32 research outputs found
Dynamic relaxation oscillations in a nonlinearly driven quartz crystal
We demonstrate thermo-mechanical relaxation oscillations in a strongly driven
quartz crystal. Dynamic bifurcation leads to two stable oscillation states with
a distinct electrical impedance. Slow Joule-heating, which shifts the
susceptibility of the crystal, provides a feedback that leads to
thermally-induced oscillations, in which the amplitude of the crystal is
modulated by a relaxation cycle. The frequency of the relaxation cycle is
roughly a million times lower than the resonance frequency of the crystal, and
it can be adjusted by the detuning from the critical point for dynamic
bifurcation. The experimental observations are reproduced by a simple model
that takes into account the slow dynamics of the system.Comment: Main text: 8 pages, 4 figures. Supplementary information: 4 pages, 3
figure
Efficient readout of micromechanical resonator arrays in ambient conditions
We present a method for efficient spectral readout of mechanical resonator
arrays in dissipative environments. Magnetomotive drive and detection is used
to drive double clamped resonators in the nonlinear regime. Resonators with
almost identical resonance frequencies can be tracked individually by sweeping
the drive power. Measurements are performed at room temperature and atmospheric
pressure. These conditions enable application in high throughput resonant
sensor arrays.Comment: 4 pages, 4 figure
Magnetomotive drive and detection of clamped-clamped mechanical resonators in water
We demonstrate magnetomotive drive and detection of doubly clamped string
resonators in water. A compact 1.9 T permanent magnet is used to detect the
fundamental and higher flexural modes of long resonators.
Good agreement is found between the magnetomotive measurements and optical
measurements performed on the same resonator. The magnetomotive detection
scheme can be used to simultaneously drive and detect multiple sensors or
scanning probes in viscous fluids without alignment of detector beams.Comment: 4 pages, 3 figure
Strongly coupled modes in a weakly driven micromechanical resonator
We demonstrate strong coupling between the flexural vibration modes of a
clamped-clamped micromechanical resonator vibrating at low amplitudes. This
coupling enables the direct measurement of the frequency response via
amplitude- and phase modulation schemes using the fundamental mode as a
mechanical detector. In the linear regime, a frequency shift of
is observed for a mode with a line width of
in vacuum. The measured response is well-described by the
analytical model based on the Euler-Bernoulli beam including tension.
Calculations predict an upper limit for the room-temperature Q-factor of
for our top-down fabricated micromechanical beam
resonators.Comment: 9 pages, 2 figure
Nonlinear modal interactions in clamped-clamped mechanical resonators
A theoretical and experimental investigation is presented on the intermodal
coupling between the flexural vibration modes of a single clamped-clamped beam.
Nonlinear coupling allows an arbitrary flexural mode to be used as a
self-detector for the amplitude of another mode, presenting a method to measure
the energy stored in a specific resonance mode. Experimentally observed complex
nonlinear dynamics of the coupled modes are quantitatively captured by a model
which couples the modes via the beam extension; the same mechanism is
responsible for the well-known Duffing nonlinearity in clamped-clamped beams.Comment: 5 pages, 3 figure
Q-factor control of a microcantilever by mechanical sideband excitation
We demonstrate the coupling between the fundamental and second flexural mode
of a microcantilever. A mechanical analogue of cavity-optomechanics is then
employed, where the mechanical cavity is formed by the second vibrational mode
of the same cantilever, coupled to the fundamental mode via the geometric
nonlinearity. By exciting the cantilever at the sum and difference frequencies
between fundamental and second flexural mode, the motion of the fundamental
mode of the cantilever is amplified and damped. This concept makes it possible
to enhance or suppress the Q-factor over a wide range.Comment: 9 pages, 3 figure
Interactions between directly and parametrically driven vibration modes in a micromechanical resonator
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.Comment: 5 pages, 4 figure