Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Area of Science:

• Acoustics
• Solid Mechanics
• Fluid Dynamics

Background:

• Nonlinear acoustic wave propagation in orthotropic thin circular cylindrical waveguides is investigated.
• The study considers non-planar modes with small but finite amplitudes in an ideal, inviscid fluid with no mean flow.
• Donnell's nonlinear theory for thin cylindrical shells models the waveguide.

Purpose of the Study:

• To analyze amplitude modulation governed by the Nonlinear Schrödinger Equation (NLSE) and its stability.
• To identify frequencies of higher harmonic interactions between primary waves and their harmonics.
• To validate the linear terms in the NLSE derived from asymptotic analysis.

Main Methods:

• Approximate solutions for acoustic velocity potential using the method of multiple scales (MMS) in space and time.
• Third-order calculations of the small parameter.
• Asymptotic analysis of the dispersion equation.

Main Results:

• Amplitude modulation is governed by the NLSE at specific frequencies, with the nonlinear term's sign determining stability.
• Frequencies of higher harmonic interactions were identified.
• Linear terms in the NLSE were validated through asymptotic analysis of the dispersion equation.

Conclusions:

• The study successfully met all objectives, providing insights into nonlinear acoustic wave behavior in cylindrical waveguides.
• The findings contribute to understanding wave stability and harmonic interactions in such systems.
• The validation of linear terms using dispersion analysis confirms the accuracy of the MMS approach.