结构阻尼时域本构模型及其应用
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摘要
阻尼合金作为一种新型结构功能材料在不少领域已获应用,由于其阻尼值较大且随频率呈复杂变化关系,传统的线性粘性阻尼理论或经典的非频变结构阻尼理论难以精确地描述其耗能行为。本文应用粘弹性阻尼理论,根据阻尼合金储能模量和损耗因子在频域的实测数据,应用最优化方法拟合出标准线性体模型中的本构参数;根据积分形式的三参量本构关系和变形体虚功原理,推导出了有限元形式的动力学方程;讨论了三参数初值的选取;对包含卷积积分的有限元动力学方程通过数学推导将其化为三阶线性微分方程组,再转化为标准状态变量方程,应用数值求解。数值计算实例证明了所提方法的正确和有效性。
As a kind of new structural and functional material, the damping alloy has been applied in many areas. Because the internal damping of damping alloy is high and varies nonlinearly with the vibration frequency, it is difficult to describe its energy dissipation behavior accurately by the viscous damping theory or classical structural damping model with constant loss factor. In this paper, the standard three parameters model of viscoelastic mechanics is introduced as the constitutive equation for damping alloy. Based on the experimental data of energy storage module and loss factor for a specific kind of damping alloy in a given frequency span, these three parameters are confirmed in using an optimization algorithm. The finite element dynamic equations are derived through the established three parameters constitution in integral form and the virtual work principle. The established finite element equations containing convolution integration are transformed into third order ordinary differential equations, and then to be transformed into standard state variable model. Numerical examples are given to show the effectiveness of the present method in studying dynamic characteristics of structure and machines containing damping alloy components.
As a kind of new structural and functional material, the damping alloy has been applied in many areas. Because the internal damping of damping alloy is high and varies nonlinearly with the vibration frequency, it is difficult to describe its energy dissipation behavior accurately by the viscous damping theory or classical structural damping model with constant loss factor. In this paper, the standard three parameters model of viscoelastic mechanics is introduced as the constitutive equation for damping alloy. Based on the experimental data of energy storage module and loss factor for a specific kind of damping alloy in a given frequency span, these three parameters are confirmed in using an optimization algorithm. The finite element dynamic equations are derived through the established three parameters constitution in integral form and the virtual work principle. The established finite element equations containing convolution integration are transformed into third order ordinary differential equations, and then to be transformed into standard state variable model. Numerical examples are given to show the effectiveness of the present method in studying dynamic characteristics of structure and machines containing damping alloy components.
引文
[1] 胡海岩.结构阻尼模型及系统时域动响应[J].应用力学学报,1993,10(1):34-43.(HuHaiyan.Structuraldampingmodelandsystem'stime-domaindynamicresponse[J].ChineseJournalofAppliedMechanics,1993,10(1):34-43.(inChinese))
[2] BertCW.Materialdamping:anintroductoryreviewofmathematicalmodels,measuresandexperimentaltechniques[J].JSound&Vib1973,29:129-135.
[3] 张忠明,刘宏昭,王锦程,等.材料阻尼及阻尼材料的研究进展[J].功能材料,2001,32(3):227-230.(ZhangZhongming,LiuHongzhao,WangJincheng,etal.Dampingofmaterialsandprogressinthedampingmaterials[J].ChineseJournalofFunctionalMaterials,2001,32(3):227-230.(inChinese))
[4] LagariasJC,ReedsJA,WrightMH,etal.Convergencepropertiesofthenelder-meadsimplexmethodinlowdimensions[J].SIAMJournalofOptimization,1998,9(1):112-147.
[5] 陈 前,朱德懋.弹性-粘弹性复合结构模态理论[J].固体力学学报,1990,11(1):23-33.(ChenQian,ZhuDemao.Modaltheoryofelastic-viscoelasticitycompositestructures[J].ActaMechanicaSolidaSinica,1990,11(1):23-33.(inChinese))
[6] 周正华,廖振鹏,丁海平.一种时域复阻尼本构方程.地震工程与工程振动,1999,19(2):37-44.(ZhouZhenghua,LiaoZhenpeng,DingHaiping.Atime-domaincomplex-dampingcostitutiveequation[J].EarthquakeEngineeringandEngineeringVibration,1999,19(2):37-44.(inChinese))
[7] MilneHK.Theimpulseresponsefunctionofasingledegreeoffreedomsystemwithhystereticdamping[J].JSound&Vib,1985,100:590-593.
[2] BertCW.Materialdamping:anintroductoryreviewofmathematicalmodels,measuresandexperimentaltechniques[J].JSound&Vib1973,29:129-135.
[3] 张忠明,刘宏昭,王锦程,等.材料阻尼及阻尼材料的研究进展[J].功能材料,2001,32(3):227-230.(ZhangZhongming,LiuHongzhao,WangJincheng,etal.Dampingofmaterialsandprogressinthedampingmaterials[J].ChineseJournalofFunctionalMaterials,2001,32(3):227-230.(inChinese))
[4] LagariasJC,ReedsJA,WrightMH,etal.Convergencepropertiesofthenelder-meadsimplexmethodinlowdimensions[J].SIAMJournalofOptimization,1998,9(1):112-147.
[5] 陈 前,朱德懋.弹性-粘弹性复合结构模态理论[J].固体力学学报,1990,11(1):23-33.(ChenQian,ZhuDemao.Modaltheoryofelastic-viscoelasticitycompositestructures[J].ActaMechanicaSolidaSinica,1990,11(1):23-33.(inChinese))
[6] 周正华,廖振鹏,丁海平.一种时域复阻尼本构方程.地震工程与工程振动,1999,19(2):37-44.(ZhouZhenghua,LiaoZhenpeng,DingHaiping.Atime-domaincomplex-dampingcostitutiveequation[J].EarthquakeEngineeringandEngineeringVibration,1999,19(2):37-44.(inChinese))
[7] MilneHK.Theimpulseresponsefunctionofasingledegreeoffreedomsystemwithhystereticdamping[J].JSound&Vib,1985,100:590-593.
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