Propagation of Proper Waves in a Viscoelastic Timoshenko Plate of Variable Thickness

Propagation of Proper Waves in a Viscoelastic Timoshenko Plate of Variable Thickness

© 2023 by IJETT Journal
Volume-71 Issue-1
Year of Publication : 2023
Author : I. I. Safarov, M. Kh. Teshaev, Z. I. Boltaev, M.R.Ishmamatov, T.R.Ruziyev
DOI : 10.14445/22315381/IJETT-V71I1P203

How to Cite?

I. I. Safarov, M. Kh. Teshaev, Z. I. Boltaev, M.R.Ishmamatov, T.R.Ruziyev, "Propagation of Proper Waves in a Viscoelastic Timoshenko Plate of Variable Thickness," International Journal of Engineering Trends and Technology, vol. 71, no. 1, pp. 25-30, 2023. Crossref,

Elastic distribution waves in lamellar bodies have been studied for more than a hundred years, but work in this direction continues, which indicates a continuing interest in this problem. In this paper, the wave propagation problem in a viscoelastic thin film is considered—a plate of variable cross-section subordinating to the Timoshenko hypothesis. The article's main purpose is to study the distribution of natural waves in an infinite viscoelastic lamellar waveguide with a wedge cross-section based on the Timoshenko hypothesis. The variation of complex natural frequencies and waveforms depending on various waveguide parameters (wavenumber and geometric parameters) is investigated. Integro-differential equations of waveguide motion are obtained based on the variational principle. After applying the freezing method, a system of differential equations with complex coefficients is obtained, which is further solved using the orthogonal run method with a combination of the Muller method on complex arithmetic. Based on the obtained results, it is established that with an increase in the wave number, the real and imaginary parts of normal modes in the Timoshenko wedge-shaped plate tend to have constant values. In this case, the localization of motion is observed near the sharp edge of the waveguide. It is also found that comparing the results obtained according to the Kirchhoff and Timoshenko theories for small wedge angles differs by up to 10%. Real and imaginary parts of a complex function of the propagation velocity of the Azov wave, the propagation velocity of the first mode in a wedge-shaped plate practically does not depend on the Poisson's ratio (a change within 0.5 %). In general, the numerical analysis of edge waves in Kirchhoff and Timoshenko plates allows us to conclude that Kirchhoff's hypotheses are quite suitable for calculating wave processes in wedge-shaped plates, including at frequencies with a wavelength of the order of plate thickness. This discrepancy with the classical results of the theory of Kirchhoff plates of constant thickness is explained by the phenomenon of localization of the waveform with increasing frequency, which occurs only in plates of variable thickness. At the same time, the relative simplicity of the mathematical apparatus of the Kirchhoff plate theory makes it possible to study the dispersion characteristics of waveguides with a more complex cross-section configuration, which is very difficult to construct in the framework of a three-dimensional theory. The results of this work can be applied in calculations of engineering structures consisting of extended plates of constant and variable cross-sections.

Damped wave, Viscoelastic plate sector cross-section, Navier equation, Spectral boundary value problem, Orthogonal run.

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