Wave transmission and reflection analysis through complex media based on the second strain gradient theory

Zhu, Guang; Zine, Abdelmalek; Droz, Christophe; Ichchou, Mohamed

doi:10.1016/j.euromechsol.2021.104326

Cited by 4 publications

(3 citation statements)

References 32 publications

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“…As shown in Fig. 4, the black lines denote the WFEM results and the red lines represent the results from an analytical method [19]. The diffusion is different from the case presented in Fig.…”

Section: Numerical Applicationsmentioning

confidence: 88%

“…υ (q)± =diag exp ∓iκ (q) j x (0 ≤ x ≤ L (q) ), symbol q=c for coupling element, q=k, k+1 for unit cells. On the other hand, the force components of coupling element (c) and unit cells (k, k+1) can be expressed as: F(q)± = Ψ (q)± F υ (q)± P (q)± , (19) in which…”

Section: Finite Element Discretizationmentioning

confidence: 99%

“…The influence of non-local interactions caused by higher-order parameters can be reflected by this model. On the other hand, an analytical method [19], shown by the red lines, is used to valid the WFEM results for bending and tension. As we can see, for the reflection coefficient, the result obtained by WFEM is very close to the one by the analytical method at low frequency, but the results are different at high frequencies.…”

Section: Numerical Applicationsmentioning

confidence: 99%

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Wave Transmission and Reflection Analysis Based on the Three-dimensional Second Strain Gradient Theory

Yang

Ichchou²,

Droz³

et al. 2022

Mechanisms and Machine Science

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The scattering of guided waves through a coupling region is a crucial information when studying waveguides. In this paper, the second strain gradient theory (SSG) is used to describe wave transmission and reflection in a three-dimensional micro-sized medium. First, the constitutive relation of 3D SSG model is derived while six quintic Hermite polynomial shape functions are used for the displacement field. Then Hamilton's principle is used for the weak formulation of the unit-cell's stiffness matrix finite element stiffness, mass matrices and force vector. Eventually the wave diffusion (i.e. including reflection and transmission coefficients) are computed and discussed for various coupling conditions.

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Section: Numerical Applicationsmentioning

confidence: 88%

Section: Finite Element Discretizationmentioning

confidence: 99%

Section: Numerical Applicationsmentioning

confidence: 99%

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