Mechanical Hardening
Dynamic structural changes increase the resonant frequency of a flexure as internal tensile loads rise. In micromachined systems, stress-stiffening occurs when an applied force creates a geometric tension that resists further displacement more effectively than the base stiffness alone. This non-linear relationship is significant in thin membranes and high-aspect-ratio beams where axial load is not negligible.
Mechanism Detail
Potential energy storage inside the beam increases with the stretching of its neutral axis. During high-amplitude oscillation, stress-stiffening causes the device response to lean, creating the classic hard-spring behavior seen in non-linear resonators. This effect can be used to broaden the bandwidth of a harvester but is generally avoided in high-stability clocks.
The magnitude of the effect grows as the displacement square.
Calibration Gap
Linear approximation models fail to predict device behavior once the operational load enters this regime. Accuracy in measurement relies on identifying the exact point where stress-stiffening overtakes the small-deflection stiffness. Environmental tests often intentionally overload sensors to map the onset of this behavior.
Control logic for these sensors must include coefficients to counteract the frequency drift as the tension fluctuates.
Structural Boundary
Safety margins for these devices are measured against the tensile limit of the material itself. Because stress-stiffening pulls the lattice tight, it can push a sensor toward brittle fracture during peak transients. Verification in the field involves monitoring frequency stability under heavy vibration.
If the stiffening effect becomes unpredictable, it suggests the structure is near its mechanical failure point.
