复杂边界条件板壳耦合结构振动分析
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摘要
板壳类结构在工程领域被广泛应用,使得板壳耦合结构动力学特性成为备受关注的研究话题。针对现有研究方法在复杂耦合结构动力学特性分析方面的局限性,构建复杂边界条件下板壳耦合结构振动分析模型,采用二维改进傅里叶级数对弹性板和圆柱壳结构各位移函数分别进行描述,复杂边界条件通过不同组合的弹性约束来模拟,并依赖四类耦合弹簧充分考虑结构之间弯矩、横向剪力、面内纵向力以及面内剪切力的机械耦合效应,进而基于哈密顿原理和瑞利-里兹方法得到板壳耦合结构系统的特征方程与振动响应。研究结果表明,该方法预测板壳耦合结构模态参数优于文献结果,预测强迫响应结果与测试结果吻合良好,验证了该分析方法的正确性。建立的板壳耦合结构分析模型可适用于各类复杂边界条件,无需重新进行理论推导和计算程序编写,是一种可靠而高效的分析手段,可为开展复杂耦合结构的振动分析与动力学设计提供通用性的分析模型基础。
Plate-shell coupled structures are extensively applied in practical engineering fields. The dynamic characteristics of plate-shell coupled structures become a study topic receiving many attentions. Here,an analysis model for vibration of plate-shell coupled structures under complex boundary conditions was constructed. Each displacement of a plate-shell coupled structure system was described with two-dimensional improved Fourier series. The complex boundary conditions were simulated with different combinations of elastic restraints. 4 types of coupling springs were introduced to fully consider mechanical coupling effects among bending moments,transverse shear forces,in-plane longitudinal forces and in-plane shear forces on structures ' interfaces. Furthermore,based on Hamilton 's principle and Rayleigh-Ritz method,the characteristic equation of the plate-shell coupled structural system was derived and the system vibration responses were gained. The study results showed that the correctness of the proposed method is verified through comparing the calculated results using the proposed method with those published in literatures and tests; the established analysis model for plate-shell coupled structure systems here is applicable to various complex boundary conditions,and it is a reliable and effective analysis means; the results provide an analysis model basis for vibration analysis and dynamic design of complex coupled structures.
Plate-shell coupled structures are extensively applied in practical engineering fields. The dynamic characteristics of plate-shell coupled structures become a study topic receiving many attentions. Here,an analysis model for vibration of plate-shell coupled structures under complex boundary conditions was constructed. Each displacement of a plate-shell coupled structure system was described with two-dimensional improved Fourier series. The complex boundary conditions were simulated with different combinations of elastic restraints. 4 types of coupling springs were introduced to fully consider mechanical coupling effects among bending moments,transverse shear forces,in-plane longitudinal forces and in-plane shear forces on structures ' interfaces. Furthermore,based on Hamilton 's principle and Rayleigh-Ritz method,the characteristic equation of the plate-shell coupled structural system was derived and the system vibration responses were gained. The study results showed that the correctness of the proposed method is verified through comparing the calculated results using the proposed method with those published in literatures and tests; the established analysis model for plate-shell coupled structure systems here is applicable to various complex boundary conditions,and it is a reliable and effective analysis means; the results provide an analysis model basis for vibration analysis and dynamic design of complex coupled structures.
引文
[1]PETERSON M R,BOYD D E.Free vibrations of circular cylinders with longitudinal,interior partitions[J].Journal of Sound and Vibration,1978,60(1):45-62.
[2]LANGLEY R S.A dynamic stiffness technique for the vibration analysis of stiffened shell structures[J].Journal of Sound and Vibration,1991,156(3):521-540.
[3]HUANG D T,SOEDEL W.Natural frequencies and modes shapes of a circular plates welded to a circular cylindrical shell at arbitrary axial positions[J].Journal of Sound and Vibration,1993,162(3):403-427.
