| Abstract: | A method of studying the natural vibrations of highly inhomogeneous shells of revolution is developed. The method is based
on a nonclassical theory of shells that allows for transverse shear and reduction. By separating variables, the two-dimensional
problem is reduced to a sequence of one-dimensional eigenvalue problems. The inverse iteration method is used to reduce these
problems to a sequence of inhomogeneous boundary-value problems solved by the orthogonal sweep method. The capabilities of
the method are illustrated by solving certain representative problems and comparing their solutions with those obtained using
the three-dimensional theory of elasticity, the classical theory of shells, and the refined Timoshenko model
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 38–47, September 2007. |
