The natural vibrations of shell structures taking into account dissipative properties and structural heterogeneity

The paper considers the natural oscillations of shell structures. In general, these structures are a set of deformable elements with different rheological properties. An algorithm for solving the viscoelastic dynamic problems has been developed for the complex axisymmetric structures. The physical properties of the viscoelastic structural elements are described by linear Boltzmann-Voltaire relations with integral difference cores. The three-parameter core of Rzhanitsyn-Koltunov was used as the relaxation core. In general, the problem is reduced to solving the systems of first-order ordinary differential equations in the complex variables. A frequency equation is obtained, for the solution where the Muller method is applied. The calculated values of the natural frequencies of oscillations with a given degree of accuracy are given.

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