负刚度非线性能量阱减震控制性能研究
|
摘要
提出设置含负刚度特性的非线性能量阱(NES)来实现结构地震响应控制,针对典型的单层和双层层模型,在附加质量占主质量5%的限定条件下,对采用负刚度NES、立方NES和经典质量调谐阻尼器(TMD)控制方式的装置参数进行数值寻优,对优化的减震控制性能进行对比分析。结果表明,负刚度NES减震控制性能全面优于已有的立方NES,对主结构动力特性变化的鲁棒性优于TMD,对地震动峰值变化的鲁棒性与TMD相当。应用数值小波变换对体系的地震响应时程进行功率谱分析,揭示了在地震作用过程中,负刚度NES总体上对主结构产生更为显著、更为持续的瞬时内共振俘获行为,因而其减震效率较高,且由于这种瞬时内共振俘获是在多频域上同时展开的,使其减震控制性能具有强鲁棒性。
A nonlinear energy sink(NES) with negative stiffness is presented for structural seismic response control. Typical analysis model is studied by attaching a NES with negative stiffness, a NES with cubic nonlinear stiffness, or a classical tuned mass damper(TMD). The parameters of different devices are optimized numerically,and their control performaces are compared under the condition that the attaching mass is less than 5% of the parimary structure. The anlysis results shows that the seismic control performance of the present NES with negative stiffness is thoroughly superior to that with cubic stiffness. As the dynamic characteristics vary, its control performance shows stronger robustness than that of the TMD. As the peak ground accceration varies, it shows similar robustness performance as the TMD. The numerical wavelet transformation is applied to analyze the structural seismic response histories by power spectra. The results indicate that more intense and durable transient internal resonance captures can be obtained by the NES with negative stiffness, and thus it shows higher control efficiency. Furthermore, as such transient internal resonance captures can be derived in a wide frequency domain, particularly as those transient subharmonic resonance captures are insensitive to variation of foundamental frequency of the primary structure, its control performance possesses strong robustness.
A nonlinear energy sink(NES) with negative stiffness is presented for structural seismic response control. Typical analysis model is studied by attaching a NES with negative stiffness, a NES with cubic nonlinear stiffness, or a classical tuned mass damper(TMD). The parameters of different devices are optimized numerically,and their control performaces are compared under the condition that the attaching mass is less than 5% of the parimary structure. The anlysis results shows that the seismic control performance of the present NES with negative stiffness is thoroughly superior to that with cubic stiffness. As the dynamic characteristics vary, its control performance shows stronger robustness than that of the TMD. As the peak ground accceration varies, it shows similar robustness performance as the TMD. The numerical wavelet transformation is applied to analyze the structural seismic response histories by power spectra. The results indicate that more intense and durable transient internal resonance captures can be obtained by the NES with negative stiffness, and thus it shows higher control efficiency. Furthermore, as such transient internal resonance captures can be derived in a wide frequency domain, particularly as those transient subharmonic resonance captures are insensitive to variation of foundamental frequency of the primary structure, its control performance possesses strong robustness.
引文
[1]Vakakis A F,Gendelman O V,Bergman L A,et al.Nonlinear targeted energy transfer in mechanical and structural systems I&II[M].Berlin,Springer Springer Science&Business Media,2008.
[2]Gendelman O,Manevitch L I,Vakakis A F,et al.Energy pumping in nonlinear mechanical oscillators:Part I-Dynamics of the underlying hamiltonian systems[J].ASME Journal of Applied Mechanics,2001,68(1):34―41.
[3]Vakakis A F,Gendelman O.Energy pumping in nonlinear mechanical oscillators.Part II-Resonance capture[J].ASME Journal of Applied Mechanics,2001,68(1):42―48.
[4]Manevitch L I,Musienko A I,Lamarque C H.New analytical approach to energy pumping problem in strongly nonhomogeneous 2dof systems[J].Meccanica,2007,42(1):77―83.
[5]张也弛.非线性能量阱的力学特性与振动抑制效果研究[D].哈尔滨:哈尔滨工业大学,2012.Zhang Yechi.Research on the dynamics and performance of vibration suppression of nonlinear energy sink[D].Harbin:Harbin Institute of Technology,2012.(in Chinese)
[6]刘中坡,吕西林,王栋,等.非线性能量阱刚度优化计算与振动台试验[J].振动与冲击,2016,36(20):77―84.Liu Zhongpo,LüXilin,Wang Dong,et al.Stiffness optimization of nonlinear energy sink and shaking table test[J].Journal of Vibration and Shock,2016,36(20):77―84.(in Chinese)
[7]谭平,刘良坤,陈洋洋,等.非线性能量阱减振系统受基底简谐激励的分岔特性分析[J].工程力学,2017,34(12):67―74.Tan Ping,Liu Liangkun,Chen Yangyang,et al.Bifurcation analysis of nonlinear energy sink absorption system under ground harmonic excitation[J].Engineering Mechanics,2017,34(12):67―74.(in chinese)
[8]Mcfarland D M,Bergman L A,Vakakis A F.Experimental study of non-linear energy pumping occurring at a single fast frequency[J].International Journal of Non-Linear Mechanics,2005,40(6):891―899.
