Complex eigenfrequencies and damping properties of an elongated plate with integral damping coating

In this paper, we consider the classical methods of surface damping of bending vibrations of thin-walled structures and a promising integral method of a damping coating consisting of two layers of material with pronounced viscoelastic properties between which a thin reinforcing layer of high modulus material is located. A finite element with 14 degrees of freedom has been developed for modeling an elongated plate with the specified damping coating taking into account the effect of transverse compression of the damping layers under high-frequency oscillations of the plate. A generalized problem of complex eigenvalues in the lower part of the spectrum of complex forms and frequencies of free vibrations of a damped plate is solved using iterations with consideration of the frequency dependence of the dynamic elastic moduli of the material. The damping properties of the plate are determined from the imaginary parts of the complex eigenfrequencies and the relative energy dissipation at resonance.