Dynamical modeling and non-planar coupled behavior of inclined CFRP cables under simultaneous internal and external resonances
|
摘要
A dynamic model for an inclined carbon ?ber reinforced polymer(CFRP)cable is established, and the linear and nonlinear dynamic behaviors are investigated in detail. The partial differential equations for both the in-plane and out-of-plane dynamics of the inclined CFRP cable are obtained by Hamilton's principle. The linear eigenvalues are explored theoretically. Then, the ordinary differential equations for analyzing the dynamic behaviors are obtained by the Galerkin integral and dimensionless treatments.The steady-state solutions of the nonlinear equations are obtained by the multiple scale method(MSM) and the Newton-Raphson method. The frequency-and force-response curves are used to investigate the dynamic behaviors of the inclined CFRP cable under simultaneous internal(between the lowest in-plane and out-of-plane modes) and external resonances, i.e., the primary resonances induced by the excitations of the in-plane mode,the out-of-plane mode, and both the in-plane mode and the out-of-plane mode, respectively. The effects of the key parameters, e.g., Young's modulus, the excitation amplitude,and the frequency on the dynamic behaviors, are discussed in detail. Some interesting phenomena and results are observed and concluded.
A dynamic model for an inclined carbon ?ber reinforced polymer(CFRP)cable is established, and the linear and nonlinear dynamic behaviors are investigated in detail. The partial differential equations for both the in-plane and out-of-plane dynamics of the inclined CFRP cable are obtained by Hamilton's principle. The linear eigenvalues are explored theoretically. Then, the ordinary differential equations for analyzing the dynamic behaviors are obtained by the Galerkin integral and dimensionless treatments.The steady-state solutions of the nonlinear equations are obtained by the multiple scale method(MSM) and the Newton-Raphson method. The frequency-and force-response curves are used to investigate the dynamic behaviors of the inclined CFRP cable under simultaneous internal(between the lowest in-plane and out-of-plane modes) and external resonances, i.e., the primary resonances induced by the excitations of the in-plane mode,the out-of-plane mode, and both the in-plane mode and the out-of-plane mode, respectively. The effects of the key parameters, e.g., Young's modulus, the excitation amplitude,and the frequency on the dynamic behaviors, are discussed in detail. Some interesting phenomena and results are observed and concluded.
A dynamic model for an inclined carbon ?ber reinforced polymer(CFRP)cable is established, and the linear and nonlinear dynamic behaviors are investigated in detail. The partial differential equations for both the in-plane and out-of-plane dynamics of the inclined CFRP cable are obtained by Hamilton's principle. The linear eigenvalues are explored theoretically. Then, the ordinary differential equations for analyzing the dynamic behaviors are obtained by the Galerkin integral and dimensionless treatments.The steady-state solutions of the nonlinear equations are obtained by the multiple scale method(MSM) and the Newton-Raphson method. The frequency-and force-response curves are used to investigate the dynamic behaviors of the inclined CFRP cable under simultaneous internal(between the lowest in-plane and out-of-plane modes) and external resonances, i.e., the primary resonances induced by the excitations of the in-plane mode,the out-of-plane mode, and both the in-plane mode and the out-of-plane mode, respectively. The effects of the key parameters, e.g., Young's modulus, the excitation amplitude,and the frequency on the dynamic behaviors, are discussed in detail. Some interesting phenomena and results are observed and concluded.
