Meaning
Mathematical formulations enable engineers to predict the behavior of complex piezoelectric systems under stress. By applying the Tiersten stress equations, designers can calculate how mechanical loads alter the resonant frequency of a quartz plate.
Mathematical Modeling
Theoretical calculations of stress-induced frequency shifts require a detailed analysis of the resonator’s strain state. These equations couple the mechanical deformation of the crystal plate with its acoustic wave equations. This coupling allows engineers to model the frequency response to acceleration, mounting forces, and thermal expansion.
These simulations are essential for developing high-stability oscillators.
Design Optimization
Structural design of crystal mounts utilizes these calculations to minimize frequency drift. By identifying the points of high stress sensitivity, designers can place the mounting supports at optimal positions. This application of the Tiersten stress equations leads to the development of resonators that are highly resistant to vibration.
These optimized designs are particularly useful for military and aerospace applications.
Contractual Warranty
Component specifications in high-reliability contracts often reference these mathematical standards to define design limits. A manufacturer may be required to prove that their mounting design was optimized using the Tiersten stress equations to secure the contract. This requirement ensures that the supplied oscillators meet the stringent vibration resistance standards required by the customer.
If a delivery fails to meet these standards in field tests, the supplier is liable for replacing the defective units.
