Effect of Initial Stresses on Surface Acoustic Waves Propagating in Infinite Elastic Plates

Initial stresses are inevitable in acoustic wave devices due to the complicated manufacturing process with ubiquitous thermal treatment procedures and environmental temperature changes. In addition, acoustic waves have been utilized as force sensors which require a good stress-frequency relationship for measurement applications. In other words, for both device performance improvement and precision sensors, a detailed analysis of the effect of initial stresses on surface acoustic wave velocity is essential in the device design and analysis. With bulk acoustic wave force sensors based on the thickness vibration mode of piezoelectric plates available as products, we are naturally encouraged to study the relationship between initial stresses and phase velocity of surface acoustic waves in a finite solid for possible applications with the advantageous higher frequency. In this study, we start from general equations of an elastic body under initial stresses for Rayleigh waves in a semi-infinite solid, and the velocity equation under initial stresses is obtained. We found that there is a good correspondence between the stress and velocity change, offering an opportunity to utilize the sensitivity of surface acoustic waves to stresses for sensor applications. We further extended the results to an elastic plate with finite thickness for the velocity and initial stress relationship in a structure close to actual surface acoustic wave resonators. We found that for plates with different thickness, the velocity versus stress exhibits a relationship similar in semi-infinite solids. Since surface acoustic wave resonators are made with piezoelectric materials such as quartz crystals, we use the ST-cut of quartz crystal to calculate the surface wave velocity versus plate thickness relations under initial stresses. These methods and procedures can be applied to other piezoelectric crystals used in acoustic wave resonators for stress sensors.