wěn)態(tài)、瞬態(tài)穩(wěn)態(tài)、瞬態(tài)【引用】184.4粘彈性材料本構(gòu)模型粘彈性材料本構(gòu)模型Basic viscoelastic conceptsViscoelasticity may be defined as material response that exhibits

18、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 propertiesi

19、t 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, acr

20、ylics, 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 co

21、mplex 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, environmen

22、tal 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.191. Effects of temperatureThe temperature is perhaps the most important env

23、ironmental 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

24、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 beca

25、use 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 da

26、mping 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 in

27、creases 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

28、 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 temperaturefrequency superposition pr

29、inciple that is used to transform material properties from the frequency domain to temperature domain, and vice versa 9.204.5表面阻尼處理簡單結(jié)構(gòu)元件的分析方法表面阻尼處理簡單結(jié)構(gòu)元件的分析方法簡單結(jié)構(gòu)元件（Structural Elements）是指形狀規(guī)則的簡單結(jié)構(gòu)，如均勻直梁、圓環(huán)、圓柱殼等結(jié)構(gòu)。上述三種結(jié)構(gòu)元件是目前最廣泛深入研究的對象。通常采用復(fù)剛度法進(jìn)行分析。需要建立結(jié)構(gòu)的控制方程，通過適當(dāng)?shù)倪吔缭O(shè)定求得封閉的解析解。采用有限元方法對上述結(jié)構(gòu)元件進(jìn)行分析的研究

30、也有很多，主要是用來提出和驗證新的有限元建模方法。4.6表面阻尼處理復(fù)雜結(jié)構(gòu)的分析方法表面阻尼處理復(fù)雜結(jié)構(gòu)的分析方法對于復(fù)雜結(jié)構(gòu)，主要是由于幾何結(jié)構(gòu)的復(fù)雜性，無法建立結(jié)構(gòu)的控制方程。因此，目前只能采用基于有限元分析的應(yīng)變能方法對其進(jìn)行求解。求解方法包括三種，即復(fù)特征值方法、模態(tài)應(yīng)變能方法和直接頻率響應(yīng)方法。建模分析軟件主要采用 NASTRAN。5 自由阻尼結(jié)構(gòu)的設(shè)計自由阻尼結(jié)構(gòu)的設(shè)計5.1參數(shù)優(yōu)化設(shè)計參數(shù)優(yōu)化設(shè)計變量：阻尼層的厚度、模量。優(yōu)化設(shè)計目標(biāo)：輕量化、最大損耗因子。215.2拓?fù)洌ú贾茫﹥?yōu)化設(shè)計拓?fù)洌ú贾茫﹥?yōu)化設(shè)計變量：阻尼層在結(jié)構(gòu)上的的分布。優(yōu)化設(shè)計目標(biāo)：輕量化、最大損耗因子。6 粘

31、彈性阻尼在汽車中的應(yīng)用粘彈性阻尼在汽車中的應(yīng)用Ref：Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes By Rao.Passive damping as a technology has been dominant in the non-commercial aerospace industry since the early 1960s. Advances in the material technology along with new

32、er and more efficient analytical and experimental tools for modeling the dynamical behavior of materials and structures have led to many applications such as inlet guide vanes of jet engines, helicopter cabins, exhaust stacks, satellite structures, equipment panels, antenna structures, truss systems

33、, and space stations, etc.The use of surface damping treatments in the automotive, commercial airplane, appliance and other industries has only been in recent years. The eventual application into these industries is made possible by the advancement in manufacturing processes which are cost-effective

34、 and are suitable for high volume production. Multilayer damped laminates consisting of two metal skins with a viscoelastic core can now be manufactured by a continuous process in coil form using existing equipment and technology rather than by the conventional laminating press procedure.6.1概述概述Redu

35、ction of interior noise and vibration in passenger vehicles is a major requirement for Achieving world-class vehicle quality, performance and customer satisfaction. Noise, vibration and harshness (NVH) is being considered as a design parameter in the design of current and future generation of vehicl

36、es. Automotive interior noise usually arises from the transmission of vibration energy of different systems such as engine, power train, climate control systems and road inputs, etc., into the vehicle via various paths (engine mounts, suspensions, body panels, and floor panels, etc.). The vibration

37、of these elements is responsible for about 90% of the harshness-related acoustical energy in the automotive interior.22236.2約束阻尼層新技術(shù)約束阻尼層新技術(shù) 2conformal constrained layer dampingThe adhesion of constrained-layer damping to complex contours such as ribs is also an issue which is somewhat overcome with

38、 conformal constrained layer (CCL) type damping treatments. The CCL is basically a constrained-layer damping tape that can be bent or shaped to conform to the contour of the base structure. 6.3自由阻尼層新技術(shù)自由阻尼層新技術(shù)A new class of extensional damping treatment in the form of spray dampers have emerged as a

39、ttractive candidates for floor panels 17,18. The sprayable type has a cost-advantage since it can be robotically applied thus allowing the placement of the material at selected locations. Sprayable dampers, however require significant up-front capital costs associated with pumping and robotic equipm

40、ent. Fig. 7(a) shows the application of a recent water-based spray damper made of acrylic elastomers for floor panel applications. These dampers, supplied in large cans, are robotically sprayed to floor panels and wheelhouses to thicknesses between 1 and 3mm and cured in an oven. The data shown in F

