Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar

Kaplunov, Julius; Шестакова, А. А.; Aleynikov, I.; Hopkins, Brad; Talonov, A. V.

doi:10.1007/s11043-015-9256-x

Cited by 8 publications

(5 citation statements)

References 9 publications

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“…The analysis of multilayered structures is often more difficult than standard singlelayer structures due to inhomogeneous material characteristics among the layers of the structure. Different researchers have examined many dissimilar problems and analyzed vibrational response inhomogeneous beam composed of alternating stiffsoft components [6], three-layered laminate [7], three-layered plate [8][9][10][11][12][13], five-layered plate [14], multicomponent elastic rod, bar and wave-guides [15][16][17][18][19] due to the extensive uses of layered structures in current innovative and hybrid technology. Furthermore, the authors [20][21][22][23][24][25][26][27] have highlighted the effects of external forces such as damping effects, magneto-electroelastic, thermal stress, hygrothermal response, magnetic fields, and rotation on the propagation of waves in multilayer media.…”

Section: Introductionmentioning

confidence: 99%

Dispersion of an inhomogeneous sandwich plate having imperfect interfaces and supported by the Pasternak foundation

Asif,

Nawaz,

Ibrahim Nuruddeen

2023

Smart Mater. Struct.

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The purpose of this investigation is to see the dispersion of an inhomogeneous sandwich plate with imperfect interfaces between the layers and supported by the two parameters Pasternak foundation under long-wave low-frequency conditions. The governing equation of motion has been considered from the perspective of an anti-plane shear propagation to achieve simplicity. The overall cut-off frequency and the exact dispersion relation are computed. In the context of the structure under investigation, one material contrast setup has been considered. The shortened polynomial dispersion relation$(SPDR)$, which corresponds to the exact dispersion relation $(EDR)$ under material contrast setup, has been reported and investigated further. Additionally, the variational effects of the Pasternak foundation parameters as well as the interface imperfect parameter on the lowest dispersion curve subject to the long-wave low-frequency domain have been investigated using numerical simulations and graphical representations based on physical data. This study is noteworthy because it sheds light on the behaviour of elastic waves in multilayered structures and may be utilized to enhance the layout of three-layered structures used in a variety of industrial fields. Furthermore, we have provided the optimum values of the involved parameters to control and confine the sandwich plate's vibration within the long-wave low-frequency regime.

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Section: Introductionmentioning

confidence: 99%

Dispersion of an inhomogeneous sandwich plate having imperfect interfaces and supported by the Pasternak foundation

Asif,

Nawaz,

Ibrahim Nuruddeen

2023

Smart Mater. Struct.

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“…The waveguides, elastic plates, beams, laminates, panels, rods, as well as cylindrical shells, are some of the structures that may be found in multiply-bond layers, to highlight a few, see Refs. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] In terms of layered structure design and structural analysis, which frequently has contrasting material and geometrical parameters, such as size, volume density, and stiffness. Layered structures offer advantages such as high resistance, lightweight, and strength; additionally, they have static and dynamic excitations.…”

Section: Introductionmentioning

confidence: 99%

“…The application of asymptotic techniques [22][23][24] enhances a better understanding of the relationship between the contrast in parameters of its components and the lowest eigenfrequencies of the structure. The authors 7,[11][12][13][17][18][19][20][21][22][23] used asymptotic analysis to investigate the elastic waves dispersion in highly inhomogeneous multilayered structures having three and five layers, exclusively sandwich structures with contrasting material parameter setups, and analyzed the cut-off frequency properties. In addition, regarding the influence of external forces like a hygro-thermal response, thermal stress, rotation, magnetic fields, and viscoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Dispersion of elastic waves in the three-layered inhomogeneous sandwich plate embedded in the Winkler foundations

Asif

Nawaz

Nuruddeen³

2023

Science Progress

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This research article investigates the behavior of elastic waves in an inhomogeneous isotropic three-layered sandwich plate with soft-core and stiff-skin layers embedded in Winkler foundations, using anti-plane shear motion. The study establishes the exact antisymmetric dispersion relation, low-frequency spectrum, and overall cut-off frequency of the wave propagation. A shortened polynomial dispersion relation is developed for the long-wave low-frequency regime by considering the contrasting material setup and compared with the exact dispersion relation. This article also provides exact and asymptotic formulas for stresses and displacements in each layer of the plate, as well as approximate one-dimensional equations of motion. The results suggest that the approximate equations of motion for the three-layered sandwich plate are valid throughout the entire low-frequency range, despite the presence of Winkler foundations on both sides of the plate. This research is significant as it provides insights into the behavior of waves in composite materials and can be used to improve the design of sandwich structures used in various engineering applications. Additionally, the findings that the approximate equations of motion for the three-layered sandwich plate are valid throughout the low-frequency range, despite the presence of Winkler foundations, can help simplify calculations and make the design process more efficient.

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Section: Introductionmentioning

confidence: 99%

“…ere are significant research efforts in examining rigid body equations' validity in modeling elastic structures, for example, [23,24]. e examination of a viscoelastic bar with end loads targeting application in rails, including more significant terms in modeling and further in the nonlinear dynamic analysis, is done in [23]. Also, in [24], the plane and antiplane dynamic problems of an elastic rectangle, with asymptotic and exact dynamic analysis, were examined to identify the limitations of the rigid body formalism in elastic structures.…”

Section: Introductionmentioning

confidence: 99%

Exact Augmented Perpetual Manifolds: Corollary about Different Mechanical Systems with Exactly the Same Motions

Georgiades

2021

Mathematical Problems in Engineering

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Perpetual points have been defined in mathematics recently, and they arise by setting accelerations and jerks equal to zero for nonzero velocities. The significance of perpetual points for the dynamics of mechanical systems is ongoing research. In the linear natural, unforced mechanical systems, the perpetual points form the perpetual manifolds and are associated with rigid body motions. Extending the definition of perpetual manifolds, by considering equal accelerations, in a forced mechanical system, but not necessarily zero, the solutions define the augmented perpetual manifolds. If the displacements are equal and the velocities are equal, the state space defines the exact augmented perpetual manifolds obtained under the conditions of a theorem, and a characteristic differential equation defines the solution. As a continuation of the theorem herein, a corollary proved that different mechanical systems, in the exact augmented perpetual manifolds, have the same general solution, and, in case of the same initial conditions, they have the same motion. The characteristic differential equation leads to a solution defining the augmented perpetual submanifolds and the solution of several types of characteristic differential equations derived. The theory in a few mechanical systems with numerical simulations is verified, and they are in perfect agreement. The theory developed herein is supplementing the already-developed theory of augmented perpetual manifolds, which is of high significance in mathematics, mechanics, and mechanical engineering. In mathematics, the framework for specific solutions of many degrees of freedom nonautonomous systems is defined. In mechanics/physics, the wave-particle motions are of significance. In mechanical engineering, some mechanical system’s rigid body motions without any oscillations are the ultimate ones.

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Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar

Cited by 8 publications

References 9 publications

Dispersion of an inhomogeneous sandwich plate having imperfect interfaces and supported by the Pasternak foundation

Dispersion of an inhomogeneous sandwich plate having imperfect interfaces and supported by the Pasternak foundation

Dispersion of elastic waves in the three-layered inhomogeneous sandwich plate embedded in the Winkler foundations

Exact Augmented Perpetual Manifolds: Corollary about Different Mechanical Systems with Exactly the Same Motions

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