Numerical Modeling of Resonant Vibrations of an Elongate Plate with an Integral Damping Coating

The classical methods of surface damping of bending vibrations of thin-walled structures and a promising integrated version with a damping coating consisting of two layers of a material with pronounced viscoelastic properties and an intermediate thin reinforcing layer of a high-modulus material are discussed. A four-layer finite element for an elongate plate with an integral damping coating is developed taking into account the lateral compression of the damping layers. A system of governing equations of the finite-element method is constructed for analyzing the dynamic response of the plate during its resonant vibrations. Iterative algorithms have been developed to take into account the amplitude dependence of the logarithmic decrements of vibrations of material of the damping layers when determining the damping properties of the plate and determining its vibration eigenmodes and eigenfrequencies with consideration of frequency dependence of the dynamic elastic moduli of the material. Numerical experiments were carried out to test the finite element developed and the iterative algorithms mentioned. The influence of aerodynamic resistance forces on the overall damping level of a cantilever plate with an integral damping coating is assessed.