一类浅垂度倾斜双梁系统动力特性研究
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摘要
基于动刚度理论建立了倾斜双梁单元的动力平衡方程,给出了同时考虑双梁抗弯刚度差异、倾角、固定边界条件以及垂度等因素的系统横向动刚度阵的近似闭合解。以该闭合解为基础,分析了双梁系统横向动刚度阵的特征函数及动刚度系数在空间和频域上的分布规律。通过数值案例分析,研究了双梁系统的振动特性,进而建议了一种双梁系统模态频率贡献问题的快速判断方法。研究表明,在给定频率区间内,双梁系统的模态频率将同时受到每个单梁的影响,可以通过双梁横向动刚度阵的特征函数及动刚度系数在频域的分布规律进一步判断单梁对系统各阶频率的贡献程度。
Based on the theory of dynamic stiffness,the dynamic equilibrium equation of the inclined double-beam element is established.The approximate closed form solution of the transverse dynamic stiffness matrix of the system with simultaneously considering the bending stiffness difference of the double beam,inclination angle,fixed boundary condition and the sag effect are obtained.Based on this solution,the space and frequency domain distribution of the characteristic function and the dynamic stiffness coefficient of the transverse dynamic stiffness array are analyzed.Through a numerical case study,the vibration characteristics of the double-beam system are studied,and then a method for quickly determining the contribution of each single beam to the modal frequency of the system is proposed.The results show that the modal frequency of the double-beam system is affected by each single beam in a given frequency range.The contribution of each single beam to the system frequencies can be further determined by the distribution situationof the characteristic function of the transverse stiffness matrix and the dynamic stiffness coefficients in the frequency domain.
Based on the theory of dynamic stiffness,the dynamic equilibrium equation of the inclined double-beam element is established.The approximate closed form solution of the transverse dynamic stiffness matrix of the system with simultaneously considering the bending stiffness difference of the double beam,inclination angle,fixed boundary condition and the sag effect are obtained.Based on this solution,the space and frequency domain distribution of the characteristic function and the dynamic stiffness coefficient of the transverse dynamic stiffness array are analyzed.Through a numerical case study,the vibration characteristics of the double-beam system are studied,and then a method for quickly determining the contribution of each single beam to the modal frequency of the system is proposed.The results show that the modal frequency of the double-beam system is affected by each single beam in a given frequency range.The contribution of each single beam to the system frequencies can be further determined by the distribution situationof the characteristic function of the transverse stiffness matrix and the dynamic stiffness coefficients in the frequency domain.
引文
[1]Pai P F,Xin Q,Du X.Modeling and dynamic characteristics of spinning Rayleigh beams[J].International Journal of Mechanical Sciences,2013,68(3):291-303.
[2]Jie Z Z,Hui W R,Xia Z X,et al.Evaluation of measurement methods for tension of parallel steel strand stay cables[J].Bridge Construction,2016,46(2):42-47.
[3]Hamada Tadataka R,Nakayama H,Hayashi K.Free and forced vibrations of elastically connected doublebeam systems[J].Bulletin of the JSME,1983,26(221):1936-1942.
[4]Oniszczuk Z.Forced transverse vibrations of an elastically connected complex simply supported doublebeam system[J].Journal of Sound&Vibration,2004,270(4-5):997-1011.
[5]VU H V,Ordó1ez A M,Karnopp B H.Vibration of a double-beam system[J].Journal of Sound&Vibration,2000,229(4):807-822.
[6]Gürg9ze M,Erol H.On laterally vibrating beams carrying tip masses,coupled by several double springmass systems[J].Journal of Sound and Vibration,2004,269(1):431-438.
[7]Seelig J M,W H Hoppmann.Impact on an elastically connected double-beam system[J].Journal of Applied Mechanics,1963,31(4):621-626.
[8]Oniszczuk Z.Free transverse vibrations of an elastically connected rectangular simply supported double-plate complex system[J].Journal of Sound&Vibration,2000,232(2):387-403.
[9]Zhang Y Q,LU Y,Wang S L,et al.Vibration and buckling of a double-beam system under compressive axial loading[J].Journal of Sound&Vibration,2008,318(1):341-352.
[10]Kelly S Graham,Srinivas S.Free vibrations of elastically connected stretched beams[J].Journal of Sound&Vibration,2009,326(326):883-893.
[11]Stojanovic′Vladimir,Kozic′Predrag,Pavlovic′Ratko,et al.Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading[J].Archive of Applied Mechanics,2011,81(12):1993-2005.
[12]Stojanovic′Vladimir P Kozic′.Forced transverse vibration of Rayleigh and Timoshenko double-beam system with effect of compressive axial load[J].International Journal of Mechanical Sciences,2012,60(1):59-71.
[13]Kozic′Predrag,Pavlovic′R,Karlicˇic′D.The flexural vibration and buckling of the elastically connected parallel-beams with a Kerr-type layer in between[J].Mechanics Research Communications,2014,56(2):83-89.
[14]Seelig J M,HoppmannⅡW H.Normal mode vibrations of systems of elastically connected parallel bars[J].Journal of the Acoustical Society of America,1964,36(1):93-99.
[15]Huang Qinghua,Xie W C.Stability of SDOF linear viscoelastic system under the excitation of wideband noise[J].Journal of Applied Mechanics,2008,75(2):1377-1385.
