Self and cross-mode interactions in a weakly nonlinear two-dimensional structural-acoustic waveguide

Area of Science:

• Structural-acoustic wave propagation
• Nonlinear dynamics
• Fluid-structure interaction

Background:

• Investigates wave propagation in a 2D waveguide with one rigid and one flexible boundary.
• Includes coupled in-plane and transverse displacements for the flexible plate.
• Models acoustic fluid and plate using nonlinear equations.

Purpose of the Study:

• Analyze weakly nonlinear wave propagation in a semi-analytical structural-acoustic waveguide.
• Examine self- and cross-mode interactions of non-orthogonal propagating modes.
• Determine the impact of boundary flexibility on resonance phenomena.

Main Methods:

• Employs a semi-analytical approach for weakly nonlinear wave propagation.
• Utilizes the regular perturbation method to separate linear and nonlinear equations.
• Solves for self- and cross-mode interactions in the waveguide.

Main Results:

• Self-mode interactions show resonances in pressure and in-plane displacement at distinct frequencies.
• Cross-mode interactions exhibit spatial beats, with pressure resonance at specific frequencies.
• Boundary flexibility drastically reduces the number of resonances compared to a rigid waveguide.
• Below coincidence frequency, the bending mode dominates; above it, the acoustic mode dominates.

Conclusions:

• Flexible boundaries in waveguides significantly alter resonance characteristics.
• Mode dominance shifts from bending to acoustic modes relative to the coincidence frequency.
• Provides closed-form solutions for resonance conditions in the studied waveguide.