Anharmonic modal coupling in a bulk micromechanical resonator

Abstract

We present measurements of nonlinear coupling between various acoustic modes of a micromechanical resonator. Piezoelectric transduction allows measurement of both flexural and bulk longitudinal modes up to microwave frequencies, and we find that all modes of the device couple, regardless of type. This coupling thus provides a means of mechanical nonlinear signal processing across a wide range of frequencies. Through controlled simultaneous excitation, we quantify coupling strength by measuring the frequency shift in a detector mode in response to the known energy of a driven mode.

Parametric mode mixing in asymmetric doubly clamped beam resonators

“…In this experiment, the second mechanical oscillation mode is a 'phonon cavity' and has a higher resonance frequency and a wider resonance bandwidth than the first (fundamental) mode, playing the same role as that of an optical/microwave cavity in cavity optomechanics. Similar mode coupling was also experimentally and theoretically reported in a weak-coupling regime or as the observation of a frequency shift induced by the other mode's excitation [13][14][15][16][17][18][19]. However, these studies do not provide a detailed theoretical description including a comparison with the experimental results of parametric mode splitting.…”

“…In this section, we present a model to generate the Hamiltonian starting from the fundamental Euler-Bernoulli theorem. The model clearly shows that the parametric inter-mode mixing among odd-odd or even-even modes is caused by applying a tension to the beam [15][16][17][18][19]. Moreover, we also show that the beam nonuniformity can cause mixing between odd and even modes.…”

Experimental investigation on mode coupling of bulk mode silicon MEMS resonators

“…(5) and (6) reveal that the frequenc indeed a function of the amplitudes of bo increase or decrease depending on magnitudes of coefficients , and am…”

“…Such effects can be useful for understanding resonator parameters, as well as providing tunability for resonant frequencies and quality factor (Q) [5]. The nonlinear coupling effect has also been observed in bulk mode resonators [6], where material effects play a much larger role than geometrical effects. This work will extend previous research and discuss the effect of doping on the mode coupling behavior for bulk mode silicon resonators.…”

Interactions between directly- and parametrically-driven vibration modes in a micromechanical resonator

“…Motivated by the trend toward large scale integration of resonators, researchers study the interactions between several resonators. 17 Recently, nonlinear modal interactions between the flexural modes in a clamped-clamped beam resonator [18][19][20] and a cantilever 21 have been reported: it has been shown that the resonance frequency of one mode depends quadratically on the amplitude of another mode.…”