Sound radiation analysis with an enriched Timoshenko beam model based on second strain gradient theory

• Published in: Journal of sound and vibration Vol. 509; p. 116249
• Main Authors: Zhu, Guang, Zine, Abdelmalek, Fossat, Pascal, Ichchou, Mohamed
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 29.09.2021; Elsevier Science Ltd; Elsevier
• Subjects: Acoustics; Analysis of PDEs; Bending; Complex media; Continuum mechanics; Energy flow; Engineering Sciences; Enriched Timoshenko beam model; Enrichment; Evanescent waves; Free wave propagation; Frequency response; Functional Analysis; Heterogeneity; Materials; Mathematics; Mindlin plates; Modal densities; Numerical Analysis; Propagation; Radiation; Reactive fluid environment; Second strain gradient theory; Shear; Sound propagation; Sound radiation from non-local structure; Sound waves; Timoshenko beams; Vibration analysis; Wave propagation; Wave propagation features; Energy flow; Second strain gradient theory; Enriched Timoshenko beam model; Sound radiation from non-local structure; Modal densities; Frequency response; Wave propagation features
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2021.116249

In this work, an enriched Timoshenko beam model describing non-classical bending and shear motion is employed to study its free wave propagation, frequency response, and sound radiation while considering the local behavior of its internal heterogeneity. The enriched Timoshenko beam model is established based on Mindlin’s Second Strain Gradient (SSG) theory, which can capture the long-range interactions between underlying micro-structures in the frame of continuum mechanics. Dispersive behaviors of non-classical bending waves, shear waves, and the extra evanescent waves appearing exclusively in the SSG theory model are analyzed. Then investigations are carried forward into the modal density of non-classical bending waves, shear waves, and energy flow through the enriched model. At last, the frequency response and sound radiation of the Timoshenko beam are studied using wave approach based on its multi-modes character. The resulting non-classical frequency response and radiation features are compared with the classical elasticity theory result, upon which, impacts of local behavior in complex media on the structural dynamics and radiation features are discussed. The role of local behavior is, among others, clearly shown in the frame of the non-classical structural behavior. •Investigating the wave dispersion relation of SSG theory-based Timoshenko beam.•Formulating and validating the expression energy flow in the enriched model.•Studying the FRF and noise radiation based on the enriched model.•Physical interpretation of the exhibited complex properties.•Validation of FRF result with numerical method.