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Abstract

A nine-node Lagrangian finite element is formulated in an axisymmetric conical coordinate sys tem and used to study the vibration of truncated hollow cones. The governing elasticity equations (strain- displacement) are derived using the generalized expressions for orthogonal curvilinear coordinates. The transformation for hexagonal material constants from a Cartesian coordinate system to the conical coordi nate system is illustrated and results are presented for titanium and beryllium. Results for frequency and mode shape are presented in tabular form and graphically for hexagonal materials of class 6/mmm for a vari ety of truncated cone parameters. Vibration frequencies for isotropic cones are compared with similar results in the existing literature.

Keywords

Finite element hexagonal material hollow cones vibration

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References

Buchanan, G.R. , 1995, Theory and Problems of Finite Element Analysis, Schaum's Outline Series, McGraw-Hill, New York.

Chow, P.C. and Pagano, N.J. , 1967, Elasticity, D. Van Nostrand , Princeton, NJ. (reprinted by Dover, New York)

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Spiegel, M.R. , 1959, Theory and Problems of Vector Analysis, Schaum's Outline Series , McGraw-Hill, New York.

Vibration of Truncated Conical Cylinders of Crystal Class 6/mmm

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