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Acoustical investigation of a thin plate having a part–through surface crack surrounded by an air enclosure is studied in this paper. The enclosure comprises five rigid walls and a flexible plate based on the Kirchhoff plate theory. It is also assumed that the crack is located at an arbitrary position and orientation with a specific length. Accordingly, partial differential equation related to the coupled cracked plate–cavity system is presented. In order for the partial differential equation (PDE) to be solved, firstly, the sound pressure inside the cavity is estimated by a suitable number of the plate modes. Then, the coupled PDE decomposes to some ordinary differential equations in the time-domain by employing the Galerkin method for three different boundary conditions. In addition, the linear natural frequencies are obtained in vacuo and coupled conditions for an uncracked plate and then, a similar procedure is performed for a cracked plate. Furthermore, comparing the results with available data in the literature shows the reliability and accuracy of the present work. Finally, the influences of the crack angle, crack length, crack position, and cavity depth on the natural frequencies are investigated.

This paper deals with sound propagation through a two-layer sandwich plate in which the carbon nanotubes with functionally graded (FG) distribution are coated by a thin layer of magneto-electro-elastic (MEE) materials. Firstly, the derivation of governing equations for each layer of the sandwich plate is followed according to the three-dimensional elasticity theory. In this regard, the relationship between the equations of motion for the layer, made of MEE materials, and the electric and magnetic potentials is established. Additionally, the effective properties of the nanocomposite layer are extracted by employing the rule of mixture. Afterward, the solution is finalized by employing the approximate layer and transfer matrix technique, in accordance with the definition of state space and sound transmission loss. In the next stage, to confirm the reliability of the derived relationships, three configurations of the panel are examined. Firstly, according to the obtained results, it is evident that adding a thin coating layer of triple-phase MEE materials effectively improves the sound insulation in the sandwich plate. Secondly, considering the electromagnetic boundary conditions can lead to a noticeable enhancement in the STL in the stiffness region. Moreover, the magnetic potential, compared to the electric one, is seen to be more effective on the acoustic radiation of the sandwich panel.