[4]YIM J S,SHON D S,LEE Y S.Free vibration of clampedfree circular cylindrical shell with a plate attached at arbitrary axial position[J].Journal of Sound and Vibration,1998,213(1):75-88.
[5]MISSAOUI J,CHENG L,RICHARD M J.Free and forced vibration of a cylindrical shell with a floor partition[J].Journal of Sound and Vibration,1996,190(1):21-40.
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[7]LEE Y S,CHOI M H,KIM J H.Free vibrations of laminated composite cylindrical shells with an interior rectangular plate[J].Journal of Sound and Vibration,2003,265(4):795-817.
[8]WANG Z H,XING J T,PRICE W G.A study of power flow in a coupled plate-cylindrical shell system[J].Journal of Sound and Vibration,2004,271(3):863-882.
[9]王宇,罗忠.薄壁圆柱壳构件受迫振动的响应特征研究[J].振动与冲击,2015,34(7):103-108.WANG Yu,LUO Zhong.Forced vibration response characteristics of thin cylindrical shell[J].Joural of Vibration and Shock,2015,34(7):103-108.
[10]杨明月,孙玲玲,王晓乐.两端剪力薄膜支撑圆柱壳体的点导纳特性[J].振动与冲击,2014,33(23):100-105.YANG Mingyue,SUN Lingling,WANG Xiaole.The point mobility of circular cylindrical shells with both ends shear diaphragms supported[J].Joural of Vibration and Shock,2014,33(23):100-105.
[11]石焕文,盛美萍,孙进才,等.加纵肋平底圆柱壳振动和声辐射的FEM/BEM研究[J].振动与冲击,2006,25(2):88-92.SHI Huanwen,SHENG Meiping,SUN Jincai,et al.On FEM/BEM for the problems of vibration and acoustic radiation from an axially stiffened cylindrical shell with two and plates[J].Joural of Vibration and Shock,2006,25(2):88-92.
[12]吴仕昊,瞿叶高,华宏星.圆锥壳-圆柱壳-球壳组合结构自由振动分析[J].振动与冲击,2013,32(6):109-120.WU Shihao,QU Yegao,HUA Hongxing.Free vibration analysis of joined conical-cylindrical-spherical shells[J].Joural of Vibration and Shock,2013,32(6):109-120.
[13]SOONG T C.Buckling of stiffened cylindrical shells with circular arc cross-section[J].Aeronautical Quarterly,1970,24(1):263-279.
[14]HU W C L,RANEY J P.Experimental and analytical study of vibrations of joined shells[J].American Institute of Aeronautics and Astronautics Journal,2012,5(5):976-980.
[15]STEEVES E C,DURLING B J,WALTON W C.A method for computing the response of a general axisymmetric shell with an attached asymmetric structure[C]∥Proceedings of the AIAA Structural Dynamics and Aero-elasticity Specialists Conference.New York:AIAA,1969.
[16]HURTY W C.Dynamic analysis of structural systems using component modes[J].American Institute of Aeronautics and Astronautics Journal,2012,3(4):678-685.
[17]DAI Lu,YANG Tiejun,SUN Yao,et al.Influence of boundary conditions on the active control of vibration and sound radiation for a circular cylindrical shell[J].Applied Mechanics and Materials,2011,66/67/68(2):1270-1277.
[18]高跃飞.结构动力学边界条件优化设计及工程实现方法研究[D].西安:西北工业大学,2005.
[19]DAI L,YANG T J,LI W L,et al.Dynamic analysis of circular cylindrical shells with general boundary conditions using modified Fourier series method[J].Journal of Vibration and Acoustics,2012,134(4):041004.
[20]FLGGE W.Stresses in shells[M].Berlin:SpringerVerlag,1962.
[2]LANGLEY R S.A dynamic stiffness technique for the vibration analysis of stiffened shell structures[J].Journal of Sound and Vibration,1991,156(3):521-540.
[3]HUANG D T,SOEDEL W.Natural frequencies and modes shapes of a circular plates welded to a circular cylindrical shell at arbitrary axial positions[J].Journal of Sound and Vibration,1993,162(3):403-427.