[9]Wierschem N E,Luo J,Hubbard S,et al.Experimental testing of a large 9-story structure equipped with multiple nonlinear energy sinks subjected to an impulsive loading[C].Proceeding of ASCE Structures Congress 2013:2241―2252.
[10]Wierschem N E,Luo J,Al-Shudeifat M,et al.Experimental testing and numerical simulation of a six-story structure incorporating two-degree-of-freedom nonlinear energy sink[J].ASCE Journal of Structural Engineering,2014,140(6):04014027-1―04014027-10.
[11]Li T,Seguy S,Berlioz A.Dynamics of cubic and vibro-impact nonlinear energy sink(NES):analytical,numerical,and experimental analysis[J].ASME Journal of Vibration&Acoustics,2016,138(3):031010-1―031010-9.
[12]Nucera F,Lacono F L,Mcfarland D M,et al.Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame:Experimental results[J].Journal of Sound&Vibration,2008,313(1):57―76.
[13]Nucera F,Mcfarland D M,Bergman L A,et al.Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame:Computational results[J].Journal of Sound&Vibration,2010,329(1):2973―2994.
[14]Wierschem N E,Luo J,Hubbard S,et al.Synergistic combination of multiple nonlinear energy sinks in a large-scale building structure subjected to seismic ground motion[C].Proceeding of Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics,2013:298―308.
[15]Luo J,Wierschem N E,Hubbard S A,et al.Large-scale experimental evaluation and numerical simulation of a system of nonlinear energy sinks for seismic mitigation[J].Engineering Structures,2014,77:34―48.
[16]刘中坡,吕西林,鲁正,等.轨道型非线性能量阱振动控制的振动台试验研究[J].建筑结构学报,2016,37(11):1―9.(in Chinese)Liu Zhongpo,Lu Xilin,Lu Zheng,et al.Experimental inerstigation on vibration control effect of track nonlinear energy sink[J].Journal of Building Structures,2016,37(11):1―9.(in Chinese)
[17]Wang J,Wierschem N,Spencer B F,et al.Experimental study of track nonlinear energy sinks for dynamic response reduction[J].Engineering Structures,2015,94:9―15.
[18]Wang J,Wierschem N,Spencer B F,et al.Numerical and experimental study of the performance of a single-sided vibro-impact track nonlinear energy sink[J].Earthquake Engineering&Structural Dynamics,2016,45(4):635―652.
[19]Lu X,Liu Z,Lu Z.Optimization design and experimental verification of track nonlinear energy sink for vibration control under seismic excitation[J].Structural Control&Health monitoring,2017,DOI:10.1002/stc.2033.
[20]Vaurigaud B,Savadkoohi A T,Lamarque C H.Targeted energy transfer with parallel nonlinear energy sinks.Part I:Design theory and numerical results[J].Nonlinear Dynamics,2011,66(4):763―780.
[21]Savadkoohi A T,Vaurigaud B,Lamarque C H,et al.Targeted energy transfer with parallel nonlinear energy sinks,Part II:Theory and experiments[J].Nonlinear Dynamics,2012,67(1):37―46.
[22]Nucera F,Iacono F L,Mcfarland D M,et al.Targeted energy transfers for seismic mitigation induced by attachments with essential stiffness nonlinearities[C].International Symposium on Recent Advances in Mechanics,Dynamical Systems and Probability Theory,2007:460―471.
[23]Nucera F,Vakakis A F,Mcfarland D M,et al.Targeted energy transfers in vibro-impact oscillators for seismic mitigation[J].Nonlinear Dynamics,2007,50(3):651―677.
[24]Ahmadi M,Attari N K A,Shahrouzi M.Structural seismic response mitigation using optimized vibro-impact nonlinear energy sinks[J].Journal of Earthquake Engineering,2014,19(2):193―219.
[25]Gendelman O V,Alloni A.Dynamics of forced system with vibro-impact energy sink[J].Journal of Sound&Vibration,2015,358(2015):301―314.
[26]Li T,Seguy S,Berlioz A.On the dynamics around targeted energy transfer for vibro-impact nonlinear energy sink[J].Nonlinear Dynamics,2017,87(3):1453―1466.
[27]Wang J,Wierschem N E,Spencer B F,et al.Track nonlinear energy sink for rapid response reduction in building structures[J].ASCE Journal of Engineering Mechanics,2015,141(1):04014104-1―04014104-10.
