Non-Linear Dynamics of a Double-Plate System Coupled by a Layer with Viscoelastic and Inertia Properties

 

Julijana Simonović

 

The paper considers multi-frequency vibrations of a system of two isotropic circular plates interconnected by a rolling viscoelastic layer of nonlinear characteristics. The considered physical system should be of interest to many researchers in the field of vibration and acoustics absorbers. The interconnecting layer is modeled as a continually distributed layer of discrete standard rheological elements with damping properties and nonlinear elasticity.

The mathematical model of the system is derived in the form of a system of partial differential equations of transverse oscillations of a double circular plate system coupled with a layer of viscous nonlinear elastic and inertia properties, excited by external excitation continually distributed along the plate surfaces. The system of ordinary differential equations of the first order with respect to the amplitudes and the corresponding number of the phases is derived in the first asymptotic averaged approximation for different corresponding multi-frequency nonlinear vibration regimes. These equations are considered analytically and numerically in the light of stationary and non-stationary resonant regimes, as well as in the light of the interactions of nonlinear modes and the number of resonant jumps in the cases without rolling elements and in the cases with two different mass values of rolling elements.

Such an analysis proves that the presence of rolling coupling elements in the interconnecting layer of two plates  causes a frequency overlap of the resonant regions of nonlinear modes, together with the increase of their interaction.

 

Key words: system dynamics, nonlinear dynamics, oscillations, plate, resonant regime, resonant jumps, mathematical model, partial differential equations.