Nie Guo-hua. Non-Linear Vibration of Rectangular Retlculated Shallow Shell Structures[J]. Applied Mathematics and Mechanics, 1994, 15(6): 495-504.
Citation: Nie Guo-hua. Non-Linear Vibration of Rectangular Retlculated Shallow Shell Structures[J]. Applied Mathematics and Mechanics, 1994, 15(6): 495-504.

Non-Linear Vibration of Rectangular Retlculated Shallow Shell Structures

  • Received Date: 1992-09-26
  • Publish Date: 1994-06-15
  • This paper deals with non-linear vibration of rectangular reticulated shallow shells by applying non-linear elastic theory of such structures established by the author. Using the assumed(generalized) Fourier series solutions for transverse deflection(lattice joint transverse displacement) and force function,weighted means of the trial functions lead to the relations among the coefficients related to the solutions and vibration equation which determines the unknown time function, and then the amplitude-frequency relations for free vibration and forced vibration due to harmonic force are derived with the aid of the regular perturbation method and Galerkin procedure, respectively.Numerical ezamples are given as well.
  • loading
  • [1]
    Ellington,J,P.and H,McCallion,The free vibration of grillages,ASME J,Appl.Mech,26(1959),603-807.
    Renton,J,D.,On the analysis of triangular mesh grillages,Int.J,Solids Structures,2(1996).307-318.
    McDaniel,T,J,and K.J.Chang,Dynamics of rotationally periodic large space structures,J,Sound and Vibration,68(3)(1980).351-368.
    Williams,F.W.,An algorithm for exact eigenvalue calculations for rotationally periodic structures,Int.J,for Num.Meth,in Eng.,23 (1986),609-622.
    Williams,F.W.,Exact eigenvalue calculations for structures with rotationally periodic substructures,Int.I,for Nurn.Meth,in Eng.,23(1986),895-706.
    Anderson,M.S.,Buckling of periodic lattice structures,AIAA J.,19(6) (1981).782-788.
    Anderson,M.S.,Vibration of prestrcssed periodic lattice structures,AIAA J.,20(1982).551-556.
    Anderson,M,S.and F.W,Williams,Natural vibration and buckling of general periodic lattice structures,AIAA J.,24(1)(1986),163-169.
    Dean,D,L.,Discrete field Analgsis of Structural Sgstems,Course No.203,Int,Center for Mech,Sci.,Udine,Italy,Pergamon Press(1976).
    Wah,T,and L,R.Calcote,Structural Analysis by Finite Difference Calculus,von Nostrand Reinhold Co.New York(1970).
    Kollar,L.,Continuum equations of timber lattice shells,Acta Technica Aeademiae Scientiarurn Hungaricae,94(3-4)(1982),133-141.
    Noor,A,K.,et al.,Continuum models for beam-and platelike lattice structures,AIAA J.,16(12)(1978),1219-1228.
    Noor,A.K.and M,P.Nemeth,Anaysis of spatial beamlike lattices with rigid joints,Computer Meth,in Appl,Mech,Eng.,24(1980),35-59.
    Nie Guo-hua,A non-linear theory of reticulated shallow shells,Proceedings of the 22nd Midwestern Mechanics Conference,Rolla.Missouri,USA(1991).
    Liu Ren-huai,Li Dong,Nie Guo-hua and Cheng Zheng-qiang,Non-linear buckling of squarely-latticed shallow spherical shells,Int,J.Non-Linear Mech.,26(5) (1991),547-565.
    Chia,C,Y.,Nonlinear Analbsis of Plates,McGraw-Hill New York (1980).
  • 加载中


    通讯作者: 陈斌,
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1927) PDF downloads(518) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint