Abstract
A vibrational statement, method and algorithm to assess the damping capacity of structurally inhomogeneous viscoelastic mechanical systems, consisting of a package of rectangular plates and shells with point relations and concentrated masses at different rheological properties of deformable elements, are proposed in the paper. To describe rheological properties of the material, the linear hereditary Boltzmann-Volter theory was used. To assess the damping capacity of the system, the problem in question in each case was reduced to solving the proper problems of algebraic equations with complex parameters solved by the Muller method. The accuracy of the methods was demonstrated by comparing the calculated results with known published data and a numerical experiment. Complex natural frequency of the system was used to assess the damping capacity of inhomogeneous viscoelastic systems. Various eigenvalue problems have been solved for structurally inhomogeneous mechanical systems consisting of a package of plate and shell systems with concentrated masses and shock absorbers. A number of new mechanical effects have been discovered, related to the manifestation of the damping capacity of mechanical systems under consideration.
Highlights
Many technical structures are widely used shell and plate structures
Various eigenvalue problems have been solved for structurally inhomogeneous mechanical systems consisting of a package of plate and shell systems with concentrated masses and shock absorbers
1) The mathematical formulation and methods for solving the problem of natural vibrations of structurally inhomogeneous dissipatively homogeneous and heterogeneous mechanical systems consisting of a package of plates with point supports and attached masses are formulated
Summary
Many technical structures are widely used shell and plate structures. Thin-walled pipes (shells), plates and panels in real conditions, as a rule, interact. If under static loads these features cause a local redistribution of stress and strain fields, in dynamic problems point connections significantly affect all the dynamic characteristics of a plate or shell—the spectrum of natural frequencies, the forms of natural vibrations, resonant frequencies and amplitudes, etc., for example: Leissa [1] [2] developed exact solutions for problems with free vibrational vibrations of rectangular plates
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