A wave and finite element method for calculating sound transmission through rectangular panels

• Published in: Mechanical systems and signal processing Vol. 151; p. 107357
• Main Authors: Yang, Yi, Kingan, Michael J., Mace, Brian R.
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 01-04-2021; Elsevier BV
• Subjects: Computational fluid dynamics; Exact solutions; Far fields; Finite element analysis; Finite element method; Free wave propagation; Incident waves; Mathematical models; Modal behaviour; Rectangular; Rectangular panels; Resonant frequencies; Sound transmission; Sound transmission loss; Transmission loss; Wave and finite element; Wave propagation; Sound transmission loss; Modal behaviour; Rectangular; Wave and finite element
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2020.107357

•Fourier transforms used to decompose the blocked pressure into harmonics.•Modelling the responses of finite-sized panels using an infinite panel.•WFE based formulations developed to calculate panel’s natural frequencies.•Hybrid model developed to capture the modal effects on the transmission loss.
A wave based methodology is proposed to investigate sound transmission through rectangular, rigidly-baffled panels, including the modal behaviour of the structure. The panel is homogeneous in-plane, but the through-thickness construction can be of arbitrary complexity. The fluids are modelled analytically, the structure by the wave and finite element method: a small segment of the structure is meshed to predict the behaviour of an infinite panel with the same properties. The transverse displacement of the panel is modelled as a sum of sine terms, each associated with a specific mode. Neglecting fluid loading, the blocked pressure of the incident wave is decomposed into space harmonics with given trace wavenumbers. An equivalent, infinite plate, excited by a periodic continuation of the loading on the finite panel, is considered. The natural frequencies of the finite panel follow from free wave propagation, its response estimated from that of the infinite panel. The far-field acoustic pressure and sound transmission loss are presented. Numerical results agree well with analytical solutions, other numerical solutions and measurements. The proposed method takes the modal effects fully into account, and is efficient and straightforward to implement.