[28]Schmidt F,Lamarque C H.Energy pumping for mechanical systems involving non-smooth saint-venant terms[J].International Journal of Non-Linear Mechanics,2010,45(9):866―875.
[29]Lamarque C H,Savadkoohi A T.Targeted energy transfer between a system with a set of saint-venant elements and a nonlinear energy sink[J].Continuum Mechanics and Thermodynamics,2015,27(4):819―833.
[30]Al-Shudeifat M A.Asymmetric magnet-based nonlinear energy sink[J].Journal of Computational&Nonlinear Dynamics,2015,10(1):.
[31]Fang X,Wen J,Yin J,et al.Highly efficient continuous bistable nonlinear energy sink composed of a cantilever beam with partial constrained layer damping[J].Nonlinear Dynamics,2017,87(4):2677―2695.
[32]Gendelman O V,Sigalov G,Manevitch L I,et al.Dynamics of an eccentric rotational nonlinear energy sink[J].ASME Journal of Applied Mechanics,2012,79(1),011012:1―9.
[33]Al-Shudeifat M A,Wierschem N E,Bergman L A,et al.Numerical and experimental investigations of a rotating nonlinear energy sink[J].Meccanica,2017,52(4-5):763―779.
[34]Al-Shudeifat M A.Highly efficient nonlinear energy sink[J].Nonlinear Dynamics,2014,76(4):1905―1920.
[35]成礼智.小波与离散变换理论及工程实践[M].北京:清华大学出版社,2005.Cheng Lizhi.Wavelet,discrete transform theory and engineering practice[M].Beijing:Tsinghua University Press,2005.(in Chinese)
[2]Gendelman O,Manevitch L I,Vakakis A F,et al.Energy pumping in nonlinear mechanical oscillators:Part I-Dynamics of the underlying hamiltonian systems[J].ASME Journal of Applied Mechanics,2001,68(1):34―41.
[3]Vakakis A F,Gendelman O.Energy pumping in nonlinear mechanical oscillators.Part II-Resonance capture[J].ASME Journal of Applied Mechanics,2001,68(1):42―48.
[4]Manevitch L I,Musienko A I,Lamarque C H.New analytical approach to energy pumping problem in strongly nonhomogeneous 2dof systems[J].Meccanica,2007,42(1):77―83.
[5]张也弛.非线性能量阱的力学特性与振动抑制效果研究[D].哈尔滨:哈尔滨工业大学,2012.Zhang Yechi.Research on the dynamics and performance of vibration suppression of nonlinear energy sink[D].Harbin:Harbin Institute of Technology,2012.(in Chinese)
[6]刘中坡,吕西林,王栋,等.非线性能量阱刚度优化计算与振动台试验[J].振动与冲击,2016,36(20):77―84.Liu Zhongpo,LüXilin,Wang Dong,et al.Stiffness optimization of nonlinear energy sink and shaking table test[J].Journal of Vibration and Shock,2016,36(20):77―84.(in Chinese)
[7]谭平,刘良坤,陈洋洋,等.非线性能量阱减振系统受基底简谐激励的分岔特性分析[J].工程力学,2017,34(12):67―74.Tan Ping,Liu Liangkun,Chen Yangyang,et al.Bifurcation analysis of nonlinear energy sink absorption system under ground harmonic excitation[J].Engineering Mechanics,2017,34(12):67―74.(in chinese)
[8]Mcfarland D M,Bergman L A,Vakakis A F.Experimental study of non-linear energy pumping occurring at a single fast frequency[J].International Journal of Non-Linear Mechanics,2005,40(6):891―899.
[9]Wierschem N E,Luo J,Hubbard S,et al.Experimental testing of a large 9-story structure equipped with multiple nonlinear energy sinks subjected to an impulsive loading[C].Proceeding of ASCE Structures Congress 2013:2241―2252.
[10]Wierschem N E,Luo J,Al-Shudeifat M,et al.Experimental testing and numerical simulation of a six-story structure incorporating two-degree-of-freedom nonlinear energy sink[J].ASCE Journal of Structural Engineering,2014,140(6):04014027-1―04014027-10.
[11]Li T,Seguy S,Berlioz A.Dynamics of cubic and vibro-impact nonlinear energy sink(NES):analytical,numerical,and experimental analysis[J].ASME Journal of Vibration&Acoustics,2016,138(3):031010-1―031010-9.
[12]Nucera F,Lacono F L,Mcfarland D M,et al.Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame:Experimental results[J].Journal of Sound&Vibration,2008,313(1):57―76.
[13]Nucera F,Mcfarland D M,Bergman L A,et al.Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame:Computational results[J].Journal of Sound&Vibration,2010,329(1):2973―2994.
