Biot本构模型黏弹夹芯梁振动特性分析及其实验研究
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摘要
黏弹夹芯结构广泛用于薄壁构件的振动和噪声抑制,对其动力学行为的研究一直广受重视。以黏弹夹芯梁为研究对象,提出了一种建立其有限元动力学模型的方法。建模时弹性表面层按欧拉梁处理,中间黏弹性层不可压缩,认为阻尼来只自其纵向剪切变形。Biot本构模型用来描述黏弹性材料参数的频率依赖性动力学行为,通过耗散坐标将其引入到黏弹夹芯梁的有限元方程中。最后对黏弹夹芯梁结构的振动和阻尼特性进行了数值分析及实验研究。结果表明所提出的夹芯梁有限元建模方法是正确、简单和有效的,对工程实际应用具有一定的参考价值。
The viscoelastic sandwich structure is widely used in the vibration and noise suppression of thin-walled components.The study of its dynamic behavior has been widely considered.Taking the viscoelastic sandwich beam as the research object,a method for establishing its finite element dynamic model is proposed.In the modeling,the elastic surface layers are treated as Euler beams,and the middle viscoelastic layer is incompressible where the damping is considered to be derived from its longitudinal shear deformation.The Biot constitutive model is used to describe the frequency-dependent dynamic behavior of the viscoelastic material layer,which is introduced into the finite element equation of a viscoelastic sandwich beam by means of dissipative coordinates.Finally,the vibration and damping characteristics of viscoelastic sandwich beams are analyzed numerically and experimentally.The results show that the Biot model parameter determination and the sandwich beam finite element modeling method proposed in this paper are correct,simple and effective,and have certain reference value for the practical application.
The viscoelastic sandwich structure is widely used in the vibration and noise suppression of thin-walled components.The study of its dynamic behavior has been widely considered.Taking the viscoelastic sandwich beam as the research object,a method for establishing its finite element dynamic model is proposed.In the modeling,the elastic surface layers are treated as Euler beams,and the middle viscoelastic layer is incompressible where the damping is considered to be derived from its longitudinal shear deformation.The Biot constitutive model is used to describe the frequency-dependent dynamic behavior of the viscoelastic material layer,which is introduced into the finite element equation of a viscoelastic sandwich beam by means of dissipative coordinates.Finally,the vibration and damping characteristics of viscoelastic sandwich beams are analyzed numerically and experimentally.The results show that the Biot model parameter determination and the sandwich beam finite element modeling method proposed in this paper are correct,simple and effective,and have certain reference value for the practical application.
引文
[1]Soni M L.Finite element analysis of viscoelastically damped sandwich structures[J].Shock and Vibration Bulletin,1981,55(1):97-109.
[2]Zapfe J A,Lesieutre G A.A discrete layer beam finite element for the dynamic analysis of composite sandwich beams with integral damping layers[J].Computers&Structures,1999,70(6):647-666.
[3]Chen Q,Chan Y W.Integral finite element method for dynamical analysis of elastic-viscoelastic composite structures[J].Computers&Structures,2000,74(1):51-64.
[4]Galucio A C,De U J,Ohayon R.Finite element formulation of viscoelastic sandwich beams using fractional derivative operators[J].Computational Mechanics,2004,33(4):282-291.
[5]Madeira J F A,Araújo A L,Mota Soares C M,et al.Multiobjective optimization of viscoelastic laminated sandwich structures using the Direct MultiSearch method[J].Computers&Structures,2015,147:229-235.
[6]石银明,华宏星,傅志方.约束层阻尼梁的有限元分析[J].上海交通大学学报,2000,34(9):1289-1290.Shi Y M,Hua H X,Fu Z F.Finite element analysis of constrained layer damping beams[J].Journal of Shanghai Jiaotong University,2000,34(9):1289-1290.
[7]王攀,王正亚,孔德飞,等.机敏约束层阻尼薄板的μ综合鲁棒控制研究[J].振动工程学报,2017,30(5):781-789.WANG Pan,WANG Zheng-ya,KONG De-fei,et al.Study onμ-synthesis control of the thin plate with smart constrained layer damping[J].Journal of Vibration Engineering,2017,30(5):781-789.
