Free vibration analysis and optimisation of axisymmetric plates and shells—I. Finite element formulation

Abstract This paper deals with the free vibration analysis of shells of revolution using the finite element method. A family of variable thickness, curved C (0) Mindlin-Reissner axisymmetric finite elements is presented which include shear deformation and rotatory inertia effects. The accuracy, convergence and efficiency of these newly developed elements are explored through a series of free vibration analyses of axisymmetric shell structures and the results are compared with those obtained by other analytical and numerical methods. The comparisons show that the method yields very good results with a relatively small number of elements and that estimates for the higher modes can be obtained without any difficulties. A companion paper will consider the structural optimisation of axisymmetric shells undergoing free vibrations.

[1]  Lindi M. Wahl,et al.  Finite element analysis of free-free shells of revolution , 1992 .

[2]  Gen Yamada,et al.  Natural Frequencies of Mindlin Circular Plates , 1980 .

[3]  P. E. Grafton,et al.  Analysis of Axisymmetrical Shells by the Direct Stiffness Method , 1963 .

[4]  S. C. Fan,et al.  General free vibration analysis of shells of revolution using the spline finite element method , 1989 .

[5]  G. Yamada,et al.  Natural Frequencies of Thick Annular Plates , 1982 .

[6]  Hyman Garnet,et al.  Axisymmetric Free Vibrations of Conical Shells , 1964 .

[7]  H. Kunieda.  Flexural axisymmetric free vibrations of a spherical dome: Exact results and approximate solutions , 1984 .

[8]  C. L. Amba-Rao,et al.  Axisymmetric vibrations of annular plates of variable thickness , 1975 .

[9]  William C. Schnobrich,et al.  Free Vibrations of Hyperboloidal Shells of Revolution , 1969 .

[10]  T. Charnley,et al.  Normal modes of the modern English church bell , 1983 .

[11]  Gen Yamada,et al.  Free vibration of a conical shell with variable thickness , 1982 .

[12]  Phillip L. Gould,et al.  Free Vibration of Shells of Revolution Using FEM , 1974 .

[13]  Rajendra Singh,et al.  Modal analysis of a hermetic can , 1990 .

[14]  Gen Yamada,et al.  Free vibration of a mindlin annular plate of varying thickness , 1979 .

[15]  R. S. Srinivasan,et al.  Axisymmetric vibration of thick conical shells , 1989 .

[16]  Yoshihiro Narita,et al.  Natural frequencies of simply supported circular plates , 1980 .

[17]  R. L. Nelson.  Analyses of cooling tower dynamics , 1981 .

[18]  M. S. Tavakoli,et al.  Eigensolutions of joined/hermetic shell structures using the state space method , 1989 .

[19]  Mustafa Özakça,et al.  Free vibration analysis and shape optimization of prismatic folded plates and shells with circular curved planform , 1994 .

[20]  Ernest Hinton,et al.  Numerical methods and software for dynamic analysis of plates and shells , 1988 .

[21]  G. Z. Harris,et al.  THE NORMAL MODES OF A CIRCULAR PLATE OF VARIABLE THICKNESS , 1968 .

[22]  J. Kirkhope,et al.  Vibration of circular and annular plates using finite elements , 1972 .