A method of calculating bilateral estimates of the natural frequencies of composite shells with a three-dimensional inhomogeneous density distribution

Abstract

As is known, approximations obtained for the eigenvalues of self-adjoint boundary-value problems by using the Ritz method tend to their limit values from above [I, 9]. In a number of cases it is interesting to construct methodologies assuring uniformly convergent bilateral estlmates of the eigenvalues, which produces the possibility of a real control on the degree of calculation accuracy. In this paper a method is constructed to obtain bilateral estimates of the natural frequencies of laminar shells with inhomogeneous density distribution by using certain abstract results of the theory of nonanalytic perturbations of linear operators.