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Vibroacoustic behavior of a plate surrounded by a cavity containing an inclined part–through surface crack with arbitrary position

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.