Numerical modeling of ultrasonic touchscreen

Transient Lamb waves induced by finite piezoelectric transducers have been widely used in ultrasonic touch systems, where a tactile object is localized through its interaction with the Lamb waves. However, this problem has not been looked in-depth theoretically, which is essential for development of robust systems. The two-dimensional theory often fails to provide a true picture as the diffraction effects are of great significance in these technologies. Reduced order models such as the plate theories, on the other hand, can support diffraction. However, they fail to support mid to higher spectrum of the Lamb modes. Moreover, many introduce errors in the range of the supported modes. Hence, for many problems, the design confidence level is only achieved upon a three-dimensional theory. We present the mathematical modeling of piezoelectrically induced elastic waves propagating through homogeneous plates subjected to a tactile object. We use a finite element method to solve the model problem. The model is validated against the experimental data.