[4]YIM J S,SHON D S,LEE Y S.Free vibration of clampedfree circular cylindrical shell with a plate attached at arbitrary axial position[J].Journal of Sound and Vibration,1998,213(1):75-88.
[5]MISSAOUI J,CHENG L,RICHARD M J.Free and forced vibration of a cylindrical shell with a floor partition[J].Journal of Sound and Vibration,1996,190(1):21-40.
[6]LEE Y S,CHOI M H.Free vibrations of circular cylindrical shells with an interior plate using the receptance method[J].Journal of Sound and Vibration,2001,248(3):477-497.
[7]LEE Y S,CHOI M H,KIM J H.Free vibrations of laminated composite cylindrical shells with an interior rectangular plate[J].Journal of Sound and Vibration,2003,265(4):795-817.
[8]WANG Z H,XING J T,PRICE W G.A study of power flow in a coupled plate-cylindrical shell system[J].Journal of Sound and Vibration,2004,271(3):863-882.
[9]王宇,罗忠.薄壁圆柱壳构件受迫振动的响应特征研究[J].振动与冲击,2015,34(7):103-108.WANG Yu,LUO Zhong.Forced vibration response characteristics of thin cylindrical shell[J].Joural of Vibration and Shock,2015,34(7):103-108.
[10]杨明月,孙玲玲,王晓乐.两端剪力薄膜支撑圆柱壳体的点导纳特性[J].振动与冲击,2014,33(23):100-105.YANG Mingyue,SUN Lingling,WANG Xiaole.The point mobility of circular cylindrical shells with both ends shear diaphragms supported[J].Joural of Vibration and Shock,2014,33(23):100-105.
[11]石焕文,盛美萍,孙进才,等.加纵肋平底圆柱壳振动和声辐射的FEM/BEM研究[J].振动与冲击,2006,25(2):88-92.SHI Huanwen,SHENG Meiping,SUN Jincai,et al.On FEM/BEM for the problems of vibration and acoustic radiation from an axially stiffened cylindrical shell with two and plates[J].Joural of Vibration and Shock,2006,25(2):88-92.
[12]吴仕昊,瞿叶高,华宏星.圆锥壳-圆柱壳-球壳组合结构自由振动分析[J].振动与冲击,2013,32(6):109-120.WU Shihao,QU Yegao,HUA Hongxing.Free vibration analysis of joined conical-cylindrical-spherical shells[J].Joural of Vibration and Shock,2013,32(6):109-120.
[13]SOONG T C.Buckling of stiffened cylindrical shells with circular arc cross-section[J].Aeronautical Quarterly,1970,24(1):263-279.
[14]HU W C L,RANEY J P.Experimental and analytical study of vibrations of joined shells[J].American Institute of Aeronautics and Astronautics Journal,2012,5(5):976-980.
[15]STEEVES E C,DURLING B J,WALTON W C.A method for computing the response of a general axisymmetric shell with an attached asymmetric structure[C]∥Proceedings of the AIAA Structural Dynamics and Aero-elasticity Specialists Conference.New York:AIAA,1969.
[16]HURTY W C.Dynamic analysis of structural systems using component modes[J].American Institute of Aeronautics and Astronautics Journal,2012,3(4):678-685.
[17]DAI Lu,YANG Tiejun,SUN Yao,et al.Influence of boundary conditions on the active control of vibration and sound radiation for a circular cylindrical shell[J].Applied Mechanics and Materials,2011,66/67/68(2):1270-1277.
[18]高跃飞.结构动力学边界条件优化设计及工程实现方法研究[D].西安:西北工业大学,2005.
[19]DAI L,YANG T J,LI W L,et al.Dynamic analysis of circular cylindrical shells with general boundary conditions using modified Fourier series method[J].Journal of Vibration and Acoustics,2012,134(4):041004.
[20]FLGGE W.Stresses in shells[M].Berlin:SpringerVerlag,1962.