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

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.

Automated summary

In this work, an enriched Timoshenko beam model is utilized to study the free wave propagation, frequency response, and sound radiation under non-classical bending and shear motion, considering the local behavior of internal heterogeneity. Dispersive behaviors, modal density, and energy flow are analyzed, revealing the significance of local behavior in non-classical structural behavior.