Elastic waveguides: History and the state of the art. I

Meleshko, V. V.; Bondarenko, A. A.; Dovgiy, S. A.; Trofimchuk, A. N.; Heijst, G. J. F. van

doi:10.1007/s10958-009-9623-8

Cited by 21 publications

(7 citation statements)

References 77 publications

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“…(9) is the Muller method [18], which was used here. Without revealing the frequency to determine, and calculating at each step only (8) (1) n ( ), c 13 = 2(n 2 − 1) H (1) n−1 ( ) − nH (1) n ( ) − 2 H (1) n ( ), c 21 = H (1) n−1 ( ) − (n + 1)H (1) n ( ), c 22 = H (1) n−1 ( ) − (n + 1)H (1) n ( ), c 23 = (2n 2 + n −̄2)H (1) n ( ) − 2 H (1) n−1 ( ), c 31 = H (1) n−1 ( ) − nH (1) n ( ), c 32 = (1 − 2 ∕2̄2)(H (1) n−1 ( ) − nH (1) n ( )), c 33 = n 2 H (1) n ( ).…”

Section: Statement Of the Problem And Methods Of Solutionmentioning

confidence: 99%

“…As an example, consider the propagation of free axisymmetric waves in a cylindrical cavity located in an elastic medium (8). Then the corresponding radial and tangential stresses in the displacement potentials take the form (13) (1) 1 ( r)e i(− t+̄z) , u r = u z = 0.…”

Section: Andmentioning

confidence: 99%

“…Decay rate uz from ν does not depend. Components u r and uz are always in quadrature, and, thus, the movement of particles in a substance during the propagation of axisymmetric waves along the surface of a cylindrical cavity is completely (20) H01 ( ) = H (1) 0 ( )∕H (1) 1…”

Section: Andmentioning

confidence: 99%

“…In the absence of losses, Rayleigh waves are continuous, without dispersion waves (their phase velocity along the surface does not depend on frequency) and exist in the entire frequency range in which the elastic medium filling the half-space can be considered uniform and isotropic. The oscillation equations of an elastic rod with a circular cross section were presented to the world in the classical article by Pochgammer 1876, he also analyzed extreme cases of low (ω → 0) and high (ω → ∞) frequencies [1]. Since then, many effects have been devoted to these effects, wave characteristics have been studied in more complex structures [2], including shells, and attacks in systems filled with anisotropic media [3].…”

Section: Introductionmentioning

confidence: 99%

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On the Distribution of Free Waves on the Surface of a Viscoelastic Cylindrical Cavity

Теshaev

Safarov

Kuldashov

et al. 2019

J. Vib. Eng. Technol.

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Background In this article, to the development of the theory and methods for calculating vibrations of dissipative mechanical systems consisting of solids, which include both deformable and non-deformable bodies is discussed. Theoretically, the problem in the mathematical aspect, there are not enough developed solution methods and algorithms for dissipative mechanical systems has not yet been posed. The problems of choosing a nucleus and its rheological parameters, their influence on the frequency and damping coefficient systems have not been studied Purpose The goal of the work is to formulate the statement, develop the solution methods and the algorithm for studying the problems of the dynamics of dissipative mechanical systems consisting of thin-walled plates (or shells) with attached masses and point development theory. Methods A method and algorithm for solving problems of eigen and forced vibrations of dissipative mechanical systems consisting of rigid and deformable bodies, based on the methods of Muller, Gauss, Laplace and Runge integral transform, are developed. Results To describe the dissipative properties of the system as a whole, the concept of a global damping coefficient (GDC) is introduced. In the case of a dissipatively homogeneous system of the GDC, it is determined by the imaginary part of the first modulo complex natural frequency. In the role of GDC in the case of a dissipatively inhomogeneous system, are the imaginary parts of both the first and second frequencies. Moreover, the “Change of Roles” occurs with the characteristic value of the stiffness coefficient of the deformable elements; the real parts of the first and second frequencies are closest. At the indicated characteristic value of the deformable elements, the global damping coefficient has a pronounced maximum. A change in the parameter, on which the global damping coefficient so substantially depends, can be achieved by varying physical properties or geometrical dimensions, thereby opening up the promising possibility of effectively controlling the damping properties of dissipative-inhomogeneous mechanical systems. Conclusions The developed solution methods, algorithms and programs allow determining the dissipative properties of a mechanical system depending on various physic-mechanical parameters, geometrical dimensions and boundary conditions. A method for estimating the dissipative properties of the system as a whole (with forced vibrations) depending on the instantaneous values of the deformable elements (shock absorbers) has been developed. The developed method allows to reduce (several times) the amplitudes of displacements and stresses.

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Section: Statement Of the Problem And Methods Of Solutionmentioning

confidence: 99%

Section: Andmentioning

confidence: 99%

Section: Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Distribution of Free Waves on the Surface of a Viscoelastic Cylindrical Cavity

Теshaev

Safarov

Kuldashov

et al. 2019

J. Vib. Eng. Technol.

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“…The waveguide has very simple (two-dimensional) boundary conditions, i.e., one or two surfaces and no edges. Analytical and numerical solutions for these equations have been addressed by different authors [3]. In reality, a plate cannot be infinitely wide or long, however, when the thickness of the plate and wavelength of the guided wave are small compared to the other two dimensions Lamb wave theory can be used without considering interactions between waves and edges or defects.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Study on the Excitation of Guided Waves in Rectangular Plates Using Multiple Point Sources

Duan

Niu

Gan

et al. 2017

Metals

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Ultrasonic guided waves are widely used to inspect and monitor the structural integrity of plates and plate-like structures, such as ship hulls and large storage-tank floors. Recently, ultrasonic guided waves have also been used to remove ice and fouling from ship hulls, wind-turbine blades and aeroplane wings. In these applications, the strength of the sound source must be high for scanning a large area, or to break the bond between ice, fouling and plate substrate. More than one transducer may be used to achieve maximum sound power output. However, multiple sources can interact with each other, and form a sound field in the structure with local constructive and destructive regions. Destructive regions are weak regions and shall be avoided. When multiple transducers are used it is important that they are arranged in a particular way so that the desired wave modes can be excited to cover the whole structure. The objective of this paper is to provide a theoretical basis for generating particular wave mode patterns in finite-width rectangular plates whose length is assumed to be infinitely long with respect to its width and thickness. The wave modes have displacements in both width and thickness directions, and are thus different from the classical Lamb-type wave modes. A two-dimensional semi-analytical finite element (SAFE) method was used to study dispersion characteristics and mode shapes in the plate up to ultrasonic frequencies. The modal analysis provided information on the generation of modes suitable for a particular application. The number of point sources and direction of loading for the excitation of a few representative modes was investigated. Based on the SAFE analysis, a standard finite element modelling package, Abaqus, was used to excite the designed modes in a three-dimensional plate. The generated wave patterns in Abaqus were then compared with mode shapes predicted in the SAFE model. Good agreement was observed between the intended modes calculated in SAFE and the actual, excited modes in Abaqus.

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On Waves Processes in Transversally-Inhomogeneous Waveguides

Vatul’yan

Yurov

2019

Springer Proceedings in Mathematics &Amp; Statistics

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Elastic waveguides: History and the state of the art. I

Cited by 21 publications

References 77 publications

On the Distribution of Free Waves on the Surface of a Viscoelastic Cylindrical Cavity

On the Distribution of Free Waves on the Surface of a Viscoelastic Cylindrical Cavity

A Numerical Study on the Excitation of Guided Waves in Rectangular Plates Using Multiple Point Sources

On Waves Processes in Transversally-Inhomogeneous Waveguides

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