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

Abstract

The interactions between parametrically-and directly-driven vibration modes of a clamped-clamped beam resonator are studied. An integrated piezoelectric transducer is used for direct and parametric excitation. First, the parametric amplification and oscillation of a single mode are analyzed by the power and phase dependence below and above the threshold for parametric oscillation. Then, the motion of a parametrically-driven mode is detected by the induced change in resonance frequency in another mode of the same resonator. The resonance frequency shift is the result of the nonlinear coupling between the modes by the displacement-induced tension in the beam. These nonlinear modal interactions result in the quadratic relation between the resonance frequency of one mode and the amplitude of another mode. The amplitude of a parametrically-oscillating mode depends on the square root of the pump frequency. Combining these dependencies yields a linear relation between the resonance frequency of the directly-driven mode and the frequency of the parametrically-oscillating mode.

Phase Synchronization of Two Anharmonic Nanomechanical Oscillators

“…In particular, nanoscale mechanics exhibits enhanced nonlinearity [14,15] and tunability [16,17], which has been used to suppress feedback noise [18,19] and create new types of electromechanical oscillators [20][21][22]. These oscillators may find application as mass [23], gas [24,25], or force sensors [26], without the need of an external frequency source.…”

Strong and tunable mode coupling in carbon nanotube resonators

“…Nonlinear modal interactions have been studied recently in micro-and nanoresonators. [13][14][15][16][17][18] These studies concentrated on mechanical coupling between the modes via the geometric nonlinearity or via the displacement-induced tension, the same mechanism responsible for the Duffing nonlinearity in doubly clamped resonators. By employing a different mode of the same resonator as a phonon cavity, the mechanical mode can be controlled in situ, and its damping characteristics can be modified to a great extent, leading to cooling of the mode and parametric mode splitting.…”

“…13,16 The nonlinear coupling can also be used to detect resonance modes that would otherwise be inaccessible by the experiment 18 to increase the dynamic range of resonators by tuning the nonlinearity constant 18 and for mechanical frequency conversion. 17 Additionally, nonlinear coupling has been proposed as a quantum nondemolition scheme to probe mechanical resonators in their quantum ground state 19 and as a way of generating entanglement between different mechanical modes. 20 Furthermore, a recent theoretical paper suggests that the interaction between mechanical resonances could be responsible for the spectral broadening in carbon nanotubes, thus, limiting their Q factor at room temperature.…”

Review of Response and Damage of Linear and Nonlinear Systems under Multiaxial Vibration

“…Fortunately, these microstructural components' behavior can be formulated based on the Euler-Bernoulli beam or Timoshenko beam theory [81][82][83][84][85]. Researchers have investigated both linear and nonlinear vibration based energy harvesting devices, in which these devices were modeled using beam theory [84,[86][87][88][89][90]. Beam theory was also extended to nanomechanical cantilevers, such as the efforts performed by Villanueva et al [91].…”