分数导数三参数标准固体黏弹性材料的耗散性能
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摘要
对分数导数三参数黏弹固体性材料的耗散性能进行了研究.基于黏弹性理论和分数阶导数理论,建立了分数导数黏弹性三参数标准固体模型,得到了分数导数黏弹性三参数固体模型的复柔量,并在此基础上得到了其耗损比和内摩擦角,以数值算例的形式分析了耗损比和内摩擦角随频率的变化规律.结果表明:在低频下的材料接近弹性材料;相反,在高频下,在每个周期有一个微小的耗散,并且趋近于一个有限值.频率越高,三参数固体的内耗频谱峰值所对应的横坐标值越接近1.
The dissipative properties of fractional derivative three-parameter standard solid model were investigated. Fractional derivative three-parameter viscoelastic standard solid model was established base on the viscoelastic theory and the theory of fractional derivative,the compliance of fractional derivative three-parameter viscoelastic solid model was calculated,then its loss ratio and angle of internal friction angel were worked out. Finally,in the form of numerical calculation,the changing characteristics of loss ratio and internal friction's angle with the frequency were analyzed. The results showed that the materials were close to the elastic material under low frequency. On the contrary,the materials have a tiny dissipation in each cycle and tend to a finite value under high frequency. The abscissa value of three-parameter solid's peak internal friction approximates to one with higher frequency.
The dissipative properties of fractional derivative three-parameter standard solid model were investigated. Fractional derivative three-parameter viscoelastic standard solid model was established base on the viscoelastic theory and the theory of fractional derivative,the compliance of fractional derivative three-parameter viscoelastic solid model was calculated,then its loss ratio and angle of internal friction angel were worked out. Finally,in the form of numerical calculation,the changing characteristics of loss ratio and internal friction's angle with the frequency were analyzed. The results showed that the materials were close to the elastic material under low frequency. On the contrary,the materials have a tiny dissipation in each cycle and tend to a finite value under high frequency. The abscissa value of three-parameter solid's peak internal friction approximates to one with higher frequency.
引文
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[2]茅人杰.正交异性黏弹性材料的比阻尼和复模量[J].复合材料学报,1987,4(4):8-17.MAO Renjie.Specific damping and complex moduli of viscoelastic orthotropic materials[J].Acta Materiae Compositae Sinica,1987,4(4):8-17.
[3]杨加明,钟小丹,赵艳影.复合材料夹杂双层黏弹性材料的应变能和阻尼性能分析[J].工程力学,2010,27(3):212-216.YANG Jiaming,ZHONG Xiaodan,ZHAO Yanying.Strain energy and damping analysis of composite laminates with two interleaved viscoelastic layers[J].Engineering Mechanics,2010,27(3):212-216.
[4]任伟伟,李宏伟.基于波速法的黏弹性材料高频阻尼性能测试研究[J].材料开发与应用,2013,28(5):55-58.REN Weiwei,LI Hongwei.High frequencies damping performance testing research of viscoelastic materials based on wave-speed method[J].Development and Application of Materials,2013,28(5):55-58.
[5]陈立群.一类质量-黏弹性弹簧系统的简谐受迫振动[J].力学与实践,2001,23(5):49-51.CHEN Liqun.Harmonically forced vibrations of amass-viscoelastic spring system[J].Mechanics in Engineering,2001,23(5):49-51.
[6]刘林超,张卫.服从分数代数Maxwell本构模型的黏弹性阻尼材料性能分析[J].材料科学与工程学报,2004,22(6):860-862.LIU Linchao,ZHANG Wei.On the damping properties of viscoelastic materials modeled by fractional maxwell[J].Materials Science and Engineering,2004,22(6):860-862.
[7]孙海忠,张卫.服从分数导数Kelvin本构模型的黏弹性阻尼器的阻尼性能分析及试验研究[J].振动工程学报,2008,21(1):48-53.SUN Haizhong,ZHANG Wei.Analysis and experiment on damping properties of visco-elastic damper modeled by fractional Kelvin method[J].Journal of Vibration Engineering,2008,21(1):48-53.
[8]闫启方,陈哲,刘林超.分数阶Kelvin黏弹性材料的力学特性研究[J].机械科学与技术,2009,28(7):917-920.YAN Qifang,CHEN Zhe,LIU Linchao.Mechanical properties of viscoelastic materials described by franctional kelvin model[J].Mechanical Science and Technology for Aerospace Engineering,2009,28(7):917-920.
[9]段玮玮,闻敏杰,李强.饱和分数导数型黏弹性土层竖向振动放大效应[J].工程力学,2013,30(4):235-241.DUAN Weiwei,WEN Minjie,LI Qiang.Vertical vibration amplification of a saturated fractional derivative type viscoelastic soil layer[J].Engineering Mechanics,2013,30(4):235-241.
[10]赵永玲,侯之超.基于分数导数的橡胶材料两种黏弹性本构模型[J].清华大学学报(自然科学版),2013,53(3):378-383.ZHAO Yongling,HOU Zhichao.Two viscoelastic constitutive models of rubber materials using fractional derivations[J].Journal of Tsinghua University(Sci&Tech),2013,53(3):378-383.
[11]周光泉,刘晓敏.黏弹性理论[M].合肥:中国科学技术大学出版社,1996:19-69.ZHOU Guangquan,LIU Xiaomin.Theory of viscoelasticity[M].Hefei:Press of University of Science and Technology of China,1996:19-69.