引文
[1]IRVINE,H.M.Cable Structures,MIT Press,Cambridge(1981)
[2]TRIANTAFYLLOU,M.S.Dynamics of cables,towing cables and mooring systems.Shock and Vibration Digest,23,3-8(1991)
[3]STAROSSEK,U.Cable dynamics:a review.Structural Engineering International,4,171-176(1994)
[4]REGA,G.Nonlinear vibrations of suspended cables,part I:modeling and analysis.Applied Mechanics Reviews,57,443-478(2004)
[5]REGA,G.Nonlinear vibrations of suspended cables,part II:deterministic phenomena.Applied Mechanics Reviews,57,479-514(2004)
[6]WEI,M.H.,XIAO,Y.Q.,and LIU,H.T.Bifurcation and chaos of a cable-beam coupled system under simultaneous internal and external resonances.Nonlinear Dynamics,67,1969-1984(2012)
[7]LUONGO,A.and ZULLI,D.Dynamic instability of inclined cables under combined wind flow and support motion.Nonlinear Dynamics,67,71-87(2012)
[8]GHOLIPOUR,A.,FAROKHI,H.,and GHAYESH,M.H.In-plane and out-of-plane nonlinear size-dependent dynamics of microplates.Nonlinear Dynamics,79,1771-1785(2015)
[9]GHAYESH,M.H.,FAROKHI,H.,and AMABILI,M.In-plane and out-of-plane motion characteristics of microbeams with modal interactions.Composites Part B:Engineering,60,423-439(2014)
[10]GHAYESH,M.H.and FAROKHI,H.Nonlinear dynamics of microplates.International Journal of Engineering Science,86,60-73(2015)
[11]MEI,K.,SUN,S.,JIN,G.,and SUN,Y.Static and dynamic mechanical properties of long-span cable-stayed bridges using CFRP cables.Advances in Civil Engineering,2017,1-11(2017)
[12]LIU,Y.Carbon fiber reinforced polymer(CFRP)cables for orthogonally loaded cable structures:advantages and feasibility.Structural Engineering International,26,179-181(2016)
[13]KREMMIDAS,S.C.Improving Bridge Stay Cable Performance under Static and Dynamic Loads,Ph.D.dissertation,University of California,San Diego(2004)
[14]KAO,C.S.,KOU,C.H.,and XIE,X.Static instability analysis of long-span cable-stayed bridges with carbon fiber composite cable under wind load(in Chinese).Tamkang Journal of Science and Engineering,9,89-95(2006)
[15]KOU,C.H.,XIE,X.,GAO,J.S.,and HUANG,J.Y.Static behavior of long-span cable-stayed bridges using carbon fiber composite cable(in Chinese).Journal of Zhejiang University,39,137-142(2005)
[16]FAN,Z.,JIANG,Y.,ZHANG,S.,and CHEN,X.Experimental research on vibration fatigue of CFRP and its influence factors based on vibration testing.Shock and Vibration,2017,1-18(2017)
[17]XIE,X.,LI,X.,and SHEN,Y.Static and dynamic characteristics of a long-span cable-stayed bridge with CFRP cables.Materials,7,4854-4877(2014)
[18]XIE,X.,GAO,J.S.,KOU,C.H.,and HUANG,J.Y.Structural dynamic behavior of longspan cable-stayed bridges using carbon fiber composite cable(in Chinese).Journal of Zhejiang University,39,728-733(2005)
[19]KANG,H.J.,ZHU,H.P.,ZHAO,Y.Y.,and YI,Z.P.In-plane non-linear dynamics of the stay cables.Nonlinear Dynamics,73,1385-1398(2013)
[20]KANG,H.J.,ZHAO,Y.Y.,and ZHU,H.P.Linear and nonlinear dynamics of suspended cable considering bending stiffness.Journal of Vibration and Control,21,1487-1505(2015)
[21]LEPIDI,M.and GATTULLI,V.Static and dynamic response of elastic suspended cables with thermal effects.Int.Journal of Solids and Structure,49,1103-1116(2012)
[22]LUONGO,A.,REGA,G.,and VESTRONI,F.Monofrequent oscillations of a non-linear model of a suspended cable.Journal of Sound and Vibration,82,247-259(1982)
[23]RICCIARDI,G.and SAITTA,F.A continuous vibration analysis model for cables with sag and bending stiffness.Engineering Structures,30,1459-1472(2008)
[24]SOUSA,R.A.,SOUZA,R.M.,FIGUEIREDO,F.P.,CAMBIER P.,OLIVEIRA,A.C.,and SOUZA,R.M.The influence of bending and shear stiffness and rotational inertiain vibrations of cables:an analytical approach.Engineering Structures,33,689-695(2011)
[25]CEBALLOS,M.A.and PRATO,C.A.Determination of the axial force on stay cables accounting for their bending stiffness and rotational end restraints by free vibration tests.Journal of Sound and Vibration,317,127-141(2008)
[26]NAYFEH,A.H.and MOOK,D.T.Nonlinear Oscillations,Wiley,New York(1979)
[27]DING,H.,HUANG,L.,MAO,X.,and CHEN,L.Primary resonance of traveling viscoelastic beam under internal resonance.Applied Mathematics and Mechanics(English Edition),38(1),1-14(2017)https://doi.org/10.1007/s10483-016-2152-6
[28]GUO,T.,KANG,H.,WANG,L.,and ZHAO,Y.Triad mode resonant interactions in suspended cables,Science China:Physics,Mechanics and Astronomy,59,1-14(2016)