41、ig. 7(b) shows the effectiveness of applying spray damper to a vehicle floor panel when compared to the same panel with no damping treatment.6.4約束阻尼層新技術(shù)約束阻尼層新技術(shù) 2laminated vibration damped steelCurrently efforts are underway to use a new laminated vibration damped steel (LVDS) for dash panel applica

42、tion. These LVDS structures are being designed with the aid of computer aided engineering (CAE) to reduce both air- and structure-borne powertrain noises into the interior. This is basically a designed-in damping concept of replacing the original panel with new damping panel (instead of add-on treat

43、ments) similar to damped powertrain components shown in Table 1. Significant improvement in interior sound quality was noticed with these dash panels as evidenced by lower values of measured interior loudness and articulation index 19. Fig. 8 shows one design of a dash panels using LVDS.24SAE Techni

44、cal Papers Title:Title: Laminate Dash Ford Taurus Noise and Vibration Performance6.5車身底板的阻尼處理技術(shù)車身底板的阻尼處理技術(shù)1、SD-Tools 設(shè)計車身底板的阻尼處理：25262、Quiet Steel DAMP 設(shè)計車身底板的阻尼處理：272829306.6其它結(jié)構(gòu)阻尼處理技術(shù)其它結(jié)構(gòu)阻尼處理技術(shù)31327 表面阻尼處理材料和結(jié)構(gòu)產(chǎn)品供應(yīng)商表面阻尼處理材料和結(jié)構(gòu)產(chǎn)品供應(yīng)商7.1表面阻尼處理材料表面阻尼處理材料公司常州市蘭陵橡膠廠航天部北京材料工藝研究所無錫減振器廠南洋阻尼材料廠美國 3M 公司美國 EA

45、R 公司美國 SoundCoat Co.常州市蘭陵橡膠廠：阻尼材料阻尼材料33 類型：自粘型、熱融型、復(fù)合型和磁性阻尼材料 我廠生產(chǎn)的粘彈性阻尼材料，已廣泛應(yīng)用于航天航空、汽車、家用電器、工程機(jī)械，起減振降噪作用。材料主要與上海大眾，上海通用，南京依維柯等公司配套，用于汽車底板、車門、側(cè)面及頂蓬等部位，使用效果很好，其主要性能指標(biāo)達(dá)國內(nèi)領(lǐng)先水平。該產(chǎn)品根據(jù)用戶要求可加工成各種形狀和不同厚度，使用安裝簡單方便，適宜于大規(guī)模和流水線作業(yè)。 347.2約束阻尼處理結(jié)構(gòu)約束阻尼處理結(jié)構(gòu)公司網(wǎng)址Quiet SDLVDSQuiet Steel：QUIET STEELQuiet Steel is a sui

46、te of engineered multilayer composites with various viscoelastic cores among layers of metal. These 100% recyclable laminated steel materials offer significant cost reduction opportunities and enhanced Noise, Vibration, and Harshness (NVH) performance characteristics. Each Quiet Steel material is de

47、signed specifically to meet the damping, temperature, stiffness and operating environment needs of its intended component. In simpler terms, Quiet Steel is engineered quiet.Click here (plates005.swf)to for an audio demo and to learn more about how Quiet Steel technology works. MSCs multilayer materi

48、als are used in a variety of industries. Quiet Steel is 35MSCs trade name for its suite of multilayer materials engineered for automotive applications. MSCs multiple viscoelastic core variations and layered constructions, however, have yielded similar materials with different names for other industr

49、ies. MSCs Consumer & Industrial material family is called Sound Trap and the Electronic and Electrical equivalent is named NRG Damp. MSC offers numerous additional material solutions for these industries.HOW QUIET STEEL WORKS.The dramatic reductions in noise and vibration in sheet metal panels m

50、ade from Quiet Steel are due to the very high levels of dampingdamping inherent in the material. The effect of dampingdamping is to reduce the vibration amplitude of a system which is being excited at, or near its resonant frequency.Since it is the vibration of a panel that generates radiated noise,

51、 the reduction in vibration amplitude due to damping directly leads to reduced noise radiated from the panel. But hearing is believing. Click the Quiet Steel logo below to hear the difference between Quiet Steel and standard steel.36A typical sheet metal panel has many resonances and the resulting v

52、ibration response has many “peaks” at these resonances. The effect of Quiet Steel on a typical steel panel is dramatic as can be seen below:Click here to learn more about our Automotive Energy Management materials.AUTOMOTIVE QUIETQUIET STEELSTEELMSC Engineered Materials and Solutions Groups core bus

53、iness centers on our proprietary continuous coil coating and constrained layer laminating processes. Quiet Steel is one of our unique families of Noise, Vibration, and Harshness (NVH) damping materials and can be provided as continuous coil or in blanked sheets. Each material is designed specificall

54、y to meet the damping, temperature, stiffness and operating environment needs of its intended vehicle component. Learn more about how Quiet Steel works in our technology section.37ENERGY MANAGEMENT MATERIALSQUIET STEELMSC Engineered Materials and Solutions Groups core business centers on our proprie

55、tary continuous coil coating and constrained layer laminating processes. Quiet Steel is one of our unique families of Noise, Vibration, and Harshness (NVH) damping materials and can be provided as continuous coil or in blanked sheets. Each material is designed specifically to meet the damping, temperature, stiffness