A pre-stressed modal analysis is where the modal response of a structure is analyzed when a mechanical stress is applied to the structure. In MEMS devices the stress is applied either as a direct mechanical load or indirectly by applying an electrostatic or piezoelectirc generated force to the structure. This pre-stress is used by MEMS designers to adjust or fine tune the response of the structure. For example, the resonant frequency of an electrostatic comb drive oscillator can be shifted to a higher frequency by applying a DC bias to the structure. In many systems this effect is used to compensate from variations a device geometry and material properties (primarily due to fabrication process variations).
ANSYS Multiphysics supports the following types of pre-stressed modal analysis:
A pre-stressed modal analysis was performed on a MEMS beam steerer, 5V was applied across the piezoelectric. The first four modes with this pre-stress were computed to be: 94.5Hz, 132.5Hz, 216 Hz, 931 Hz.
The above image shows each of the four modes in sequence (courtesy Waveprecision, A division of GSI Lumonics).
A pre-stress electrostatic force can can be applied to a model by using the TRANS126 electromechanical transducer (EMT) element. First an electrostatic analysis must be performed to characterize the force/capacitance versus displacement of the device, then the electrostatic part of the model is replaced with the TRANS126. A mechanical analysis can then be performed to understand how the pre-stres (i.e. DC bias) applied to the TRANS126 effects the modal or even transient response of the device.
The following image shows a simple MEMS beam with a TRANS126 applied to one end. The beam is tethered at the opposite end, and a modal analysis is performed to understand how the resonant frequency changes with the DC bias applied to the TRANS126. (Note, in this example the TRANS126 is simulating the capacitance- displacement relationship of a single tooth-pair of an electrostatic comb drive):
First mode shape:
Table of results:
The pre-stress "stiffens" the structure causing an increase in the frequency of each of the modes.
Mode |
NO Pres-Stress / Hz |
With Pre-Stress/ Hz |
||
Analytical |
ANSYS |
Analytical |
ANSYS |
|
1 |
343.1 |
343.1 |
351.7 |
351.7 |
2 |
1372.5 |
1372.5 |
1381.2 |
1380.8 |
3 |
3088.1 |
3086.2 |
3096.8 |
3094.9 |