Vibrations of viscoelastic orthotropic shells in various media

Mavlyanov, T.; Koltunov, M. A.

doi:10.1007/bf00859647

Cited by 3 publications

(2 citation statements)

References 2 publications

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“…The equations of motion of this structure satisfy the Lamé equations in a cylindrical coordinate system and are solved in the displacement potentials [14]. Let us introduce three scalar potential functions , , , which are solutions of equations [14].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Vibrations of Cylindrical Shell Structures Filled With Layered Viscoelastic Material

et al. 2021

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A thin-walled shell and a thick-walled mass (cylinder) in contact with it, made of a different material, are structural elements of many machines, apparatus, and structures. The paper considers forced steady-state vibrations of cylindrical shell structures filled with a layered viscoelastic material. The study aims to determine the damping properties of vibrations of a structurally inhomogeneous cylindrical mechanical system under the influence of harmonic loads. The dynamic stress-strain state of a three-layer cylindrical shell filled with a viscoelastic material under the action of internal time-harmonic pressure is investigated. The oscillatory processes of the filler and the bonded shell satisfy the Lamé equations. At the contact between the shell and the filler, the rigid contact conditions are satisfied. Dependences between stresses and strains for a linear viscoelastic material are presented in the form of the Boltzmann-Voltaire integral. The method of separation of variables, the method of the theory of potential functions (special functions), and the Gauss method are used to solve this problem. Based on the analysis of the numerical results, it was found that the dependence of the resonant amplitude of the shell displacements on the viscous properties of the filler is 12-15%. Analysis of the results obtained shows that the study of vibrations of shells containing fillers according to the rod theory will lead to rather large erroneous results (up to 20%).

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Section: Formulation Of the Problemmentioning

confidence: 99%

Vibrations of Cylindrical Shell Structures Filled With Layered Viscoelastic Material

et al. 2021

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“…Kiiko and Akhmedov (1975) examined the influence of material viscoelasticity on the transverse vibrations of an elastic cylindrical shell completely or partially filled with an ideal incompressible liquid subjected to the action of an axial parametric force and normal pressure. Mavlyanov and Koltunov (1975) obtained and solved the equation of motion of an orthotropic viscoelastic cylindrical shell in various media. Markus (1976) used the classical thin shell theory to estimate the damping of cylindrical shells coated with unconstrained layers of viscoelastic material either on one side of the shell (inside or outside) or on both sides.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Viscoelastic Effects on Free Vibrations of a Submerged Fluid-filled Thin Cylindrical Shell

Hasheminejad

Shahsavarifard

2008

Journal of Vibration and Control

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The novel features of the Havriliak-Negami model for dynamic description of viscoelastic material behavior along with the Donnell theory of shell motion are applied to study free vibrational and damping characteristics of an infinitely long viscoelastic thin circular cylindrical shell submerged in and filled with acoustic fluids. The analytical results are illustrated with numerical examples in which two fluid-filled shells of distinctive viscoelastic material properties are undergoing free vibrations in a surrounding ideal fluid medium. The natural frequencies and the associated modal loss factors as a function of the circumferential mode number at selected axial wave lengths and submergence conditions are numerically evaluated and discussed. The numerical results reveal the imperative influence of dynamic viscoelastic properties on the vibrational characteristics of the fluid-coupled system. They demonstrate an interesting correlation between the modal loss factor and the material loss factor in the vicinity of the calculated natural frequency. In particular, the modal loss factor (natural frequency) is found to be highly dependent on (fairly insensitive to) the frequency dependence of the loss factor in the viscoelastic material. A limiting case involving a thin elastic steel shell submerged in water is considered and fair agreement with a well-known solution is established.

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Control of resonant oscillations of viscoelastic systems

Safarov,

Teshaev

2024

Theor appl mech (Belgr)

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Structures in the form of cylindrical ribbed shells and panels are widely used in engineering and construction. The problem of the action of moving loads on an infinitely long cylindrical shell, reinforced along the outer surface with longitudinal stiffeners and containing a viscoelastic inertial filler, is considered. The moving load is transferred to the shell only through the ribs, and there is no load outside the ribs. The discreteness of the location of the ribs is taken into account by writing the equations of motion of the beams, followed by the satisfaction of the conjugation conditions. The influence of the number and stiffness of ribs on the nature of the distribution of shell displacements and contact pressure at the boundary of a viscoelastic filler is shown. The movement of the shell is described by classic equations based on the Kirchhoff-Love hypothesis; for the filler, dynamic equations of the theory of visco-elasticity are used. It has been established that the reinforcement of shells with longitudinal ribs (oscillations of a cantilevered cylindrical shell) leads to a decrease in natural frequencies and damping coefficients in some shells, an increase in the density of the spectrum of natural frequencies, and the appearance of intermediate forms and forms with the same wave numbers, but with different frequencies. External forces increase natural frequencies and damping coefficients. It is found that the frequencies for the inner edges are lower than for the outer edges. In the high-frequency zone, any efforts reduce the natural frequencies and the damping coefficient. This means that additional mass plays a more significant role than additional rigidity. Consequently, the longitudinal strengthening of the shell worsens its dynamic properties.

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Vibrations of viscoelastic orthotropic shells in various media

Cited by 3 publications

References 2 publications

Vibrations of Cylindrical Shell Structures Filled With Layered Viscoelastic Material

Vibrations of Cylindrical Shell Structures Filled With Layered Viscoelastic Material

Dynamic Viscoelastic Effects on Free Vibrations of a Submerged Fluid-filled Thin Cylindrical Shell

Control of resonant oscillations of viscoelastic systems

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