ANALYTICAL AND NUMERICAL STUDY OF AMPLITUDE-DEPENDENT BANDGAP TUNING IN A ۱D NONLINEAR ACOUSTIC METAMATERIAL UNDER CONVECTIVE FLOW

This paper investigates amplitude-dependent bandgap (ADB) behavior in a one-dimensional nonlinear acoustic metamaterial (NAM) composed of mass-spring resonators with cubic stiffness embedded in a fluid medium under mean convective flow. Using perturbation theory and harmonic balance, a closed-form analytical dispersion relation is derived, showing that both lower and upper bandgap edges shift upward quadratically with excitation amplitude (Am × A۲). Convective flow introduces a Doppler-like term that accelerates nonlinear distortion and enhances effective amplitude along propagation. MATLAB simulations confirm analytical predictions with only ۳.۲۸% relative error. At normalized amplitude A = ۰.۹, the lower bandgap edge shifts upward by ۵.۹%, while the bandgap width remains nearly constant. Convective flow at Mach ۰.۳ shortens the nonlinear distortion distance by ۳۰%, confirming the flow-enhanced tuning mechanism. The results provide a theoretical and numerical foundation for flow-adaptive metamaterials suitable for aeroacoustic noise control in systems such as aircraft engines and wind turbines.

کلیدواژه ها:

nonlinear acoustic metamaterials ، amplitude-dependent bandgap ، convective flow ، perturbation method ، MATLAB simulation