黏弹性材料等效标准固体模型的时域延拓方法
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摘要
为了精确计算黏弹性阻尼器在任意荷载作用下的时域动力响应,提出了一种针对黏弹性材料等效标准固体模型的时域延拓方法.该方法首先将频域内的等效标准固体模型延拓到拉氏域内,再采用高精度拉氏逆变换数值求解方法将拉氏域表达式转换到时域,得到黏弹性阻尼器的时域动力响应.针对无锡减震器厂生产的9050A型号黏弹性阻尼材料的计算结果表明:在正弦激励下,采用时域延拓法计算的储能模量G_1的最大误差为0.005 4%,损耗因子η的最大误差为0.279 7%;在随机荷载激励下,相比于等效线性化近似方法,采用时域延拓法计算得到的El Centro和Kobe地震波作用下最大出力的计算精度提高22.2%以上;所提方法避免建立复杂的时域微分方程,简化了计算过程.
To accurately calculate the dynamic response of viscoelastic dampers in time domain under arbitrary excitations, a time domain extension method for the equivalent standard solid model of viscoelastic materials is proposed. First, the equivalent standard solid mode in frequency domain is extended to Laplace domain. Then, the Laplace expression is transformed into time domain by the numerical high-precision Laplace inverse transformation method, and the time domain response of the viscoelastic damper can be obtained. The results of 9050 A viscoelastic damping materials produced by Wuxi Shock Absorber Factory show that under harmonic excitation, the maximum error of the storage module G_1 is 0.005 4% and the maximum error of loss factor η is 0.279 7% by the time domain extension method. As for random excitation, compared with the equivalent linearization approximation method, the calculation accuracy of the maximum force under El Centro and Kobe earthquake excitations by the time domain extension method is improved by more than 22.2%. The proposed method avoids the establishment of complex time-domain differential equations and simplifies the calculation process.
To accurately calculate the dynamic response of viscoelastic dampers in time domain under arbitrary excitations, a time domain extension method for the equivalent standard solid model of viscoelastic materials is proposed. First, the equivalent standard solid mode in frequency domain is extended to Laplace domain. Then, the Laplace expression is transformed into time domain by the numerical high-precision Laplace inverse transformation method, and the time domain response of the viscoelastic damper can be obtained. The results of 9050 A viscoelastic damping materials produced by Wuxi Shock Absorber Factory show that under harmonic excitation, the maximum error of the storage module G_1 is 0.005 4% and the maximum error of loss factor η is 0.279 7% by the time domain extension method. As for random excitation, compared with the equivalent linearization approximation method, the calculation accuracy of the maximum force under El Centro and Kobe earthquake excitations by the time domain extension method is improved by more than 22.2%. The proposed method avoids the establishment of complex time-domain differential equations and simplifies the calculation process.
引文
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[7] Xu Z D,Xu C,Hu J.Equivalent fractional Kelvin model and experimental study on viscoelastic damper[J].Journal of Vibration and Control,2015,21(13):2536-2552.DOI:10.1177/1077546313513604.
[8] 张为民,张淳源.分数指数模型的热力学分析及其应用[J].工程力学,2002,19(2):95-99.DOI:10.3969/j.issn.1000-4750.2002.02.019.Zhang W M,Zhang C Y.Thermodynamic analysis and application of fractional exponential model[J].Engineering Mechanics,2002,19(2):95-99.DOI:10.3969/j.issn.1000-4750.2002.02.019.(in Chinese)
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[10] Xu Z D,Wang S A,Xu C.Experimental and numerical study on long-span reticulate structure with multidimensional high-damping earthquake isolation devices[J].Journal of Sound and Vibration,2014,333(14):3044-3057.DOI:10.1016/j.jsv.2014.02.013.
[11] Xu Z D,Gai P P,Zhao H Y,et al.Experimental and theoretical study on a building structure controlled by multi-dimensional earthquake isolation and mitigation devices[J].Nonlinear Dynamics,2017,89(1):723-740.DOI:10.1007/s11071-017-3482-5.
[12] Mehrabi M H,Suhatril M,Ibrahim Z,et al.Modeling of a viscoelastic damper and its application in structural control[J].PLoS One,2017,12(6):e0176480.DOI:10.1371/journal.pone.0176480.
[13] Bhatti A Q.Performance of viscoelastic dampers (VED) under various temperatures and application of magnetorheological dampers (MRD) for seismic control of structures[J].Mechanics of Time-Dependent Materials,2013,17(3):275-284.DOI:10.1007/s11043-012-9180-2.
[14] 徐赵东,赵鸿铁,周云.粘弹性阻尼器的等效标准固体模型[J].建筑结构,2001,31(3):67-69,71.DOI:10.19701/j.jzjg.2001.03.027.Xu Z D,Zhao H T,Zhou Y.Equivalent standard solid model of the viscoelastic damper[J].Building Structure,2001,31(3):67-69,71.DOI:10.19701/j.jzjg.2001.03.027.(in Chinese)
[15] Valsa J,Bran.Approximate formulae for numerical inversion of Laplace transforms[J].International Journal of Numerical Modelling:Electronic Networks,Devices and Fields,1998,11(3):153-166.DOI:10.1002/(sici)1099-1204(199805/06)11:3153::aid-jnm299>3.0.co;2-c.