[14]Wierschem N E,Luo J,Hubbard S,et al.Synergistic combination of multiple nonlinear energy sinks in a large-scale building structure subjected to seismic ground motion[C].Proceeding of Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics,2013:298―308.
[15]Luo J,Wierschem N E,Hubbard S A,et al.Large-scale experimental evaluation and numerical simulation of a system of nonlinear energy sinks for seismic mitigation[J].Engineering Structures,2014,77:34―48.
[16]刘中坡,吕西林,鲁正,等.轨道型非线性能量阱振动控制的振动台试验研究[J].建筑结构学报,2016,37(11):1―9.(in Chinese)Liu Zhongpo,Lu Xilin,Lu Zheng,et al.Experimental inerstigation on vibration control effect of track nonlinear energy sink[J].Journal of Building Structures,2016,37(11):1―9.(in Chinese)
[17]Wang J,Wierschem N,Spencer B F,et al.Experimental study of track nonlinear energy sinks for dynamic response reduction[J].Engineering Structures,2015,94:9―15.
[18]Wang J,Wierschem N,Spencer B F,et al.Numerical and experimental study of the performance of a single-sided vibro-impact track nonlinear energy sink[J].Earthquake Engineering&Structural Dynamics,2016,45(4):635―652.
[19]Lu X,Liu Z,Lu Z.Optimization design and experimental verification of track nonlinear energy sink for vibration control under seismic excitation[J].Structural Control&Health monitoring,2017,DOI:10.1002/stc.2033.
[20]Vaurigaud B,Savadkoohi A T,Lamarque C H.Targeted energy transfer with parallel nonlinear energy sinks.Part I:Design theory and numerical results[J].Nonlinear Dynamics,2011,66(4):763―780.
[21]Savadkoohi A T,Vaurigaud B,Lamarque C H,et al.Targeted energy transfer with parallel nonlinear energy sinks,Part II:Theory and experiments[J].Nonlinear Dynamics,2012,67(1):37―46.
[22]Nucera F,Iacono F L,Mcfarland D M,et al.Targeted energy transfers for seismic mitigation induced by attachments with essential stiffness nonlinearities[C].International Symposium on Recent Advances in Mechanics,Dynamical Systems and Probability Theory,2007:460―471.
[23]Nucera F,Vakakis A F,Mcfarland D M,et al.Targeted energy transfers in vibro-impact oscillators for seismic mitigation[J].Nonlinear Dynamics,2007,50(3):651―677.
[24]Ahmadi M,Attari N K A,Shahrouzi M.Structural seismic response mitigation using optimized vibro-impact nonlinear energy sinks[J].Journal of Earthquake Engineering,2014,19(2):193―219.
[25]Gendelman O V,Alloni A.Dynamics of forced system with vibro-impact energy sink[J].Journal of Sound&Vibration,2015,358(2015):301―314.
[26]Li T,Seguy S,Berlioz A.On the dynamics around targeted energy transfer for vibro-impact nonlinear energy sink[J].Nonlinear Dynamics,2017,87(3):1453―1466.
[27]Wang J,Wierschem N E,Spencer B F,et al.Track nonlinear energy sink for rapid response reduction in building structures[J].ASCE Journal of Engineering Mechanics,2015,141(1):04014104-1―04014104-10.
[28]Schmidt F,Lamarque C H.Energy pumping for mechanical systems involving non-smooth saint-venant terms[J].International Journal of Non-Linear Mechanics,2010,45(9):866―875.
[29]Lamarque C H,Savadkoohi A T.Targeted energy transfer between a system with a set of saint-venant elements and a nonlinear energy sink[J].Continuum Mechanics and Thermodynamics,2015,27(4):819―833.
[30]Al-Shudeifat M A.Asymmetric magnet-based nonlinear energy sink[J].Journal of Computational&Nonlinear Dynamics,2015,10(1):.
[31]Fang X,Wen J,Yin J,et al.Highly efficient continuous bistable nonlinear energy sink composed of a cantilever beam with partial constrained layer damping[J].Nonlinear Dynamics,2017,87(4):2677―2695.
[32]Gendelman O V,Sigalov G,Manevitch L I,et al.Dynamics of an eccentric rotational nonlinear energy sink[J].ASME Journal of Applied Mechanics,2012,79(1),011012:1―9.
[33]Al-Shudeifat M A,Wierschem N E,Bergman L A,et al.Numerical and experimental investigations of a rotating nonlinear energy sink[J].Meccanica,2017,52(4-5):763―779.
[34]Al-Shudeifat M A.Highly efficient nonlinear energy sink[J].Nonlinear Dynamics,2014,76(4):1905―1920.
[35]成礼智.小波与离散变换理论及工程实践[M].北京:清华大学出版社,2005.Cheng Lizhi.Wavelet,discrete transform theory and engineering practice[M].Beijing:Tsinghua University Press,2005.(in Chinese)