[8]贺红林,袁维东,夏自强,等.约束阻尼结构的改进准则法拓扑减振动力学优化[J].振动与冲击,2017,36(9):20-27.HE Honglin,YUAN Weidong,XIA Ziqiang,et al.Topology optimization of plates with constrained damping based on improved optimal criteria[J].Journal of Vibration and Shock,2017,36(9):20-27.
[9]Lesieutre G A,Bianchini E.Time domain modeling of linear viscoelasticity using anelastic displacement fields[J].Journal of Vibration and Acoustics,1995,117(4):424-430.
[10]Bagley R L,Torvik J.Fractional calculus-a different approach to the analysis of viscoelastically damped structures[J].AIAA Journal,1983,21(5):741-748.
[11]Golla D F,Hughes P C.Dynamics of viscoelastic structures-a time-domain,finite element formulation[J].ASME Journal Applied Mechanics,1985,52(4):897-906.
[12]Mctavish D J,Hughes P C.Finite element modeling of linear viscoelastic structures-The GHM method[C].33rd Structures,Structural Dynamics and Materials Conference,Dallas,TX,USA,1992:1753-1763.
[13]Biot M A.Variational principles in irreversible thermodynamics with application to viscoelasticity[J].Physical Review,1955,97(6):1463-1469.
[14]Baber T T,Maddox B A,Orazco C E.A finite element model for harmonically excited viscoelastic sandwich beams[J].Computers&Structures,1998,66(1):105-113.
[2]Zapfe J A,Lesieutre G A.A discrete layer beam finite element for the dynamic analysis of composite sandwich beams with integral damping layers[J].Computers&Structures,1999,70(6):647-666.
[3]Chen Q,Chan Y W.Integral finite element method for dynamical analysis of elastic-viscoelastic composite structures[J].Computers&Structures,2000,74(1):51-64.
[4]Galucio A C,De U J,Ohayon R.Finite element formulation of viscoelastic sandwich beams using fractional derivative operators[J].Computational Mechanics,2004,33(4):282-291.
[5]Madeira J F A,Araújo A L,Mota Soares C M,et al.Multiobjective optimization of viscoelastic laminated sandwich structures using the Direct MultiSearch method[J].Computers&Structures,2015,147:229-235.
[6]石银明,华宏星,傅志方.约束层阻尼梁的有限元分析[J].上海交通大学学报,2000,34(9):1289-1290.Shi Y M,Hua H X,Fu Z F.Finite element analysis of constrained layer damping beams[J].Journal of Shanghai Jiaotong University,2000,34(9):1289-1290.
[7]王攀,王正亚,孔德飞,等.机敏约束层阻尼薄板的μ综合鲁棒控制研究[J].振动工程学报,2017,30(5):781-789.WANG Pan,WANG Zheng-ya,KONG De-fei,et al.Study onμ-synthesis control of the thin plate with smart constrained layer damping[J].Journal of Vibration Engineering,2017,30(5):781-789.
[8]贺红林,袁维东,夏自强,等.约束阻尼结构的改进准则法拓扑减振动力学优化[J].振动与冲击,2017,36(9):20-27.HE Honglin,YUAN Weidong,XIA Ziqiang,et al.Topology optimization of plates with constrained damping based on improved optimal criteria[J].Journal of Vibration and Shock,2017,36(9):20-27.
[9]Lesieutre G A,Bianchini E.Time domain modeling of linear viscoelasticity using anelastic displacement fields[J].Journal of Vibration and Acoustics,1995,117(4):424-430.
[10]Bagley R L,Torvik J.Fractional calculus-a different approach to the analysis of viscoelastically damped structures[J].AIAA Journal,1983,21(5):741-748.
[11]Golla D F,Hughes P C.Dynamics of viscoelastic structures-a time-domain,finite element formulation[J].ASME Journal Applied Mechanics,1985,52(4):897-906.
[12]Mctavish D J,Hughes P C.Finite element modeling of linear viscoelastic structures-The GHM method[C].33rd Structures,Structural Dynamics and Materials Conference,Dallas,TX,USA,1992:1753-1763.
[13]Biot M A.Variational principles in irreversible thermodynamics with application to viscoelasticity[J].Physical Review,1955,97(6):1463-1469.
[14]Baber T T,Maddox B A,Orazco C E.A finite element model for harmonically excited viscoelastic sandwich beams[J].Computers&Structures,1998,66(1):105-113.