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On the Problems of Emission of Sound Waves in the Dynamic Process of Deformation of Plates with Regard for External and Internal Damping

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To describe the dynamic process of deformation of a plate, we construct the corresponding equation of motion for small strains and displacements with regard for the internal and external aerodynamic damping. This equation is based on the Kirchhoff–Love kinematic hypotheses, the generalized Kelvin–Voigt constitutive model, and the solutions of hydrodynamic wave equations for the acoustic media surrounding the plate obtained in the one-dimensional approximation within the framework of the well-known hypothesis of plane reflection and emission of acoustic waves. By using the constructed equation, we find the exact analytic solutions of the problem of damped vibrations of a rectangular plate, preliminarily bent and hingedly supported over its contour and of the emission of sound waves by the plate after its liberation from constraints. We also solve the problem of emission of sound waves caused by the shock of the plate by a transverse load.

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Authors and Affiliations

  1. Scientific-Engineering Center for the Problems of Dynamics and Strength, Tupolev Kazan National Research Technical University (KNITU-KAI), Kazan, Russia

    V. N. Paimushin

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  1. V. N. Paimushin
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 2, pp. 72–85, April–June, 2013.

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Paimushin, V.N. On the Problems of Emission of Sound Waves in the Dynamic Process of Deformation of Plates with Regard for External and Internal Damping. J Math Sci 203, 87–103 (2014). https://doi.org/10.1007/s10958-014-2092-8

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