Most vibration-based energy harvesters, including piezoelectric harvester system, perform efficiently at only its resonant frequency as linear resonators, usually at very high frequency which are out of the range of frequency of interest. In real life applications, these linear resonators are impractical since real ambient vibrations are simply having varying lower frequencies. Hence, design a tuneable vibration energy harvester at a lower and useful frequency range of interest are essential in allowing promising energy output to meet intended power input at a more practical approach. In this paper, the piezoelectric voltage energy harvester (PVEH) was designed with a flexible fixture with the aim to reduce its first fundamental natural frequency. Two thickness of elastic fixtures were applied to generate power on PVEH. Three experimental techniques were used to measure the vibration characteristics of PVEH. First, the full-field optical technique, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) measured simultaneously the resonant frequencies and mode shapes. This is followed by the pointwise measurement system, laser Doppler vibrometer (LDV) in which the resonant frequencies were measured by dynamic signal swept-sine analysis. The resonant frequencies and anti-resonant frequencies were also obtained by impedance analysis. The results obtained from experimental measurements were compared with finite element numerical calculation. It is found that the boundary conditions under the elastic fixtures can effectively reduce the resonant frequency of the PVEH with a reasonable voltage output. The fundamental natural frequency of PVEH with the thickness of 0.58-mm elastic fixture is reduced to 37 Hz maintaining at 7.1 volts (1.2 mW), in comparison with the natural frequency on cantilevered PVEH at 78 Hz that produces 7.7 volts (6.5 mW).

The purpose of this study was to investigate the influence of a diaphragm material on the performance of a microspeaker. The finite element method was adopted to analyze the mode shapes and the displacement of the diaphragm under a force load. The Rayleigh integral was then calculated to determine the radiated sound pressure and frequency response of a loudspeaker. The location of the voice coil was also investigated. Locating the voice coil at approximately 53% to 76% of coil-radius/diaphragm-radius ratio yielded a favorable mode shape distribution and performance for the loudspeaker. In addition, two loudspeaker designs, Models A and B, were analyzed to determine the effects of the diaphragm material. The numerical results of Models A and B, indicated that the mode shape is a crucial factor when considering the materials used in a loudspeaker diaphragm. The property of a material at the inflection point of a mode shape obviously affects the modal frequency. According to this observation, the most crucial first and second axial symmetric modes in a loudspeaker design can be adjusted and the performance can be improved.

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.

For a controlled structure, the changes of physical characteristics like naturalfrequencies, modal damping coefficients, and what’s more on mode shapes will destabilizethe controlled system. To keep the control performance and guarantee its robustness, a newmodal control method using real-time identification is proposed to overcome theinstability of controlled structure, especially induced by the inversion of mode shape. Inthis paper, a modal model of time-varying mechanical structure is supplied by anidentifier. The choice of the kind of control permits to use this time-varying model foroptimizing and self-adapting the controller. In order to supply the controller, a modalobserver is used and also updated. For illustrative purpose, this proposed methodology iscarried out on a simple but representative time-varying mechanical structure. On thisexample, an inertia modification leads not only to low modal frequency shifts but also toinversion of a mode shape. This mode shape inversion is shown to destabilize thecontrolled structure when the control system is not updated. The overall procedure will bedescribed through simulations and performed for different operating conditions, which willprove that mode shapes have to be precisely determined and updated in the controller andobserver to guarantee a robust modal control with high performances in spite of thechanges of structure.

This paper presents the ultrasonic atomizer composed of the lead zirconate titanate (PZT) ring actuator and the Ni nozzle plate with numerous minute nozzles. The atomizer operates at its resonant frequency in out-of-plane vibration. De-ionized (DI) water is fed by the open trough to the porous sponge that is in contact with one face of the nozzle plate and it is ejected through nozzles. Micro-droplets are formed at the opposite face of the nozzle plate. The resonance frequencies of the PZT ring are investigated and compared in theoretical analysis, three-dimensional (3-D) finite-element models (FEM) numerical simulation, and experimental measurement. The performance of the atomizer is examined. This ring shape design of ultrasonic atomizer demonstrates advantage of high atomization rate (64.3ml/min) and high atomization efficiency (l,007ml/h/W) at low power consumption (8.244W).

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.