LOW FREQUENCY EXTENSIONAL VIBRATIONS OF THIN ANISOTROPIC DISCS.
Interim technical rept. no. 2,
COLUMBIA UNIV NEW YORK DEPT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS
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In this paper use is made of the theory of perturbation for solving an eigenvalue problem in anisotropic elasticity. Using the concept of the nearest isotropic tensor, the eigenvalues of our original problem are approximated in terms of the known eigenvalues of the isotropic problem. Explicit perturbation formulas are given and it is shown how they differ from well-known formulas. Finally, the problem of contour vibrations of a circular AT-type quartz disk is treated in detail, and it is shown that the formulas developed herein lead to a convergent sequence of eigenvalues. The phenomenon of bifurcation of eigenvalues is also explained. Author
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