On the fractional homogenization of one-dimensional elastic metamaterials with viscoelastic foundation

Ding, Wei; Hollkamp, John P.; Patnaik, Sansit; Semperlotti, Fabio

doi:10.1007/s00419-022-02170-w

Cited by 7 publications

(4 citation statements)

References 74 publications

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“…At high frequencies, the effect of the presence of the elastic foundation on dispersion decreases. This low frequency band gap can be associated with the dynamic properties of elastic metamaterials using elastic resonators, and additionally, these findings are in line with the literature [8,15,20].…”

Section: Frequency Spectrum Of the Infinite Periodic Beamsupporting

confidence: 90%

“…The allowed k c values are found by applying the periodic boundary conditions (BC's) (20). The periodic BC's lead to the following equation, which may be derived from Equation ( 21) by applying the Floquet-Bloch theorem:…”

Section: Generalized Transfer Matrix and Dispersion Equation For The ...mentioning

confidence: 99%

“…In another study, dynamic problems of periodic Timoshenko beams resting on a two-parameter elastic foundation were investigated with the same method [19]. Ding et al [20] investigated the effect of foundation parameters on the dispersion behavior of an infinite biperiodic rods resting on a viscoelastic foundation.…”

Section: Introductionmentioning

confidence: 99%

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Wave Propagation in Shear Beams Comprising Finite Periodic Lumped Masses and Resting on Elastic Foundation

Özmutlu

2022

Symmetry

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In this study, the dispersion of an infinite shear beam with a lumped mass connected at periodic distances and resting on an elastic foundation was examined. The effect of periodicity in the finite region of the lumped masses on wave propagation was investigated through a one-dimensional model. The dispersion relationship for Bragg scattering, which consists of one-dimensional periodic lumped masses, was derived using the transfer matrix method. Subsequently, to evaluate the effect of parameters such as the magnitude of the lumped mass and foundation stiffness on the dynamic response of the shear beam, several simulations were performed. The band frequency characteristics of the shear beam are demonstrated with respect to the variations in stiffness and mass. Using the wave-based approach, the effect of periodic masses on wave propagation in a finite region of an infinite beam was revealed. Periodic masses have been shown to have a positive effect on the displacement amplitude; in other words, a lumped mass barrier is effective in providing wave attenuation.

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Section: Frequency Spectrum Of the Infinite Periodic Beamsupporting

confidence: 90%

Section: Generalized Transfer Matrix and Dispersion Equation For The ...mentioning

confidence: 99%

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Wave Propagation in Shear Beams Comprising Finite Periodic Lumped Masses and Resting on Elastic Foundation

Özmutlu

2022

Symmetry

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“…Ding et al [14] studied the use of space-time fractional-order operators in simulating linear elastic waves in 1D periodic structures on viscoelastic foundations. They develop a homogenised model capable of capturing both material and geometric inhomogeneity and viscoelastic behavior.…”

Section: Introductionmentioning

confidence: 99%

The Classical Wave Equation: A Guide to Theoretical Concepts for Enhanced Student Understanding

Yearwood,

Manohar,

Khan

et al. 2023

JAMCS

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Aims/Objectives: To develop an intuitive guide for enhanced students' understanding of the classical one-dimensional wave equation, bridging the gap between theoretical derivations and practical applications. The focus was on understanding wave propagation by modeling the elastic properties of a beam structure as a one-dimensional string.Study Design: The study employed foundational principles and theoretical derivations, and extended into the application of Fourier series techniques to elucidate concepts not typically covered in engineering mathematical textbooks.Methodology: Analytical and numerical methods were utilised to reinforce critical concepts, making abstract ideas tangible for students. Numerical analysis aids in understanding the theory by demonstrating the evolution of wave patterns, aligning with the analytical solution.Results: The comparison of analytical and numerical solutions revealed that different time step values (\(\Delta\)\(\mathit{t}\)) in uence the numerical solution only by shifting the function, \(\mathit{f}\) (\(\mathit{x}\)), in amplitude, but its shape and agreement with the analytical solution was maintained. Conclusion: This research showcased how innovative teaching techniques, combining analytical and numerical methods, can be used to enhance students' understanding of mathematical theory and its applications in engineering.

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Solvability of nonlocal fractional vector functional boundary value problems with p‐Laplacian on a half‐line at resonance

Meng,

Jiang,

Zhou

2024

Math Methods in App Sciences

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In this paper, the solvability of a system of fully nonlinear Hilfer fractional differential equations on the half‐line is studied. Firstly, considering that the half‐line as the domain has the problem of insufficient compactness, we defined the space of weighting functions and normed the convergence at infinity. Secondly, by constructing appropriate operators in these Banach spaces and using the extension for the continuous theorem, some sufficient conditions for the solvability of the problem are obtained. Finally, an example is given to illustrate the main results.

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On the fractional homogenization of one-dimensional elastic metamaterials with viscoelastic foundation

Cited by 7 publications

References 74 publications

Wave Propagation in Shear Beams Comprising Finite Periodic Lumped Masses and Resting on Elastic Foundation

Wave Propagation in Shear Beams Comprising Finite Periodic Lumped Masses and Resting on Elastic Foundation

The Classical Wave Equation: A Guide to Theoretical Concepts for Enhanced Student Understanding

Solvability of nonlocal fractional vector functional boundary value problems with p‐Laplacian on a half‐line at resonance

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