Nonlinear interactions in elastic resonators

Area of Science:

• Acoustics and Nonlinear Dynamics
• Solid Mechanics and Fluid Dynamics

Background:

• Nonlinear interactions in elastic resonators are complex due to wall yielding and energy dissipation.
• Acoustic energy dispersion and dissipation are significantly influenced by the resonator's elastic wall properties.
• Short coherence length due to unsatisfied synchronous conditions hinders effective nonlinear interactions.

Purpose of the Study:

• To investigate the conditions for subharmonic generation in elastic resonators.
• To analyze the impact of resonator wall elasticity on nonlinear acoustic phenomena.
• To develop and apply models for describing nonlinear standing waves with various loss mechanisms.

Main Methods:

• Topological and numerical analysis were employed to study subharmonic generation.
• The method of local stability was applied for analyzing nonlinear interactions.
• Modified inhomogeneous Burgers and Korteweg-de Vries-Burgers equations were derived to model the system.
• Numerical solutions of the derived model equations were obtained.

Main Results:

• Conditions for subharmonic generation were identified through topological and numerical analysis.
• Derived equations incorporate thermo-viscous, boundary layer, and wall losses, alongside dispersion effects.
• Numerical simulations demonstrated unsteady solitary wave behavior.
• The influence of elastic wall properties on dispersion and dissipation was quantified.

Conclusions:

• Elastic resonator walls introduce significant dispersion and dissipation, impacting nonlinear acoustic interactions.
• The derived modified Burgers and KdV-Burgers equations provide a comprehensive model for nonlinear standing waves in elastic resonators.
• Unsteady solitary waves were investigated, offering insights into energy propagation and localization.