Multiple scattering of flexural waves on Mindlin plates with circular scatterers. Issue 8 (16th March 2021)

• Record Type: Journal Article
• Authors: Kinoshita, Yohei; Biwa, Shiro; Wang, Zuowei
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 101:Issue 8(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-03-16
• Subjects: flexural waves -- mindlin plate theory -- multiple scattering -- wave function expansion; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.202000221
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: 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. Abstract : 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….