Forced and free vibrations of thin composite plate with free layer damping located in the air

Abstract

The paper studies two coupled problems: the problem of free vibrations of a composite plate with a free layer damping made of a vibration-absorbing material with a large logarithmic decrement of vibrations, as well as the problem of forced vibrations of the plate described above under the action of a flat monoharmonic sound wave incident on it. The aerohydrodynamic interaction of a plate with acoustic media surrounding a plate is described by the generalized three-dimensional Helmholtz wave equations with the introduction of the complex sound speed to consider the energy dissipation. The mechanical behavior of a two-layer plate is described by the Kirchhoff-Love model. For the case of hinged support of the plate edges, exact analytical solutions of the problems were found. Comparison of the results obtained for a single-layer plate and a two-layer plate with a free layer damping made of rubber shows that the use of coatings with high internal damping properties (and, consequently, energy-absorbing properties) can significantly reduce the amplitude values of deformations and displacements in the plate even under resonant modes of loading, thereby forming a reduced level of sound pressure radiated by the plate.The paper studies two coupled problems: the problem of free vibrations of a composite plate with a free layer damping made of a vibration-absorbing material with a large logarithmic decrement of vibrations, as well as the problem of forced vibrations of the plate described above under the action of a flat monoharmonic sound wave incident on it. The aerohydrodynamic interaction of a plate with acoustic media surrounding a plate is described by the generalized three-dimensional Helmholtz wave equations with the introduction of the complex sound speed to consider the energy dissipation. The mechanical behavior of a two-layer plate is described by the Kirchhoff-Love model. For the case of hinged support of the plate edges, exact analytical solutions of the problems were found. Comparison of the results obtained for a single-layer plate and a two-layer plate with a free layer damping made of rubber shows that the use of coatings with high internal damping properties (and, consequently, energy-absorbing propert...