[16]Ariaratnam S T,Abdelrahman N M.Almost-sure stochastic stability of viscoelastic plates in supersonic flow[J].AIAA Journal,2001,39(3):465-472.
[17]Pavlovic′Ratko,Kozic′P,Pavlovic′I.Dynamic stability and instability of a double-beam system subjected to random forces[J].International Journal of Mechanical Sciences,2012,62(1):111-119.
[18]Williams F W,Banerjee J R.Free vibration of composite beams-an exact method using symbolic computation[J].Journal of Aircraft,1995,32(3):636-642.
[19]Dan D,Xu B,Huang H,et al.Research on the characteristics of transverse dynamic stiffness of an inclined shallow cable[J].Journal of Vibration&Control,2014,22(3):1609-1610.
[20]Davenport A G,Steels G N.Dynamic behavior of massive guy cables[J].Journal of the Structural Division,1965,91(2):43-70.
[21]Dan D,Chen Z,Yan X.Closed-form formula of the transverse dynamic stiffness of a shallowly inclined taut cable[J].Shock and Vibration,2014,2014(1):1-14.
[22]袁驷.程序结构力学[M].北京:高等教育出版社,2008.
[23]Li J,Hua H,Li X.Dynamic stiffness matrix of an axially loaded slender double-beam element[J].Struct Eng.Mech.,2010,35(6):717-733.
[2]Jie Z Z,Hui W R,Xia Z X,et al.Evaluation of measurement methods for tension of parallel steel strand stay cables[J].Bridge Construction,2016,46(2):42-47.
[3]Hamada Tadataka R,Nakayama H,Hayashi K.Free and forced vibrations of elastically connected doublebeam systems[J].Bulletin of the JSME,1983,26(221):1936-1942.
[4]Oniszczuk Z.Forced transverse vibrations of an elastically connected complex simply supported doublebeam system[J].Journal of Sound&Vibration,2004,270(4-5):997-1011.
[5]VU H V,Ordó1ez A M,Karnopp B H.Vibration of a double-beam system[J].Journal of Sound&Vibration,2000,229(4):807-822.
[6]Gürg9ze M,Erol H.On laterally vibrating beams carrying tip masses,coupled by several double springmass systems[J].Journal of Sound and Vibration,2004,269(1):431-438.
[7]Seelig J M,W H Hoppmann.Impact on an elastically connected double-beam system[J].Journal of Applied Mechanics,1963,31(4):621-626.
[8]Oniszczuk Z.Free transverse vibrations of an elastically connected rectangular simply supported double-plate complex system[J].Journal of Sound&Vibration,2000,232(2):387-403.
[9]Zhang Y Q,LU Y,Wang S L,et al.Vibration and buckling of a double-beam system under compressive axial loading[J].Journal of Sound&Vibration,2008,318(1):341-352.
[10]Kelly S Graham,Srinivas S.Free vibrations of elastically connected stretched beams[J].Journal of Sound&Vibration,2009,326(326):883-893.
[11]Stojanovic′Vladimir,Kozic′Predrag,Pavlovic′Ratko,et al.Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading[J].Archive of Applied Mechanics,2011,81(12):1993-2005.
[12]Stojanovic′Vladimir P Kozic′.Forced transverse vibration of Rayleigh and Timoshenko double-beam system with effect of compressive axial load[J].International Journal of Mechanical Sciences,2012,60(1):59-71.
[13]Kozic′Predrag,Pavlovic′R,Karlicˇic′D.The flexural vibration and buckling of the elastically connected parallel-beams with a Kerr-type layer in between[J].Mechanics Research Communications,2014,56(2):83-89.
[14]Seelig J M,HoppmannⅡW H.Normal mode vibrations of systems of elastically connected parallel bars[J].Journal of the Acoustical Society of America,1964,36(1):93-99.
[15]Huang Qinghua,Xie W C.Stability of SDOF linear viscoelastic system under the excitation of wideband noise[J].Journal of Applied Mechanics,2008,75(2):1377-1385.
[16]Ariaratnam S T,Abdelrahman N M.Almost-sure stochastic stability of viscoelastic plates in supersonic flow[J].AIAA Journal,2001,39(3):465-472.
[17]Pavlovic′Ratko,Kozic′P,Pavlovic′I.Dynamic stability and instability of a double-beam system subjected to random forces[J].International Journal of Mechanical Sciences,2012,62(1):111-119.
[18]Williams F W,Banerjee J R.Free vibration of composite beams-an exact method using symbolic computation[J].Journal of Aircraft,1995,32(3):636-642.
[19]Dan D,Xu B,Huang H,et al.Research on the characteristics of transverse dynamic stiffness of an inclined shallow cable[J].Journal of Vibration&Control,2014,22(3):1609-1610.
[20]Davenport A G,Steels G N.Dynamic behavior of massive guy cables[J].Journal of the Structural Division,1965,91(2):43-70.
[21]Dan D,Chen Z,Yan X.Closed-form formula of the transverse dynamic stiffness of a shallowly inclined taut cable[J].Shock and Vibration,2014,2014(1):1-14.
[22]袁驷.程序结构力学[M].北京:高等教育出版社,2008.
[23]Li J,Hua H,Li X.Dynamic stiffness matrix of an axially loaded slender double-beam element[J].Struct Eng.Mech.,2010,35(6):717-733.
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