Singular boundary method for band structure calculations of in-plane waves in 2D phononic crystals. (January 2023)

• Record Type: Journal Article
• Authors: Li, Weiwei; Sun, Linlin; Gu, Yan; Wang, Fajie
• Is Part Of: Engineering analysis with boundary elements. Volume 146(2023)
• Page Start: 204
• Page End: 215
• Publication Date: 2023-01
• Subjects: Singular boundary method -- Meshless collocation method -- Phononic crystals -- in-plane waves -- Band structures; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2022.10.023
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this study, the singular boundary method, which is a boundary collocation method, is first employed to calculate the band structures of in-plane waves in two-dimensional phononic crystals. When a unit cell of a phononic crystal is considered, the whole boundaries, including the continuity and periodic boundaries are discretized by the singular boundary method. Then, a linear eigenvalue equation is derived. For a given frequency, an eigenvalue that involves the Block wave can be calculated. Therefore, by sweeping the frequencies, the band structure can be obtained. The accuracy, efficiency and convergence of the proposed method are tested by several numerical examples, and the results demonstrate that the singular boundary method can provide stable and efficient results for band structure calculations of in-plane waves in two-dimensional phononic crystals.