Spread waves in a viscoelastic cylindrical body of a sector cross section with cutouts

The aim of the work is to develop algorithms and a set of programs for studying the dynamic characteristics of viscoelastic thin plates on a deformable base on which it is installed with several dynamic dampers. The theory of thin plates is used to obtain the equation of motion for the plate. The relationship between the efforts and the stirred plate obeys in the hereditary Boltzmann Voltaire integral. With this, a system of integro-differential equations is obtained which is solved by the method of complex amplitudes. As a result, a transcendental algebraic equation was obtained to determine the resonance frequencies, which is solved numerically by the Muller method. To determine the displacement of the point of the plate with periodic oscillations of the base of the plate, a linear inhomogeneous algebraic equation was obtained, which is solved by the Gauss method. The amplitude - frequency response of the midpoint of the plate is constructed with and without regard to the viscosity of the deformed element. The dependence of the stiffness of a deformed element on the frequency of external action is obtained to ensure optimal damping of vibrational vibrations of the plate.

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“…. Rzhanitsyn-Koltunova [21,22,23,24], which has a weak singularity. Here , , A β α are -material parameters.…”

Section: Numerical Resultsmentioning

confidence: 99%

Dynamic Vibration Extinguished on a Viscously Elastic Base

Ishmamatov

Kulmuratov

Хаlilov

et al. 2021

International Journal of Applied Mechanics and Engineering

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“…The problem under consideration is reduced to the problem of plane deformation of the theory of viscoelasticity. The equations of motion of a viscoelastic half-space and a circular tunnel in the absence of mass forces have the form [16]:…”

Section: Statement Of the Problem And Methods Of Solutionmentioning

confidence: 99%

Dynamic Stress-Deformed States of a Circular Tunnel of Small Position Under Harmonic Disturbances

et al. 2021

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There are many underground tunnels of various shapes located in seismically active areas that need to be protected from seismic impacts. The paper considers the impact of harmonic waves on a cylindrical shell located in a viscoelastic half-plane. The study's main purpose is to determine the stress-strain state of a cylindrical shell when exposed to harmonic waves. The basic equation of viscoelasticity in displacements with the corresponding boundary conditions is obtained. The problem posed is solved in mixed potentials that satisfy the wave equation with complex parameters. The solution is expressed in terms of special Bessel and Hankel functions. As a result of multiple reflections, a system of algebraic equations with complex coefficients is obtained. In the future, this system is solved by the Gauss method with the selection of the main element. The analytical solution is obtained in infinite series, the convergence of which is investigated numerically. The numerical results were obtained using the MATLAB software package. The reliability of the research results is confirmed by good agreement with theoretical and experimental results and those obtained by other authors.

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“…The values of the rheological parameters of the shell are taken as = 0,048; = 0,05; = 0,1. Table 1 shows the complex values of the low frequencies of a reinforced (with four rods) truncated conical shell at different shell thicknesses in the limit of the Kirchhoff -Love hypothesis [26][27][28]. It is necessary to determine the values of the complex natural frequency and the corresponding oscillation forms when both ends of the shell contour are pivotally supported ( 1 = 1 = = = = 0).…”

Section: Methods Of Solutionmentioning

confidence: 99%

Natural Vibrations of the Reinforced Tapered Shell with Taking Into Account the Viscoelastic Properties of the Material

et al. 2021

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In this paper, the integro-differential equations of natural oscillations of a viscoelastic ribbed truncated conical shell are obtained based on the Lagrange variational equation. The general research methodology is based on the variational principles of mechanics and variational methods. Geometrically nonlinear mathematical models of the deformation of ribbed conical shells are obtained, considering such factors as the discrete introduction of edges. Based on the finite element method, a method for solving and an algorithm for the equations of natural oscillations of a viscoelastic ribbed truncated conical shell with articulated and freely supported edges is developed. The problem is reduced to solving homogeneous algebraic equations with complex coefficients of large order. For a solution to exist, the main determinant of a system of algebraic equations must be zero. From this condition, we obtain a frequency equation with complex output parameters. The study of natural vibrations of viscoelastic panels of truncated conical shells is carried out, and some characteristic features are revealed. The complex roots of the frequency equation are determined by the Muller method. At each iteration of the Muller method, the Gauss method is used with the main element selection. As the number of edges increases, the real and imaginary parts of the eigenfrequencies increase, respectively.

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Spread waves in a viscoelastic cylindrical body of a sector cross section with cutouts

Cited by 11 publications

References 11 publications

Dynamic Vibration Extinguished on a Viscously Elastic Base

Dynamic Vibration Extinguished on a Viscously Elastic Base

Dynamic Stress-Deformed States of a Circular Tunnel of Small Position Under Harmonic Disturbances

Natural Vibrations of the Reinforced Tapered Shell with Taking Into Account the Viscoelastic Properties of the Material

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