Power ultrasonic applications such as cutting, welding, and sonochemistry often use Langevin transducers to generate power ultrasound. Traditionally, it has been proposed that the piezoceramic stack of a Langevin transducer should be located in the nodal plane of the longitudinal mode of vibration, ensuring that the piezoceramic elements are positioned under a uniform stress during transducer operation, maximizing element efficiency and minimizing piezoceramic aging. However, this general design rule is often partially broken during the design phase if features such as a support flange or multiple piezoceramic stacks are incorporated into the transducer architecture. Meanwhile, it has also been well documented in the literature that power ultrasonic devices driven at high excitation levels exhibit nonlinear behaviors similar to those observed in Duffing-type systems, such as resonant frequency shifts, the jump phenomenon, and hysteretic regions. This study investigates three Langevin transducers with different piezoceramic stack locations by characterizing their linear and nonlinear vibrational responses to understand how the stack location influences nonlinear behavior.

Ultrasonic surgical devices are increasingly used in oral, craniofacial and maxillofacial surgery to cut mineralized tissue, offering the surgeon high accuracy with minimal risk to nerve and vessel tissue. Power ultrasonic devices operate in resonance, requiring their length to be a half-wavelength or multiple-half-wavelength. For bone surgery, devices based on a half-wavelength have seen considerable success, but longer multiple-half-wavelength endoscopic devices have recently been proposed to widen the range of surgeries. To provide context for these developments, some examples of surgical procedures and the associated designs of ultrasonic cutting tips are presented. However, multiple-half-wavelength components, typical of endoscopic devices, have greater potential to exhibit nonlinear dynamic behaviours that have a highly detrimental effect on device performance. Through experimental characterization of the dynamic behaviour of endoscopic devices, it is demonstrated how geometrical features influence nonlinear dynamic responses. Period doubling, a known route to chaotic behaviour, is shown to be significantly influenced by the cutting tip shape, whereas the cutting tip has only a limited effect on Duffing-like responses, particularly the shape of the hysteresis curve, which is important for device stability. These findings underpin design, aiming to pave the way for a new generation of ultrasonic endoscopic surgical devices.

Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and "frequency domain hysteresis". In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant

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