自由阻尼梁高频能量流响应的解析模型
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摘要
针对自由阻尼梁的高频振动问题,基于波动理论提出了大阻尼复合结构的能量流解析模型。利用等效复刚度方法确定了完全自由阻尼梁结构的等效弯曲刚度和损耗因子,基于能量流分析方法构建了结构的能量密度控制方程,求解了结构的高频能量流响应。分析了弯曲波在阻尼结构耦合处的能量传递特性,构建了局部自由阻尼梁的高频能量流解析模型,预测了大阻尼耦合结构的高频振动特性。数值结果表明,提出的能量流解析解与经典的时空平均波动解一致逼近,因而能够精确地预测自由阻尼梁等大阻尼复合结构的高频能量流响应。
An analytical energy flow model based on wave theory is proposed to predict the vibration of large damping composite structures such as a beam with free layer damping in the high-frequency range.Using the equivalent complex stiffness model,both equivalent flexural stiffness and structural loss factor of a beam with free layer damping are obtained.Then the corresponding energy density equation is derived for a beam with full free layer damping by energy flow analysis.By analyzing the energy transfer characteristic at the interface of damping treatment,an analytical model for the energy flow response of a beam with partial free layer damping is developed to predict the vibrating characteristics of the coupled large damping structure.Various numerical analyses show that the energy density obtained by the proposed model is in a good agreement with that by the classic wave model with timeand space-average treatment.Consequently,the present model can be employed to accurately predict the structural energy flow response to high-frequency excitation for large damping composite structures such as a beam with free layer damping.
An analytical energy flow model based on wave theory is proposed to predict the vibration of large damping composite structures such as a beam with free layer damping in the high-frequency range.Using the equivalent complex stiffness model,both equivalent flexural stiffness and structural loss factor of a beam with free layer damping are obtained.Then the corresponding energy density equation is derived for a beam with full free layer damping by energy flow analysis.By analyzing the energy transfer characteristic at the interface of damping treatment,an analytical model for the energy flow response of a beam with partial free layer damping is developed to predict the vibrating characteristics of the coupled large damping structure.Various numerical analyses show that the energy density obtained by the proposed model is in a good agreement with that by the classic wave model with timeand space-average treatment.Consequently,the present model can be employed to accurately predict the structural energy flow response to high-frequency excitation for large damping composite structures such as a beam with free layer damping.
引文
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[18]KONG X J,CHEN H L,ZHU D H,et al.Study on the validity region of energy finite element analysis[J].Journal of Sound and Vibration,2014,333(9):2588-2660.
[19]LE B A.Derivation of statistical energy analysis from radiative exchanges[J].Journal of Sound and Vibration,2007,300(3):763-779.
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[21]WOHLEVER J,BERNHARD R J.Mechanical energy flow models of rods and beams[J].Journal of Sound and Vibration,1992,153(1):1-19.
[22]LASE Y,ICHCHOU M N,JEZEQUEL L.Energy flow analysis of bars and beams:Theoretical formulations[J].Journal of Sound and Vibration,1996,192(1):282-305.
[23]GOYDER H G D,WHITE R G.Vibrational power flow from machines into build-up structures,partΙ:Introduction and approximate analysis of beam and plate-like foundation[J].Journal of Sound and Vibration,1980,68(1):59-75.
[2]蔡忠云,唐文勇,张圣坤.能量有限元方法在复合材料层合梁耦合结构振动分析中的应用[J].振动与冲击,2010,29(10):23-27.CAI Z Y,TANG W Y,ZHANG S K.Application of energy finite element method in vibration analysis of composite laminated beam structures[J].Journal of Vibration and Shock,2010,29(10):23-27(in Chinese).
[3]孔祥杰,陈花铃,祝丹晖,等.附加自由阻尼梁高频响应的能量有限元模型[J].振动与冲击,2015,34(17):94-99.KONG X J,CHEN H L,ZHU D H,et al.Energy finite element analysis for high frequency vibration of beams with free layer damping treatment[J].Journal of Vibration and Shock,2015,34(17):94-99(in Chinese).
[4]王迪,朱翔,李天匀,等.基于能量有限元法的功能梯度梁振动分析[J].振动与冲击,2018,37(3):119-124.WANG D,ZHU X,LI T Y,et al.Vibration analysis of a FGM beam based on energy finite element[J].Journal of Vibration and Shock,2018,37(3):119-124(in Chinese).
[5]HAN J B,HONG S Y,SONG J H,et al.Vibrational energy flow models for the 1-D high damping system[J].Journal of Mechanical Science and Technology,2013,27(9):2659-2671.
