Subharmonic Generation in Acoustic Systems
Abstract
The report is concerned with the theoretical and experimental study of subharmonic generation in acoustic systems. The generalized formulation for lumped systems is considered for the case of three oscillators coupled through a nonlinear element. The resulting analysis indicates that the high frequency oscillation is unstable and its energy can be diverted to low frequency oscillations; that is, subharmonics are generated. Based on this mathematical model, the conditions for sustaining subharmonics are deduced in terms of the system's parameters. For distributed systems, the quasi-linear solution of the nonlinear wave equation, obtained by a two-variable (two-timing) perturbation method, shows that the nonlinear property of medium provides a coupling effect for signals of different frequencies. In a multi-resonant system, certain subharmonic modes, determined by a selection rule, can be excited by an external source. The present theory predicts the threshold for subharmonic generation as a function of the losses, nonlinearity, and detuning parameters of the system. Experimental measurements of such phenomena in an interferometer-type resonator, operated around 1.5 MHZ in water, are consistent with the analytic results, provided that cavitation in the medium is carefully avoided. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1971
- Accession Number
- AD0725604
Entities
People
- Nai-chyuan Yen
Organizations
- Harvard University