研究了不同边界条件下光滑和正交加筋圆柱壳-球壳组合结构的自由振动。通过对圆柱壳与球壳连接处进行简化处理，把球壳当成自由约束，把圆柱壳当成简支约束，根据Flügge薄壳理论，利用Rayleigh-Ritz法求得结构频率，并与有限元软件ANSYS结果进行比较,证明了该简化方法的适用性及有效性，并分析了球壳扁率及组合壳体长径比对频率的影响。结果表明：随着球心半角Φ增大，结构自振频率降低；长径比L/Rc增大，球心半角Φ对组合结构频率影响逐渐减弱，且结构自振频率逐渐降低，降低幅度在减小。
Abstract
The free vibration of joined ,smooth and orthogonal stiffened cylindrical-spherical shell withvarious boundary conditions is studied.Based on the simplification of the joined part,the spherical shell has free boundary condition and the cylindrical shell has simply supported boundary condition. The Rayleigh-Ritz method is applied to obtain natural frequencies of the structure by Flügge’s thin shell theory. The natural frequencies are calculated and compared with those of the finite element software ANSYS to confirm the applicability and validity of the simplification. The effects of the shallowness of the spherical shell and length-to-radius ratio on the free vibrational behavior of joined structure are investigated.The results indicate that as the semi-angle Φ of the sphere increases, the natural frequencies decrease. The influence of the semi-angle Φ of the sphere on the natural frequencies decreases as length-to-radius ratio L/Rc increases,and the natural frequencies decrease and the magnitude of reducing descends.
关键词
加筋圆柱壳-球壳组合结构；Flü /
gge理论；Rayleigh-Ritz法；自由振动
{{custom_keyword}} /
Key words
stiffened and joined cylindrical-spherical shell /
Flügge’s theory /
Rayleigh-Ritz method;free vibration
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Love A E H. A treatise on the mathematical theory of elasticity
[M]. Dover publication,Forth edition,1944.
[2] R N Arnold , G B Warburton. Flexural vibrations of the walls of
thin cylindrical shells having freely supported ends[J].
Proceedings of the Royal Society of London,Series A,1949,197
(1049):238-256.
[3] Kevin Forsberg. Influence of boundary conditions on the modal
characteristics of thin cylindrical shells[J]. American Institute
of Aeronautics and Astronautics, 1964,2(12): 2150-2157.
[4] HAFT E E. Natural frequencies of clamped cylindrical shells[J].American Institute of Aeronautics and Astronautics, 1968,6(4): 720-721.
[5] Galletly G D. On the in-vacuo vibrations of simply supported, ring-stiffened cylindrical shells[J]. Journal of Applied Mechanics-transactions of the ASME,1954,21(3):225-231.
[6] Egle D M. An analysis of free vibration of orthogonally stiffened cylindrical shells with stiffeners treated as discrete elements[J]. American Institute of Aeronautics and Astronautics,1968,6(3): 518-526.
[7] Mustafa B A J, Ali R. An energy method for freevibration analysis of stiffened circular cylindrical shells[J]. Computers and Structures,1989,32(2):355-363.
[8] Zhao X, Liew K M, Ng T Y. Vibrations of rotating cross-ply laminated circular cylindrical shells with stringer and ring stiffeners[J]. International Journal of Solids and Structures,
2001,39(2):529-545.
[9] Kalnins A. On Vibrations of Shallow Spherical Shells [J]. The
Journal of the Acoustical Society of America,1961,33(8):
1102-1107.
[10] Robinson A R, A numerical method for analysis of free vibration of spherical shells[J]. American Institute of Aeronautics and Astronautics,1967,5(7): 1256-1261.
[11] Pavlyuk N F,Kichaev Yu P. Vibrations of a shallow spherical shell with a hole[J]. International Applied Mechanics,1971,
7(3): 256-259.
[12] Herbert Saunders. Inextensional vibrations of a sphere-cone shell combination[J]. The Journal of the Acoustical Society of America,1959,31(5):579-583.
[13] Galletly G D, Mistry J. The free vibrations of cylindrical shells with various end closures[J]. Nuclear Engineering and Design,1974,30(2):249-268.
[14] Yim J S,Lee Y S,Sohn D S. Free vibration of clamped-free circular cylindrical shell with a plate attached at an arbitrary axial position[J]. Journal of Sound and Vibration,1998,213(1):
75-88.
[15] Young-Shin Lee,Myung-Seog Yang,Hyun-Soo Kim,Jae-Hoon Kim. A study on the free vibration of the joined cylindrical-spherical shell structures[J]. Computers and Structures,2002,80(27-30): 2405-2414.
[16] Mahdi Yusefzad,Firouz Bakhtiari nejad. A study on the free vibration of the prestressed joined Cylindrical–spherical shell structures[J]. Applied Mechanics and Materials,2013,390:
207-214.
[17] Yegao Qu , ShihaoWu,YongChen,HongxingHua. Vibration analysis of ring-stiffened conical-cylindrical-spherical shells based on a modified variational approach[J]. International Journal of Mechanical Sciences,2013,69:72-84.
[18] Kouchakzadeh M A,Shakouri M. Free vibration analysis of joined cross-ply laminated conical shells[J]. International Journal of Mechanical Sciences,2014,78:118-125.
[19] Flügge. Stresses in Shells[M]. Spring,Berlin,1962.
[20] A.Kalnins. Effect of Bending on Vibrations of Spherical Shells[J]. Journal of the Acoustical Society of America, 1964,36(1): 74-81.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(5438 KB)
