基于滞变阻尼模型的时域计算方法
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摘要
复阻尼时域运动方程的自由振动解中包含发散项,导致时域数值计算结果不能稳定收敛。在复阻尼模型的频域运动方程基础上可得到滞变阻尼模型的时域运动方程。针对滞变阻尼模型的特点,依据复平面法和地震加速度的三角级数表达式,该文提出了滞变阻尼模型的时域理论计算方法;假定时间步长内结构的振动响应为简谐振动响应,同时借助于常平均加速度法,提出了滞变阻尼模型的时域数值计算方法。算例分析表明,与复阻尼模型的时域数值计算方法相比,滞变阻尼模型的时域理论计算方法和时域数值计算方法可有效避免时域发散现象;滞变阻尼模型的时域理论计算结果和时域数值计算结果与复阻尼模型的频域计算结果近似相等,进一步证明了该文方法的正确性。
The free vibration solution of a complex damping time domain motion equation contains divergent items which make the numerical results of the time domain divergent. Based on the frequency domain motion equation of a complex damping model, the hysteretic damping time domain motion equation can be obtained.According to the characteristics of a hysteretic damping model, the time domain theoretical calculation method of the hysteretic damping model is proposed based on the complex plane method and trigonometric series expression of earthquake acceleration records. It is assumed that the structural vibration response is a harmonic vibration response in a short time step. Based on the average acceleration method, the time domain numerical calculation method of the hysteretic damping model is proposed. The analysis results show that: compared with the time domain numerical method of a complex damping model, the two proposed methods can avoid the time domain divergence phenomena effectively. The time domain calculation results of the two proposed methods are approximately equal to the frequency domain calculation results of a complex damping model. The correctness of the two proposed methods is verified.
The free vibration solution of a complex damping time domain motion equation contains divergent items which make the numerical results of the time domain divergent. Based on the frequency domain motion equation of a complex damping model, the hysteretic damping time domain motion equation can be obtained.According to the characteristics of a hysteretic damping model, the time domain theoretical calculation method of the hysteretic damping model is proposed based on the complex plane method and trigonometric series expression of earthquake acceleration records. It is assumed that the structural vibration response is a harmonic vibration response in a short time step. Based on the average acceleration method, the time domain numerical calculation method of the hysteretic damping model is proposed. The analysis results show that: compared with the time domain numerical method of a complex damping model, the two proposed methods can avoid the time domain divergence phenomena effectively. The time domain calculation results of the two proposed methods are approximately equal to the frequency domain calculation results of a complex damping model. The correctness of the two proposed methods is verified.
引文
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[2]Pan Y,Wang Y.Frequency-domain analysis of exponentially damped linear systems[J].Journal of Sound and Vibration,2013,332(7):1754-1765.
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[15]Wang J.Rayleigh coefficients for series infrastructure systems with multiple damping properties[J].Journal of Vibration and Control,2015,21(6):1234-1248.
[16]Inaudi J A,Kelly J M.Linear hysteretic damping and hilbert transform[J].Journal of Engineering Mechanics,1995,121(5):626-632.
[17]Manikanahally D N,Crocker M J.Vibration analysis of hysteretically damped mass-loaded beams[J].Journal of Sound and Vibration,1989,132(2):177-197.
[18]李鸿晶,王通,廖旭.关于法机理的一种解释[J].地震工程与工程振动,2011,31(2):55-62.Li Hongjing,Wang Tong,Liao Xu.An interpretation on Newmark beta methods in mechanism of numerical analysis[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(2):55-62.(in Chinese)
[19]周惠蒙,吴斌,王涛,等.基于速度的显式等效力控制方法的研究[J].工程力学,2016,33(6):15-22.Zhou Huimeng,Wu Bin,Wang Tao,et al.Explicit equivalent force control method based on velocity[J]..Engineering Mechanics,2016,33(6):15-22.(in Chinese)
[20]潘玉华,王元丰.复阻尼结构动力方程的高斯精细时程积分法[J].工程力学,2012,29(2):16-20.Pan Yuhua,Wang Yuanfeng.Gauss precise time-integration of complex damping vibration systems[J].Engineering Mechanics,2012,29(2):16-20.(in Chinese)
[21]刘庆林,傅学怡.基于复阻尼假定的不同材料阻尼特性混合结构抗震分析反应谱CCQC法[J].土木工程学报,2011,44(3):61-71.Liu Qinglin,Fu Xueyi.A response spectrum CCQCmethod for seismic analysis of structures of multiple material damping characteristics based on complex damping assumption[J].China Civil Engineering Journal,2011,44(3):61-71.(in Chinese)
[22]Lage Y,Cach?o H,Reis L,et al.A damage parameter for HCF and VHCF based on hysteretic damping[J].International Journal of Fatigue,2014,62:2-9.
[2]Pan Y,Wang Y.Frequency-domain analysis of exponentially damped linear systems[J].Journal of Sound and Vibration,2013,332(7):1754-1765.
