Nonlinear Dynamics of Nanomechanical and Micromechanical Resonators

Symmetry breaking in a mechanical resonator made from a carbon nanotube

“…4c. A general theory that incorporates nonlinearities in both the restoring force and damping 10,[23][24][25][26] as well as thermal vibrations is beyond the scope of this article. We note that our new technique to measure the motion of the equilibrium position allows one to study the response of the resonator over a broad parameter range in driving force.…”

Energy-dependent path of dissipation in nanomechanical resonators

“…with α 1 the Duffing nonlinear constant and F d (ω d ) the oscillating force at frequency ω d /2π [7,8]. In the absence of dephasing, the value of α 1 can be obtained from spectral measurements by plotting the shift of the resonant frequency ∆ω 1 as a function of the largest vibrational amplitude z max of the driven spectra.…”

“…From Eq. (S5) this dependence can be approximated by [8] Device ΙΙ Figure S12: Energy decay away from the exact 3:1 internal resonance condition.…”

Signal amplification through bifurcation in nanoresonators

“…These include parametric amplification, and squeezing of classical and quantum noise [1], generation of entangled pairs of photons [2], and effective actuation of micro-and nanomechanical resonators [3][4][5]. Our previous investigations of the parametric excitation of coupled nanomechanical resonators [6,7] have led to the discovery of a novel and generic amplification mechanism. Unlike previous schemes employing a static bifurcation [8], this approach is based on inducing dynamical changes to the topology of a simple bifurcation diagram through the application of a small control signal.…”

“…The resonator is driven parametrically by modulating its effective stiffness, the equation of motion is then given by [6] …”