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Contactless ultrasound power transfer (UPT) has emerged as one of the promising techniques for wireless power transfer. Physical processes supporting UPT include the vibrations at a transmitting/acoustic source element, acoustic wave propagation, piezoelectric transduction of elastic vibrations at a receiving element, and acoustic-structure interactions at the surfaces of the transmitting and receiving elements. A novel mechanism using a high-intensity focused ultrasound (HIFU) transmitter is proposed for enhanced power transfer in UPT systems. The HIFU source is used for actuating a finite-size piezoelectric disk receiver. The underlying physics of the proposed system includes the coupling of the nonlinear acoustic field with structural responses of the receiver, which leads to spatial resonances and the appearance of higher harmonics during wave propagation in a medium. Acoustic nonlinearity due to wave kinematics in the HIFU-UPT system is modeled by taking into account the effects of diffraction, absorption, and nonlinearity in the medium. Experimentally-validated acoustic-structure interaction formulation is employed in a finite element based multiphysics model. The results show that the HIFU high-level excitation can cause disproportionately large responses in the piezoelectric receiver if the frequency components in the nonlinear acoustic field coincide with the resonant frequencies of the receiver.