[2] 周颖,龚顺明,吕西林.带粘弹性阻尼器结构振动台试验设计:基于OpenSees的阻尼器尺寸选择[J].防灾减灾工程学报,2014,34(3):308-313.DOI:10.13409/j.cnki.jdpme.2014.03.012.Zhou Y,Gong S M,Lü X L.Design of shaking table test on steel structure added with viscoelastic dampers:Size selection of dampers based on OpenSees[J].Journal of Disaster Prevention and Mitigation Engineering,2014,34(3):308-313.DOI:10.13409/j.cnki.jdpme.2014.03.012.(in Chinese)
[3] 李军强,刘宏昭,王忠民.线性粘弹性本构方程及其动力学应用研究综述[J].振动与冲击,2005,24(2):116-121.DOI:10.3969/j.issn.1000-3835.2005.02.030.Li J Q,Liu H Z,Wang Z M.Review on the linear constitutive equation and its dynamics applications to viscoelastic materials[J].Journal of Vibration and Shock,2005,24(2):116-121.DOI:10.3969/j.issn.1000-3835.2005.02.030.(in Chinese)
[4] 周云.粘弹性阻尼减震结构设计理论及应用[M].武汉:武汉理工大学出版社,2013:227.
[5] Xu Z D,Wang D X,Shi C F.Model,tests and application design for viscoelastic dampers[J].Journal of Vibration and Control,2011,17(9):1359-1370.DOI:10.1177/1077546310373617.
[6] 欧进萍,龙旭.速度相关型耗能减振体系参数影响的复模量分析[J].工程力学,2004,21(4):6-12,5.DOI:10.3969/j.issn.1000-4750.2004.04.002.Ou J P,Long X.Parameter analysis of passive energy dissipation systems with velocity-dependent dampers[J].Engineering Mechanics,2004,21(4):6-12,5.DOI:10.3969/j.issn.1000-4750.2004.04.002.(in Chinese)
[7] Xu Z D,Xu C,Hu J.Equivalent fractional Kelvin model and experimental study on viscoelastic damper[J].Journal of Vibration and Control,2015,21(13):2536-2552.DOI:10.1177/1077546313513604.
[8] 张为民,张淳源.分数指数模型的热力学分析及其应用[J].工程力学,2002,19(2):95-99.DOI:10.3969/j.issn.1000-4750.2002.02.019.Zhang W M,Zhang C Y.Thermodynamic analysis and application of fractional exponential model[J].Engineering Mechanics,2002,19(2):95-99.DOI:10.3969/j.issn.1000-4750.2002.02.019.(in Chinese)
[9] McTavish D J,Hughes P C.Modeling of linear viscoelastic space structures[J].Journal of Vibration and Acoustics,1993,115(1):103.DOI:10.1115/1.2930302.
[10] Xu Z D,Wang S A,Xu C.Experimental and numerical study on long-span reticulate structure with multidimensional high-damping earthquake isolation devices[J].Journal of Sound and Vibration,2014,333(14):3044-3057.DOI:10.1016/j.jsv.2014.02.013.
[11] Xu Z D,Gai P P,Zhao H Y,et al.Experimental and theoretical study on a building structure controlled by multi-dimensional earthquake isolation and mitigation devices[J].Nonlinear Dynamics,2017,89(1):723-740.DOI:10.1007/s11071-017-3482-5.
[12] Mehrabi M H,Suhatril M,Ibrahim Z,et al.Modeling of a viscoelastic damper and its application in structural control[J].PLoS One,2017,12(6):e0176480.DOI:10.1371/journal.pone.0176480.
[13] Bhatti A Q.Performance of viscoelastic dampers (VED) under various temperatures and application of magnetorheological dampers (MRD) for seismic control of structures[J].Mechanics of Time-Dependent Materials,2013,17(3):275-284.DOI:10.1007/s11043-012-9180-2.
[14] 徐赵东,赵鸿铁,周云.粘弹性阻尼器的等效标准固体模型[J].建筑结构,2001,31(3):67-69,71.DOI:10.19701/j.jzjg.2001.03.027.Xu Z D,Zhao H T,Zhou Y.Equivalent standard solid model of the viscoelastic damper[J].Building Structure,2001,31(3):67-69,71.DOI:10.19701/j.jzjg.2001.03.027.(in Chinese)
[15] Valsa J,Bran.Approximate formulae for numerical inversion of Laplace transforms[J].International Journal of Numerical Modelling:Electronic Networks,Devices and Fields,1998,11(3):153-166.DOI:10.1002/(sici)1099-1204(199805/06)11:3153::aid-jnm299>3.0.co;2-c.
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