IBRATION AN ALYSIS OF ORTHOTROPIC SHELLS OF REVOLUTION

A theoretical formulation using the finite difference variational technique is developed for the vibration analysis of orthotropic shells of revolution. The general problem is reduced to that appropriate to any special shell shape by utilizing standard results from differential geometry. The action integral of the shell involves no approximations other than the Kirchhoff-Love first approximation and linearization in the displacement components. No power series expansion in the thickness coordinate is used. This integral is simplified by expressing the displacement components and their derivatives in terms of trigonometric functions in the circumferential direction and finite difference expressions in the meridional direction. Hamilton's variational principle is utilized to derive the equations of motion. The reliability of the method is established by application to a number of examples and comparison with published results where possible. The analysis presented herein has, as its principal advantages, simplicity of form and ease of programming.

[1]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[2]  H. Langhaar.  Energy Methods in Applied Mechanics , 1962 .

[3]  A. Kalnins,et al.  Transient Vibration of Thin Elastic Shells , 1965 .

[4]  Olson,et al.  A finite cylindrical shell element and the vibrations of a curved fan blade , 1968 .

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

[6]  A difference-based variational method for shells , 1970 .

[7]  J. E. Stoneking,et al.  A theory for free vibration of orthotropic shells of revolution , 1970 .

[8]  Edward L. Wilson,et al.  Dynamic finite element analysis of arbitrary thin shells , 1971 .

[9]  O. Zienkiewicz.  The Finite Element Method In Engineering Science , 1971 .

[10]  Finite Element Analysis of Arbitrary Thin Shells , 1971 .

[11]  David Bushnell,et al.  Finite-difference energy method for nonlinear shell analysis , 1971 .

[12]  D. Bushnell,et al.  Evaluation of Various Analytical Models for Buckling and Vibration of Stiffened Shells , 1973 .

[13]  David Bushnell.  Finite-Difference Energy Models versus Finite-Element Models: Two Variational Approaches in One Computer Program , 1973 .

[14]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[15]  P L Gould,et al.  FREE VIBRATION OF SHELLS OF REVOLUTION , 1974 .

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

[17]  John Hon-Shing Lau.  Stress and Vibration Analysis of Orthotropic Shells of Revolution , 1977 .

[18]  J. Altenbach,et al.  Ashwell, D. G./Gallagher, R. H. (Hrsg.), Finite Elements for Thin Shells & Curved Members, London‐New York‐Sydney‐Toronto. John Wiley & Sons. 1976. XI, 268 S., £ 11.00. $ 22.00 . , 1977 .