Own vibrations of ribbed truncated conical shell

Abstract

In this article the integro-differential equations of own vibrations of a viscoelastic ribbed truncated conical shell are obtained on the basis of the Lagrange variational equation. Using the finite element method, a method for solving and an algorithm for the equations of own vibrations of a viscoelastic ribbed truncated conical shell with hinged and freely supported edges has been developed. The problem is reduced to solving homogeneous algebraic equations with large-order complex coefficients. For a solution to exist, the basic determinant of a system of algebraic equations must be equal to zero. From this condition, we obtain the frequency equation with complex output parameters. Complex roots of the frequency equation are determined by the Muller’s method, at each iteration of the Muller’s method, the Gauss method with the selection of the main element is applied. The study of own vibrations of viscoelastic panels of truncated conical shells is carried out and some characteristic features are revealed. With an increase in the number of edges, respectively, the real and imaginary parts of the own frequencies increase.