An asymptotic investigation of the dynamics and dispersion of an elastic five-layered plate for anti-plane shear vibration

Nawaz, Rab; Nuruddeen, Rahmatullah Ibrahim; Zia, Qazi Muhammad Zaigham

doi:10.1007/s10665-021-10133-3

Cited by 17 publications

(15 citation statements)

References 31 publications

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“…This happens when the thickness of the coating is extended to negative infinity, that is, h → −∞. Thus, the obtained frequency equation in Equation (36)…”

Section: Welded Half-spacesmentioning

confidence: 91%

“…Here, we analyze the obtained frequency equation in Equation (36) for some special and particular cases of interest. These cases include the absence of the external excitations or forces (and effects), a case of a viscoelastic half-space only, and the situation of welded half-spaces.…”

Section: Special Cases Of the Frequency Equationmentioning

confidence: 99%

“…(a) Traction-free end Now, if the half-space in the presence of the prescribed external forces, rotation, and viscoelasticity is considered to have a traction-free surface at h = 0, then the obtained frequency equation in Equation (36) reduces to the following:…”

Section: Viscoelastic Half-spacementioning

confidence: 99%

“…The techniques are computational, analytical, and asymptotic to appropriately analyze the governing model. We mention here certain methods in [27][28][29][30][31][32][33][34][35][36][37][38][39], where such methodologies were utilized, including the integral transform approach, normal mode analysis approach, harmonic solution approach, eigenvalues approach, and some numerical schemes, among others.…”

Section: Introductionmentioning

confidence: 99%

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Propagation of Surface Waves in a Rotating Coated Viscoelastic Half-Space under the Influence of Magnetic Field and Gravitational Forces

Mubaraki

Althobaiti

Nuruddeen³

2021

Fractal Fract

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The present manuscript focuses on the study of surface wave propagation in a rotating coated viscoelastic half-space and its response to external forces comprised of the magnetic field and gravitational forces. A celebrated normal mode analysis procedure is adopted as the methodology of interest for its high level of efficiency in the literature. The analytically obtained frequency equation is analyzed for certain scenarios of curiosity, in addition to the determination of the resulting displacements and stresses. Moreover, certain physical data of relevance with the viscoelasticity index of unity are considered for the numerical simulations. As for the findings, the presented graphical illustrations showed that both the magnetic field and rotation positively accelerated the dispersion of surface waves in the coated half-space, while the obtained approximate fields in the half-space are found to be oscillatory as they steadily move towards the limiting point.

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“…This happens when the thickness of the coating is extended to negative infinity, that is, h → −∞. Thus, the obtained frequency equation in Equation (36)…”

Section: Welded Half-spacesmentioning

confidence: 91%

Section: Special Cases Of the Frequency Equationmentioning

confidence: 99%

Section: Viscoelastic Half-spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Propagation of Surface Waves in a Rotating Coated Viscoelastic Half-Space under the Influence of Magnetic Field and Gravitational Forces

Mubaraki

Althobaiti

Nuruddeen³

2021

Fractal Fract

Self Cite

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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%

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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Analytical and computational analysis of vibrational behavior of axially loaded beams placed on elastic foundations

Alahmadi,

Nawaz,

Kanwal

et al. 2024

Z Angew Math Mech

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In this study, the vibrational behavior of Rayleigh and shear beams placed over the Hetényi and Pasternak foundations is investigated, with special attention paid to the effects of axial stresses (both tensile and compressive). The uniqueness of the work comes from the thorough consideration of how axial forces, shear deformation, rotational inertia, and foundation factors affect the eigenfrequencies and eigenmodes that control beam vibrations. Eigenfrequencies and eigenmodes are determined through computational analyses with the Galerkin finite element method (GFEM) employing quadratic and cubic polynomials. Comparisons between finite element results and analytical outcomes, both in generalized and specialized contexts, serve to demonstrate the correctness and effectiveness of the approximate solution. The study shows that the Hetényi foundation's influence on eigenfrequency depends on foundation stiffness and relative beam magnitudes, and that shear deformation affects eigenfrequencies more than rotary inertia does. Higher frequencies are largely unaffected by compressive and tensile stresses, but the fundamental frequency is rigorously influenced. Further demonstrating its accuracy, the finite element approach shows great agreement in forecasting eigenmodes and eigenfrequencies. A variety of real‐world situations involving elastically confined beams resting on elastic foundations and being subjected to axial forces are the focus of the study. Axial forces commonly result from external loads, thermal expansion, or structural interactions in real‐world settings. Therefore, it is crucial to understand how they affect beam vibration when designing structures that can endure expected stresses and vibrations while maintaining safety and performance criteria.

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An asymptotic investigation of the dynamics and dispersion of an elastic five-layered plate for anti-plane shear vibration

Cited by 17 publications

References 31 publications

Propagation of Surface Waves in a Rotating Coated Viscoelastic Half-Space under the Influence of Magnetic Field and Gravitational Forces

Propagation of Surface Waves in a Rotating Coated Viscoelastic Half-Space under the Influence of Magnetic Field and Gravitational Forces

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

Analytical and computational analysis of vibrational behavior of axially loaded beams placed on elastic foundations

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