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 __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 38–47, September 2007. |