[6]HAN J B,HONG S Y,SONG J H,et al.Vibrational energy flow models for the Rayleigh-Love and Rayleigh-Bishop rods[J].Journal of Sound and Vibration,2014,333(2),520-540.
[7]葛月,牛军川,刘知辉.多种激励形式下任意角度耦合板振动传递特性研究[J].机械工程学报,2017,53(7):94-103.GE Y,NIU J C,LIU Z H.On energy transmission characteristics of coupled plates with arbitrary coupling angles to multiple types of excitation[J].Journal of Mechanical Engineering,2017,53(7):94-103(in Chinese).
[8]孙丽萍,聂武能.能量有限元法在船舶结构中的应用[J].哈尔滨工业大学学报,2008,40(9):1491-1494.SUN L P,NIU W N.Application of energy finite element method in ship structures[J].Journal of Harbin Institute of Technology,2008,40(9):1491-1494(in Chinese).
[9]周红卫,陈海波,王用岩.耦合板结构的非结构零阶能量有限元分析[J].振动与冲击,2015,34(13):140-145.ZHONG H W,CHEN H B,WANG Y Y.Unstructured zero-order energy finite element method for coupled plate structures[J].Journal of Vibration and Shock,2015,34(13):140-145(in Chinese).
[10]NAVAZI H M,NOKHBATOLFOGHAHAEI A,GHOBADY,et al.Experimental measurement of energy density in a vibrating plate and comparison with energy finite element analysis[J].Journal of Sound and Vibration,2016,375:289-307.
[11]SEO S H,HONG S Y,KIL H G.Power flow analysis of reinforced beam-plate coupled structures[J].Journal of Sound and Vibration,2003,267(2):301-334.
[12]解妙霞,陈花玲,吴九汇.圆柱壳高频弯曲振动的能量有限元分析[J].西安交通大学学报,2008,42(9):1113-1116.XIE M X,CHEN H L,WU J H.Energy finite element analysis to high frequency bending vibration in cylindrical shell[J].Journal of Xi'an Jiaotong University,2008,42(9):1113-1116(in Chinese).
[13]KWON H W,HONG S Y,SONG J H.Vibrational energy flow analysis of coupled cylindrical thin shell structures[J].Journal of Mechanical Science and Technology,2016,30(9):4049-4062.
[14]陈书明,王登峰,谭刚平,等.基于能量有限元方法的声腔内部噪声预测[J].吉林大学学报(工学版),2012,42(2):303-308.CHEN S M,WANG D F,TAN G P,et al.Prediction of cavity interior noise based on energy finite element method[J].Journal of Jilin University(Engineering and Technology Edition),2012,42(2):303-308(in Chinese).
[15]JANDRON M A,KOCH R M.Effectiveness of energy finite element analysis applied to submerged undersea vehicle noise prediction[J].Journal of the Acoustical Society of America,2014,21(4):2193-2193.
[16]WU K C,VLAHOPOULOS N.Investigation of variance response in energy finite element analysis[J].Journal of the A-coustical Society of America,2017,142(4):2614.
[17]陈兆林,杨智春,王用岩,等.基于能量有限元法和虚拟模态综合法的高频冲击响应分析方法[J].航空学报,2018,39(8):221893.CHEN Z L,YANG Z C,WANG Y Y,et al.A high-frequency shock response analysis method based on energy finite element method and virtual mode synthesis and simulation[J].Acta Aeronautica et Astronautica Sinica,2018,39(8):221893(in Chinese).
[18]KONG X J,CHEN H L,ZHU D H,et al.Study on the validity region of energy finite element analysis[J].Journal of Sound and Vibration,2014,333(9):2588-2660.
[19]LE B A.Derivation of statistical energy analysis from radiative exchanges[J].Journal of Sound and Vibration,2007,300(3):763-779.
[20]LE B A,COTONI V.Validity diagrams of statistical energy analysis[J].Journal of Sound and Vibration,2010,329(2):221-235.
[21]WOHLEVER J,BERNHARD R J.Mechanical energy flow models of rods and beams[J].Journal of Sound and Vibration,1992,153(1):1-19.
[22]LASE Y,ICHCHOU M N,JEZEQUEL L.Energy flow analysis of bars and beams:Theoretical formulations[J].Journal of Sound and Vibration,1996,192(1):282-305.
[23]GOYDER H G D,WHITE R G.Vibrational power flow from machines into build-up structures,partΙ:Introduction and approximate analysis of beam and plate-like foundation[J].Journal of Sound and Vibration,1980,68(1):59-75.