Different noise reduction techniques that can be applied to the interior of aircraft cabin are investigated, to determine the most cost-effective means, without any aircraft external modifications, such as jet engine design change, or fuselage modifications, with no significant added weight. The goal of this research is to arrive at a cabin interior design that can be retrofitted to the existing aircraft interior to reduce overall cabin noise. Relaxation oscillations of the aircraft cabin model, considered as a system in forced vibrations with non-linear damping, and sub-harmonic resonances are considered. Negative and positive damping coefficients, and some techniques for noise cancelation by active means are discussed. From noise power-spectrum results for a typical aircraft cabin, amplitude versus audible frequency, one can determine the most energetic cabin vibration modes. Those modes require the highest damping. The proposed technique will utilize a regular matrix of the multiple sets of open Helmholtz resonators, with sound absorbing surfaces, that are imbedded in the cabin interior walls, just below the surface, and tuned to the highest noise level frequencies inside the cabin. The resonators dissipate the noise energy inside the aircraft at the most dominant frequencies, and hence reduce the overall cabin noise level.