[2]TRIANTAFYLLOU,M.S.Dynamics of cables,towing cables and mooring systems.Shock and Vibration Digest,23,3-8(1991)
[3]STAROSSEK,U.Cable dynamics:a review.Structural Engineering International,4,171-176(1994)
[4]REGA,G.Nonlinear vibrations of suspended cables,part I:modeling and analysis.Applied Mechanics Reviews,57,443-478(2004)
[5]REGA,G.Nonlinear vibrations of suspended cables,part II:deterministic phenomena.Applied Mechanics Reviews,57,479-514(2004)
[6]WEI,M.H.,XIAO,Y.Q.,and LIU,H.T.Bifurcation and chaos of a cable-beam coupled system under simultaneous internal and external resonances.Nonlinear Dynamics,67,1969-1984(2012)
[7]LUONGO,A.and ZULLI,D.Dynamic instability of inclined cables under combined wind flow and support motion.Nonlinear Dynamics,67,71-87(2012)
[8]GHOLIPOUR,A.,FAROKHI,H.,and GHAYESH,M.H.In-plane and out-of-plane nonlinear size-dependent dynamics of microplates.Nonlinear Dynamics,79,1771-1785(2015)
[9]GHAYESH,M.H.,FAROKHI,H.,and AMABILI,M.In-plane and out-of-plane motion characteristics of microbeams with modal interactions.Composites Part B:Engineering,60,423-439(2014)
[10]GHAYESH,M.H.and FAROKHI,H.Nonlinear dynamics of microplates.International Journal of Engineering Science,86,60-73(2015)
[11]MEI,K.,SUN,S.,JIN,G.,and SUN,Y.Static and dynamic mechanical properties of long-span cable-stayed bridges using CFRP cables.Advances in Civil Engineering,2017,1-11(2017)
[12]LIU,Y.Carbon fiber reinforced polymer(CFRP)cables for orthogonally loaded cable structures:advantages and feasibility.Structural Engineering International,26,179-181(2016)
[13]KREMMIDAS,S.C.Improving Bridge Stay Cable Performance under Static and Dynamic Loads,Ph.D.dissertation,University of California,San Diego(2004)
[14]KAO,C.S.,KOU,C.H.,and XIE,X.Static instability analysis of long-span cable-stayed bridges with carbon fiber composite cable under wind load(in Chinese).Tamkang Journal of Science and Engineering,9,89-95(2006)
[15]KOU,C.H.,XIE,X.,GAO,J.S.,and HUANG,J.Y.Static behavior of long-span cable-stayed bridges using carbon fiber composite cable(in Chinese).Journal of Zhejiang University,39,137-142(2005)
[16]FAN,Z.,JIANG,Y.,ZHANG,S.,and CHEN,X.Experimental research on vibration fatigue of CFRP and its influence factors based on vibration testing.Shock and Vibration,2017,1-18(2017)
[17]XIE,X.,LI,X.,and SHEN,Y.Static and dynamic characteristics of a long-span cable-stayed bridge with CFRP cables.Materials,7,4854-4877(2014)
[18]XIE,X.,GAO,J.S.,KOU,C.H.,and HUANG,J.Y.Structural dynamic behavior of longspan cable-stayed bridges using carbon fiber composite cable(in Chinese).Journal of Zhejiang University,39,728-733(2005)
[19]KANG,H.J.,ZHU,H.P.,ZHAO,Y.Y.,and YI,Z.P.In-plane non-linear dynamics of the stay cables.Nonlinear Dynamics,73,1385-1398(2013)
[20]KANG,H.J.,ZHAO,Y.Y.,and ZHU,H.P.Linear and nonlinear dynamics of suspended cable considering bending stiffness.Journal of Vibration and Control,21,1487-1505(2015)
[21]LEPIDI,M.and GATTULLI,V.Static and dynamic response of elastic suspended cables with thermal effects.Int.Journal of Solids and Structure,49,1103-1116(2012)
[22]LUONGO,A.,REGA,G.,and VESTRONI,F.Monofrequent oscillations of a non-linear model of a suspended cable.Journal of Sound and Vibration,82,247-259(1982)
[23]RICCIARDI,G.and SAITTA,F.A continuous vibration analysis model for cables with sag and bending stiffness.Engineering Structures,30,1459-1472(2008)
[24]SOUSA,R.A.,SOUZA,R.M.,FIGUEIREDO,F.P.,CAMBIER P.,OLIVEIRA,A.C.,and SOUZA,R.M.The influence of bending and shear stiffness and rotational inertiain vibrations of cables:an analytical approach.Engineering Structures,33,689-695(2011)
[25]CEBALLOS,M.A.and PRATO,C.A.Determination of the axial force on stay cables accounting for their bending stiffness and rotational end restraints by free vibration tests.Journal of Sound and Vibration,317,127-141(2008)
[26]NAYFEH,A.H.and MOOK,D.T.Nonlinear Oscillations,Wiley,New York(1979)
[27]DING,H.,HUANG,L.,MAO,X.,and CHEN,L.Primary resonance of traveling viscoelastic beam under internal resonance.Applied Mathematics and Mechanics(English Edition),38(1),1-14(2017)https://doi.org/10.1007/s10483-016-2152-6
[28]GUO,T.,KANG,H.,WANG,L.,and ZHAO,Y.Triad mode resonant interactions in suspended cables,Science China:Physics,Mechanics and Astronomy,59,1-14(2016)