[3]朱敏,朱镜清.逐步积分法求解复阻尼结构运动方程的稳定性问题[J].地震工程与工程振动,2001,21(4):59-62.Zhu Min,Zhu Jingqing.Studies on stability of step-by-step methods under complex damping conditions[J].Earthquake Engineering and Engineering Vibration,2001,21(4):59-62.(in Chinese)
[4]张辉东,王元丰,江辉.不同参数取值对复阻尼模型结构抗震性能的影响[J].建筑结构学报,2009,30(6):94-100.Zhang Huidong,Wang Yuanfeng,Jiang Hui.Effect of different parameters on seismic performance of complex damping structures[J].Journal of Building Structures,2009,30(6):94-100.(in Chinese)
[5]张辉东,王元丰.复阻尼模型结构地震时程响应研究[J].工程力学,2010,27(1):109-115.Zhang Huidong,Wang Yuanfeng.Study on seismic time-history response of structures with complex damping[J].Engineering Mechanics,2010,27(1):109-115.(in Chinese)
[6]潘玉华,王元丰.含复阻尼振动系统的逐步积分法稳定性研究[J].土木工程学报,2010(增刊1):206-210.Pan Yuhua,Wang Yuanfeng.Stability of step-by-step methods in solving complex damping vibration systems[J].China Civil Engineering Journal,2010(Suppl 1):206-210.(in Chinese)
[7]朱镜清,朱敏.复阻尼地震反应谱的计算方法及其它[J].地震工程与工程振动,2000,20(2):19-23.Zhu Jingqing,Zhu Min.Calculation of complex damping response spectra from earthquake records[J].Earthquake Engineering and Engineering Vibration,2000,20(2):19-23.(in Chinese)
[8]朱敏,朱镜清.复阻尼地震反应谱计算的再研究[J].地震工程与工程振动,2001,21(2):36-40.Zhu Min,Zhu Jingqing.Further studies on calculation of complex damping seismic response spectra[J].Earthquake Engineering and Engineering Vibration,2001,21(2):36-40.(in Chinese)
[9]Kang J H.Hysterically damped free and forced vibrations of axial and torsional bars by a closed form exact method[J].Journal of Sound and Vibration,2016,378:144-156.
[10]何钟怡.复本构理论中的对偶原则[J].固体力学学报,1994,15(2):177-180.He Zhongyi.The dual principle in theory of complex constitutive equations[J].Chinese Journal of Solid Mechanics,1994,15(2):177-180.(in Chinese)
[11]何钟怡,廖振鹏,王小华.关于复阻尼理论的几点注记[J].地震工程与工程振动,2002,22(1):1-6.He Zhongyi,Liao Zhenpeng,Wang Xiaohua.Some notes on theory of complex damping[J].Earthquake Engineering and Engineering Vibration,2002,22(1):1-6.(in Chinese)
[12]周正华,廖振鹏,丁海平.一种时域复阻尼本构方程[J].地震工程与工程振动,1999,19(2):38―44.Zhou Zhenghua,Liao Zhenpeng,Ding Haiping.Atime-domain complex-damping constitutive equation[J].Earthquake Engineering and Engineering Vibration,1999,19(2):38-44.(in Chinese)
[13]胡海岩.结构阻尼模型及系统时域动响应[J].振动工程学报,1992,5(1):8-15.Hu Haiyan.Structural damping modal and system dynamic response at time domain[J].Journal of Vibration Engineering,1992,5(1):8-15.(in Chinese)
[14]Reggio A,Angelis M D.Modelling and identification of structures with rate-independent linear damping[J].Meccanica,2015,50(3):617-632.
[15]Wang J.Rayleigh coefficients for series infrastructure systems with multiple damping properties[J].Journal of Vibration and Control,2015,21(6):1234-1248.
[16]Inaudi J A,Kelly J M.Linear hysteretic damping and hilbert transform[J].Journal of Engineering Mechanics,1995,121(5):626-632.
[17]Manikanahally D N,Crocker M J.Vibration analysis of hysteretically damped mass-loaded beams[J].Journal of Sound and Vibration,1989,132(2):177-197.
[18]李鸿晶,王通,廖旭.关于法机理的一种解释[J].地震工程与工程振动,2011,31(2):55-62.Li Hongjing,Wang Tong,Liao Xu.An interpretation on Newmark beta methods in mechanism of numerical analysis[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(2):55-62.(in Chinese)
[19]周惠蒙,吴斌,王涛,等.基于速度的显式等效力控制方法的研究[J].工程力学,2016,33(6):15-22.Zhou Huimeng,Wu Bin,Wang Tao,et al.Explicit equivalent force control method based on velocity[J]..Engineering Mechanics,2016,33(6):15-22.(in Chinese)
[20]潘玉华,王元丰.复阻尼结构动力方程的高斯精细时程积分法[J].工程力学,2012,29(2):16-20.Pan Yuhua,Wang Yuanfeng.Gauss precise time-integration of complex damping vibration systems[J].Engineering Mechanics,2012,29(2):16-20.(in Chinese)
[21]刘庆林,傅学怡.基于复阻尼假定的不同材料阻尼特性混合结构抗震分析反应谱CCQC法[J].土木工程学报,2011,44(3):61-71.Liu Qinglin,Fu Xueyi.A response spectrum CCQCmethod for seismic analysis of structures of multiple material damping characteristics based on complex damping assumption[J].China Civil Engineering Journal,2011,44(3):61-71.(in Chinese)
[22]Lage Y,Cach?o H,Reis L,et al.A damage parameter for HCF and VHCF based on hysteretic damping[J].International Journal of Fatigue,2014,62:2-9.