Contactless powering of small electronic components has lately received growing attention for wireless applications in which battery replacement or tethered charging is undesired or simply impossible, and ambient energy harvesting is not a viable solution. As an alternative to well-studied methods of contactless energy transfer, such as the inductive coupling method, the use of ultrasonic waves transmitted and received by piezoelectric devices enables larger power transmission distances, which is critical especially for deep-implanted electronic devices. Moreover, energy transfer by means of acoustic waves is well suited in situations where no electromagnetic fields are allowed. The limited literature of ultrasonic acoustic energy transfer is mainly centered on proof-of-concept experiments demonstrating the feasibility of this method, lacking experimentally validated modeling efforts for the resulting multiphysics problem that couples the source and receiver dynamics with domain acoustics. In this work, we present fully coupled analytical, numerical, and experimental multiphysics investigations for ultrasonic acoustic energy transfer from a spherical wave source to a piezoelectric receiver bar that operates in the 33-mode of piezoelectricity. The fluid-loaded piezoelectric receiver under free-free mechanical boundary conditions is shunted to an electrical load for quantifying the electrical power output for a given acoustic source strength of the transmitter. The analytical acoustic-piezoelectric structure interaction modeling framework is validated experimentally, and the effects of system parameters are reported along with optimal electrical loading and frequency conditions of the receiver.

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Therefore, the added damping due to fluid loading is directly given in Eq. (1), whereas the added mass at the free ends is to be accounted for as boundary conditions.

43.
Note that the rigid-body mode resulting from the positive semi-definite nature of the system (with free-free boundary conditions) is not of interest.
44.
For the case of a very high mechanical quality factor receiver (such that ζ0.001), which is preferred for larger power output, the total underwater damping would be dominated by the fluid (acoustic radiation) damping. That is, even for the extreme of ζ0 the underwater response would be bounded due to fluid damping.
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