An approximate solution of the equation of motion of a nonlinear anelastic reed at or near resonance is presented. The steady state solution reproduces the well-known nonlinear resonances. The solution also predicts the existence of auto modulations, i.e., self-excited modulations of the amplitude and phase at constant power of excitation of the reed. Numerical examples of such auto modulations are presented for an antisymmetric deformation potential. Experimental studies of finite amplitude oscillations of a magnesium reed vibrating at 72 and 431 Hz at room temperature confirm the existence of auto modulations. The experimental results can be semi quantitatively described in terms of the solution given. The assumption that finite deformation by twinning represents the essential nonlinearity leads to a self-consistent interpretation. The relaxation time of twinning is obtained from the analysis of the auto modulation and is 22 msec in the sample investigated. It is proposed that point defects control the relaxation process.
A. Aning et al., "Nonlinear Anelasticity Of Magnesium," Journal of Applied Physics, vol. 53, no. 10, pp. 6797 - 6808, American Institute of Physics, Dec 1982.
The definitive version is available at https://doi.org/10.1063/1.330068
Materials Science and Engineering
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01 Dec 1982