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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.

In this paper, we introduce a modified fabrication method for CMUTs with substrate-embedded springs (post-CMUTs or PCMUTs) to increase the fabrication yield. This modified fabrication process includes three additional steps from the previous process: vacuum cleaning prior to the wafer bonding step, thermal oxidation of the silicon piston top plate, and preservation of the 150-nm buried oxide (BOX) layer on top of the 250 nm Si layer of the bonded SOI wafer. These modifications increased the fabrication yield from 10% to 60%. For these newly fabricated PCMUT devices, we measured the electrical input impedance with a precision impedance analyzer, the plate displacement with a laser Doppler vibrometer (LDV), and the output pressure with a calibrated hydrophone. The measured electrical input impedance matches well with the FEA simulation results; the LDV measurement in air confirmed a non-flexural plate displacement; and the hydrophone measurement showed a peak-to-peak acoustic pressure of 27.6 kPa at a distance of 3.6 mm in immersion, corresponding to 1.05 MPa at the face of the transducer, for a particular test 2-D array element.

We generalize the theory of the k-space method to the case of elastic wave propagation in heterogeneous anisotropic media. The k-space operator is derived in the spatially continuous form using the displacement formalism of elastodynamics. The k-space scheme is then discretized in space using a Fourier collocation spectral method. This leads to an efficient and accurate numerical algorithm, where the time advancement can be performed in order of N operations, where N is the number of unknowns. As opposed to the classical k-space theory for the elastic waves in isotropic media [1], [2], the new algorithm does not need any field splitting. Hence, it is more efficient once used to model isotropy. The proposed method is temporally exact for homogeneous media, unconditionally stable for heterogeneous media, and also allows larger time-steps without loss of accuracy. We validate the method against canonical model problems of elastodynamics.