Combination Tones of Summed Type in Nonlinear Vibratory Systems

Abstract

When two periodic disturbing forces with frequencies Ω₁ and Ω₂ excite a nonlinear vibratory system, combination tones having a frequency Ω=Ω₁+Ω₂ appear. In the present paper, the combination tones are discussed analytically and experimentally. For a small value of frequency ratio K=Ω₂/Ω₁ (Ω₂≨Ω₁, K≨1), the response curves of combination tones are hard or soft spring type, and the magnitudes of amplitude increase with the value K and the value of the unsymmetrical nonlinearity. When the value K is somewhat large, peculiar response curves take place, and the amplitudes of harmonic oscillations become larger than those of combination tones. By introducing the conception of apparent external force, the back bone curves and the phase angles can be obtained, and further, the effects of unsymmetrical nonlinearity can be explained clearly. Generally, the amplitudes of combination tones are comparable to those of ultraharmonic oscillation.