a b s t r a c tPiezoelectric laminated slightly curved beams (PLSCB) is currently one of the most popular actuators used in smart structure applications due to the fact that these actuators are small, lightweight, quick response and relatively high force output. This paper presents an analytical model of PLSCB, which includes the computation of natural frequencies, mode shapes and transfer function formulation using the distributed transfer function method (DTFM). By setting the radius of curvature of the proposed model to infinity, a piezoelectric laminated straight beams (PLSB) model can be obtained. The DTFM is applied and extended to carry out the transfer function formulation of the PLSCB and PLSB models. This method will be used to solve for the natural frequencies, mode shapes and transfer functions of the PLSCB and PLSB models in exact and closed form solution without using truncated series of particular comparison or admissible functions. The natural frequencies of the cantilevered PLSCB and PLSB are calculated by the DTFM and the Rayleigh-Ritz method. The analysis indicates that the stretching-bending coupling due to curvature has a considerable effect on the frequency parameters. Increasing the radius of curvature of the PLSCB has its largest effect on the natural frequencies. But the inhomogeneity of the boundary conditions does not have any effects on the natural frequencies or system spectrum due to the both receptance and boundary transfer functions have the same characteristic equations. The method can also be generalized to the vibration analysis of non-piezoelectric composite beams with arbitrary boundary conditions.

Meso∕micro grasping of tiny soft objects such as biological tissues, which ranges from hundreds to thousands of micro-millimeters in dimension, plays a significant role in the fields of tele-surgery, minimally invasive surgery (MIS), and biomedical instrumentation. Recently, the authors proposed a novel piezoelectric forceps actuator (PFA), which is capable of grasping delicate soft objects. One of the advantages of the PFA over conventional MIS forceps lies in that it can be remotely controlled to achieve precision deflection and grasping force. Furthermore, it does not have any moving parts such as gears and hinges, and hence avoids problems in operation like friction, backlash, lubrication, leakage, and sterilization. In this paper, a mathematical model of the PFA is derived, based on which genetic algorithm (GA) is applied to optimize the grasping force-deflection relationship of the actuator. The model developed is experimentally verified on a prototype of the PFA.

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This paper studies the characteristic performances of a novel piezoelectric forceps actuator (PFA) that has several potential applications for minimally invasive surgery and assembly lines of semiconductor industries. The first part of the paper treats the PFA model, which is comprised of a piezoelectric slightly curved composite beam derived using Hamilton's principle. In the latter part of the paper, the distributed transfer function method is applied to evaluate the transfer function formulation of the cantilevered PFA associated with its boundary conditions. This method will be used to resolve the radial displacements and natural frequencies of the PFA in an exact and closed-form solution, which is validated by in situ fiber optic curvature sensing measurements. The theoretical model predicted the natural frequencies of the first- and second-mode responses of the experimental quite accurately. For a cyclical low-field input, the field-induced displacement appears approximately linear, which seems comparable to the theoretical prediction and reflects primarily the converse piezoelectric effect. A cyclical high-field butterfly-shaped displacement behavior is also analogous to the behavior predicted by the model in that it demonstrates the range of validity of the linear converse piezoelectric effect without consideration of the ferroelectric domain switch effect.