Using a piezoelectric unimorph vibrator with constraint-tuning modified-mode (CTMM) mechanism, a novel design of a thin-disc ultrasonic actuator was developed to drive an optical sled. The theoretical estimation of in-plane wave propagation on a thin disc is introduced to explain the novel actuating mechanism, via a modal expansion technique and modal participation factors. Furthermore, the approximate wave propagations could be illustrated by the practical estimated wave equations in this study. Applying four screws at the exact distribution of angles on the thin-disc vibrator, the actuating mechanism of ultrasonic modified modes is generated and propagated. The in-plane vibration modes could be tuned by these desired screw constraints on the piezoelectric vibrator. The ultrasonic actuator offers the output force to drive an optical sled by friction contact in bilateral motions. To implement the equilibrium structure force in bilateral directions, natural and forced analysis as well as impedance comparison of FEM software ANSYS are also introduced into the constrained design. Hence, there are two various modified modes chosen at the different resonant frequencies within the electromechanical coupling of piezoelectric material to pursue more efficiency in energy conversion. Experimental results have demonstrated consistency with the approximate theoretical approach of the in-plane wave propagation and simulations based on the concept of constrained-tuning modified modes.

This paper was written at the request of the Life Research Committee of the United Kingdom Actuarial Profession's Life Board. It concerns the valuation of U.K. with-profits business, with particular attention to the market-consistent ‘realistic reporting’ basis currently being used in the U.K. by the regulator, the Financial Services Authority (FSA). The paper surveys recent regulatory activity concerning the development and introduction of the new valuation approach, and puts it into the context of a survey of alternative methodologies, both deterministic and stochastic. The particular issues arising when considering prudential solvency are discussed, and various approaches are reviewed and compared with market consistent methods. Numerical examples are given, which demonstrate potential issues (regarding comparability and consistency) with the FSA's proposed approach — in particular the sensitivity of results to model calibration. The authors support the FSA's move to a stochastically-based framework for solvency measurement, but highlight some issues which need to be taken into account.

Multilayer piezoelectric stack actuators are widely used in many industrial applications and the investigation on the dynamic behavior of this element is needed. In this study, two optical interferometric techniques called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV) are used to experimentally investigate the vibration characteristics of a single-layer piezoelectric disc and a multilayer piezoelectric stack actuator. These two techniques are full-field measurement for AF-ESPI and point-wise displacement measurement for LDV. Because the clear fringe patterns obtained by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and corresponding vibration mode shapes of the piezoelectric disc and the multilayer piezoelectric stack actuator are obtained simultaneously by the AF-ESPI method. Interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes are demonstrated. In addition to the proposed two optical techniques, numerical computations based on a commercially available finite element package are presented for comparison with the experimental results. Good agreement between the measured data by experimental methods and the numerical results predicted by FEM is found in resonant frequencies and mode shapes for the single-layer piezoelectric disc. However, some discrepancies are observed for the results obtained by AF-ESPI and impedance analysis for the multilayer piezoelectric stack actuator. A detailed discussion is made to address important issues of this problem.