Multiple scattering and stop band characteristics of flexural waves on a thin plate with circular holes

Wang, Zuowei; Biwa, Shiro

doi:10.1016/j.jsv.2017.11.040

Cited by 14 publications

(8 citation statements)

References 29 publications

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“…This over‐determined system of equations can be solved by the least‐square method based on the generalized inverse matrix. Making the system of equations over‐determined in this way has been found to work well in the previous works [30–34] to avoid ill‐conditioning of the equations. In passing, however, it should be mentioned here that when the wave function expansions are applied to multiple scattering problems, a more standard approach is to express the expansions of the scattered fields by the other ( j ≠ i ) scatterers in Equation (17) in the single local coordinates around the i th scatterer using Graf's addition theorem [35].…”

Section: Formulationmentioning

confidence: 85%

“…Based on the fundamental relations described above, the scattering of a flexural wave by non‐overlapping scatterers distributed on the plate is considered, following the formulation in Ref. [30] based on the Kirchhoff theory and other foregoing works on multiple scattering in fiber‐reinforced media [32–34]. The number of the scatterers is denoted by N .…”

Section: Formulationmentioning

confidence: 99%

“…In order to determine the unknown expansion coefficients

E_{n}^{i}

F_{n}^{i}

G_{n}^{i}

, the numerical collocation technique, which was used in the previous works [30–34], is also employed here. Namely, the infinite series in Equation (25) are truncated with a finite number of terms, i.e., the infinite sums for

- \infty < n < \infty

are replaced by those for

- n_{\max} < n < n_{\max}

, where the integer parameter n max is set large enough to achieve sufficient accuracy.…”

Section: Formulationmentioning

confidence: 99%

“…This issue is also worthy of investigation since the more straightforward numerical analysis of the corresponding problem within the framework of three‐dimensional elasticity, with the help of commercial software, is still heavily time‐ and memory‐consuming. Therefore, the aim of the present study is to extend the previous work by Wang and Biwa [30] and to establish a numerical method to analyze the multiple scattering of flexural waves based on the Mindlin theory. Namely, the flexural wave fields in an elastic plate with multiple scatterers are expressed as the superposition of the wave function expansion, and their expansion coefficients are obtained numerically by a collocation technique.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the multiple scattering of flexural waves by a large number of inclusions was analyzed by Cai and Hambric [29] based on the formalism of multiple scattering theory of waves. Wang and Biwa [30] formulated a computational method for multiple scattering of flexural waves by circular holes based on the wave function expansion and a numerical collocation technique. Similar formulation has been applied by Wang et al.…”

Section: Introductionmentioning

confidence: 99%

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Multiple scattering of flexural waves on Mindlin plates with circular scatterers

2021

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The multiple scattering of flexural waves on an elastic plate with circular scatterers is analyzed in the frequency domain based on the Mindlin plate theory accounting for the rotary inertia and shear deformation of the plate. To this purpose, a semi‐analytical numerical method is formulated as an extension of the previous study based on the Kirchhoff plate theory. It consists of expressing the flexural wave field in terms of the superposition of the wave function expansion, and determining the expansion coefficients by a collocation technique. As demonstrative examples, the transmission of a plane flexural wave across a square array of circular through‐thickness holes or thin‐plate inclusions is analyzed using the proposed method. The comparison between the results based on the Mindlin and Kirchhoff theories is shown for the case of multiple holes. The analysis shows that the transmission amplitude of the flexural wave is reduced at certain frequencies due to the Bragg reflection by the inclusions. In the case of thin‐plate inclusions, the resonance of the inclusions also brings about a sharp decrease of the transmission amplitude.

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Section: Formulationmentioning

confidence: 85%

Section: Formulationmentioning

confidence: 99%

“…In order to determine the unknown expansion coefficients

E_{n}^{i}

F_{n}^{i}

G_{n}^{i}

- \infty < n < \infty

are replaced by those for

- n_{\max} < n < n_{\max}

, where the integer parameter n max is set large enough to achieve sufficient accuracy.…”

Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multiple scattering of flexural waves on Mindlin plates with circular scatterers

2021

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Mathematical modeling of planar physically nonlinear inhomogeneous plates with rectangular cuts in the three-dimensional formulation

et al. 2021

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Mathematical models of planar physically nonlinear inhomogeneous plates with rectangular cuts are constructed based on the three-dimensional (3D) theory of elasticity, the Mises plasticity criterion, and Birger’s method of variable parameters. The theory is developed for arbitrary deformation diagrams, boundary conditions, transverse loads, and material inhomogeneities. Additionally, inhomogeneities in the form of holes of any size and shape are considered. The finite element method is employed to solve the problem, and the convergence of this method is examined. Finally, based on numerical experiments, the influence of various inhomogeneities in the plates on their stress–strain states under the action of static mechanical loads is presented and discussed. Results show that these imbalances existing with the plate’s structure lead to increased plastic deformation.

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Multiple scattering of local nonlinear resonators on a thin plate

Wang,

2024

Applied Mathematical Modelling

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Multiple scattering and stop band characteristics of flexural waves on a thin plate with circular holes

Cited by 14 publications

References 29 publications

Multiple scattering of flexural waves on Mindlin plates with circular scatterers

Multiple scattering of flexural waves on Mindlin plates with circular scatterers

Mathematical modeling of planar physically nonlinear inhomogeneous plates with rectangular cuts in the three-dimensional formulation

Multiple scattering of local nonlinear resonators on a thin plate

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