螺栓联接梁动力学模型及其参数辨识方法
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摘要
针对处于悬臂态的螺栓联接梁,采用线性弯曲刚度和立方刚度等参数来表征该系统联接部位的非线性特性,结合边界条件和联接部位的连续性条件,建立其二自由度非线性动力学模型。采用多尺度法对该系统进行求解,获得其非线性频率响应函数。在非线性解的基础上,推导出系统的线性和非线性参数的表达式。以某悬臂螺栓联接梁为例,实测不同预紧力矩下的固有特性和响应特性,进而辨识出不同预紧力矩下该系统的线性和非线性参数。结果表明:本文提出的螺栓联接梁二自由度非线性模型以及相应的参数辨识方法具有合理性,螺栓联接梁具有典型的软式非线性特性。
For the cantilever bolted joint beam, parameters including linear bending stiffness and cubic stiffness were introduced to represent the nonlinear characteristics of the joint part. Combined with the boundary conditions and the continuity of joint part, a two degree of freedom(DOF) nonlinear dynamic model was constructed and the nonlinear frequency response function was obtained by means of multiple scales method. Based on the nonlinear solutions,expressions of linear and nonlinear parameters were deduced. A cantilever beam with bolted joint was taken as example to identify the linear and nonlinear parameters by measuring its natural characteristics and response characteristics at different preloads. The results show that the two DOF model and the identification method are reasonable. Typical"softening" nonlinearities can be also observed in the results.
For the cantilever bolted joint beam, parameters including linear bending stiffness and cubic stiffness were introduced to represent the nonlinear characteristics of the joint part. Combined with the boundary conditions and the continuity of joint part, a two degree of freedom(DOF) nonlinear dynamic model was constructed and the nonlinear frequency response function was obtained by means of multiple scales method. Based on the nonlinear solutions,expressions of linear and nonlinear parameters were deduced. A cantilever beam with bolted joint was taken as example to identify the linear and nonlinear parameters by measuring its natural characteristics and response characteristics at different preloads. The results show that the two DOF model and the identification method are reasonable. Typical"softening" nonlinearities can be also observed in the results.
引文
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[8]Iwan W D.A distributed-element model for hysteresis and its steady-state dynamic response[J].Journal of Applied Mechanics,1966,4(33):893-900.
[9]Song Y,Hartwigsen C,Mcfarland D,et al.Simulation of dynamics of beam structures with bolted joints using adjusted iwan beam elements[J].Journal of Sound and Vibration,2004,273(1):249-276.
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[12]Ouyang H,Oldfield M,Mottershead J.Experimental and theoretical studies of a bolted joint excited by a torsional dynamic load[J].International Journal of Mechanical Sciences,2006,48(12):1447-1455.
[13]Mohammad K,Worden K,Tomlinson G.Direct parameter estimation for linear and non-linear structures[J].Journal of Sound and Vibration,1992,152(3):471-499.
[14]Yasuda K,Kamiya K.Experimental identification technique of nonlinear beams in time domain[J],Nonlinear Dynamics,1999,18(2):185-202.
[15]Krauss R W,Nayfeh A H.Experimental nonlinear identification of a single mode of a transversely excited beam[J].Nonlinear Dynamics,1999,18(1):69-87.
[16]Yasuda K,Kamiya K,Komakine M.Experimental identification technique of vibrating structures with geometrical nonlinearity[J].Journal of Applied Mechanics,1997,64(2):275-290.
[17]Malatkar P.Nonlinear vibrations of cantilever beams and plates[D].Blacksburg:Virginia Polytechnic Institute and State University.Department of Engineering Science and Mechanics,2003:1-115.
[18]Ahmadian H,Jalali H.Identification of bolted lap joints parameters in assembled structures[J].Mechanical Systems and Signal Processing,2007,21(2):1041-1050.
[19]Rao S S.Mechanical vibrations[M].5th ed.Englewood Cliffs:Prentice Hall,2010:1-94.
[20]Nayfeh A H,Mook D T.Nonlinear oscillations[M].Weinheim:Wiley-VCH,1995:394-408.
[21]Ahmadian H,Mottershead J,Friswell M.Boundary condition identification by solving characteristic equations[J].Journal of Sound and Vibration,2001,247(5):755-763.
[2]Abad J,Franco J,Celorrio R,et al.Design of experiments and energy dissipation analysis for a contact mechanics 3d model of frictional bolted lap joints[J].Advances in Engineering Software,2011,45(1):42-53.
[3]Kim J,Yoon J C,Kang B S.Finite element analysis and modeling of structure with bolted joints[J].Applied Mathematical Modelling,2007,31(5):895-911.
[4]Segalman D J,Gregory D L,Starr M J,et al.Handbook on dynamics of jointed structures[R].Alberquerque:Sandia National Laboratories,2009:10-20.
[5]Ferri A.Friction damping and isolation systems[J].Journal of Vibration and Acoustics,1995,117(B):196-206.
[6]Gaul L,Nitsche R.The role of friction in mechanical joints[J].Applied Mechanics Reviews,2001,54(2):93-106.
[7]Berger E.Friction modeling for dynamic system simulation[J].Applied Mechanics Reviews,2002,55(6):535-577.
[8]Iwan W D.A distributed-element model for hysteresis and its steady-state dynamic response[J].Journal of Applied Mechanics,1966,4(33):893-900.
[9]Song Y,Hartwigsen C,Mcfarland D,et al.Simulation of dynamics of beam structures with bolted joints using adjusted iwan beam elements[J].Journal of Sound and Vibration,2004,273(1):249-276.
[10]Gaul L,Lenz J.Nonlinear dynamics of structures assembled by bolted joints[J].Acta Mechanica,1997,125(1):169-181.
[11]Hartwigsen C J,Song Y,Mcfarland D M,et al.Experimental study of non-linear effects in a typical shear lap joint configuration[J].Journal of Sound and Vibration,2004,277(1):327-351.
[12]Ouyang H,Oldfield M,Mottershead J.Experimental and theoretical studies of a bolted joint excited by a torsional dynamic load[J].International Journal of Mechanical Sciences,2006,48(12):1447-1455.
[13]Mohammad K,Worden K,Tomlinson G.Direct parameter estimation for linear and non-linear structures[J].Journal of Sound and Vibration,1992,152(3):471-499.
[14]Yasuda K,Kamiya K.Experimental identification technique of nonlinear beams in time domain[J],Nonlinear Dynamics,1999,18(2):185-202.
[15]Krauss R W,Nayfeh A H.Experimental nonlinear identification of a single mode of a transversely excited beam[J].Nonlinear Dynamics,1999,18(1):69-87.
[16]Yasuda K,Kamiya K,Komakine M.Experimental identification technique of vibrating structures with geometrical nonlinearity[J].Journal of Applied Mechanics,1997,64(2):275-290.
[17]Malatkar P.Nonlinear vibrations of cantilever beams and plates[D].Blacksburg:Virginia Polytechnic Institute and State University.Department of Engineering Science and Mechanics,2003:1-115.
[18]Ahmadian H,Jalali H.Identification of bolted lap joints parameters in assembled structures[J].Mechanical Systems and Signal Processing,2007,21(2):1041-1050.
[19]Rao S S.Mechanical vibrations[M].5th ed.Englewood Cliffs:Prentice Hall,2010:1-94.
[20]Nayfeh A H,Mook D T.Nonlinear oscillations[M].Weinheim:Wiley-VCH,1995:394-408.
[21]Ahmadian H,Mottershead J,Friswell M.Boundary condition identification by solving characteristic equations[J].Journal of Sound and Vibration,2001,247(5):755-763.