Chung-De Chen

Decoupled formulation of piezoelectric elasticity under generalized plane deformation and its application to wedge problems

Abstract This paper presents the formulation of piezoelectric elasticity under generalized plane deformation derived from the three-dimensional theory. There are four decoupled classes in the generalized plane deformation formulation, i.e. when l 3 ( μ )= l 2 * ( μ )=0, l 3 ( μ )= l 3 * ( μ )=0, l 3 * ( μ )= l 2 * ( μ )=0 or l 3 ( μ )= l 3 * ( μ )= l 2 * ( μ )=0. Only the inplane fields of the first class and the antiplane field of the second class include the piezoelectric effect. Several examples of wedge problem often encountered in smart structures, such as sensors or actuators are studied to examine the stress singularity near the apex of the structure. The bonded materials to the PZT-4 wedge are PZT-5, graphite/epoxy or aluminum (conductor). The influencing factors on the singular behavior of the electro-elastic fields include the wedge angle, material type, poling direction, and the boundary and interface conditions. The numerical results of the first case are compared with Xus graphs and some comments are made in detail. In addition, some new results regarding the antiplane stress singularity of the second class are obtained via the case study. The coupled singularity solutions under generalized plane deformation are also investigated to seek the conditions of the weakest or vanishing singular stress fields.

System Design of a Weighted-Pendulum-Type Electromagnetic Generator for Harvesting Energy From a Rotating Wheel

This paper proposes the system design of a weighted-pendulum-type electromagnetic generator for harvesting energy from a rotating wheel. Different from the traditional energy-harvesting device, the natural frequency of the suitable weighted pendulum, which oscillates due to periodic change of the tangential component of gravitational force, can match up with the rotational frequency of the wheel at any speed. In addition, the pendulum oscillates at a large angle and angular velocity so as to generate a large amount of power. The physical model of the pendulum was first constructed and the equation of motion was then derived via the Lagrange method. Then, the models of power generation were derived by using Faradays law of induction and the Lorentz force law. The nonlinear dynamic behaviors were discussed considering the characteristic length, variable electromagnetic damping, and wheel rotation speed. Finally, an experimental rig was constructed to verify the correctness of numerical results. The suitable weighted pendulum combined with coils and magnets has demonstrated the power generation of several hundred micro-Watts in the experiment.

Fracture mechanics analysis of a composite piezoelectric strip with an internal semi-infinite electrode

Abstract IA piezoelectric strip with semi-infinite electrode is investigated. Two combinations of mechanical–electrical loadings are considered. They consist of the anti-plane deformation with in-plane electrical field and the in-plane electroelastic field. Based on the Fourier transform and the Wiener–Hopf technique, the electroelastic local stress fields are found to exhibit the square root singularity near the electrode tip. The energy density factor criterion is applied to examine the fracture behavior near the electrode tip.

Natural frequency self-tuning energy harvester using a circular Halbach array magnetic disk

A novel natural frequency self-tuning energy harvester is presented, which utilizes the presence of the nonlinearity model and the well-weighted swing disk to maximize the power output and the frequency bandwidth for a wheel rotating at any speed. Kinetic energy harvesters are frequency selective, meaning that they have high power transmission efficiency only when they are excited at their natural frequency. The well-weighted swing disk with nonlinear effects can render the energy harvester more broadband, that is, it has a more steady power generation at various wheel speeds than the ill-weighted swing disk has. We integrate magnets in a novel circular Halbach array and coils into the design to augment the magnetic strength on one side of the array where the coils are placed. Therefore, the gradient of the average magnetic flux density for the circular Halbach array disk is larger than that of the multipolar magnetic disk. The dynamic models with electromechanical couplings have been established and are analyzed. In the experiments, the power output of the prototype at an optimum external resistance was approximately 300–550 µW at about 200–500 rpm and precisely matches the numerical results.

Singular electro-mechanical fields near the apex of a piezoelectric bonded wedge under antiplane shear

This paper presents the explicit forms of singular electro-mechanical field in a piezoelectric bonded wedge subjected to antiplane shear loads. Based on the complex potential function associated with eigenfunction expansion method, the eigenvalue equations are derived analytically. Contrary to the anisotropic elastic bonded wedge, the results of this problem show that the singularity orders are single-root and may be complex. The stress intensity factors of electrical and mechanical fields are dependent. However, when the wedge angles are equal (α=β), the orders become real and double-root. The real stress intensity factors of electrical and mechanical fields are then independent. The angular functions have been validated when they are compared with the results of several degenerated cases in open literatures.

A novel two-axis MEMS scanning mirror with a PZT actuator for laser scanning projection

This study presents a novel design for a two-axis scanning device driven by lead-zirconate-titanate (PZT) ceramic. The proposed device consists of a scanning mirror and a Y-shaped piezoelectric actuator. The scanning mirror was fabricated using an MEMS process involving three masks. Experimental results show that the fast and slow frequencies at resonance are 25.0 kHz and 0.56 kHz, respectively. The optical scanning angles are 27.6° and 39.9°. The power consumption of the device is 13.4 mW at a driving voltage of 10 V. This study also develops a laser projection module integrated with the scanning device. The module can project a 2-D image at a resolution of 640 x 480.

A Nonlinear Suspended Energy Harvester for a Tire Pressure Monitoring System

The objective of this study is to develop and analyze a nonlinear suspended energy harvester (NSEH) that can be mounted on a rotating wheel. The device comprises a permanent magnet as a mass in the kinetic system, two springs, and two coil sets. The mass vibrates along the transverse direction because of the variations in gravitational force. This research establishes nonlinear vibration equations based on the resonance frequency variation of the energy harvester; these equations are used for analyzing the power generation and vibration of the harvester. The kinetic behaviors can be determined according to the stiffness in the two directions of the two suspended springs. Electromagnetic damping is examined to estimate the power output and effect of the kinematic behaviors on NSEH. The power output of the NSEH with a 52 Ω resistor connected in series ranged from approximately 30 to 4200 μW at wheel speeds that ranged from nearly 200 to 900 rpm.

Singular stresses near apex of wedge by finite element analysis

Abstract Based on the theoretical solution of stress singularity order, the corresponding stress intensity factors for a one or two‐bonded wedge, under mechanical or thermal load, is determined using the finite element approach. The r-λ (λ is real or complex) and ln(r) stress singularity types are the major concern. For a wedge with two singularity orders, a modified least square method is proposed. Good agreement was observed when analytical results compared to experimental results. In the case that λ is complex, the numerical errors in calculating the angular functions expressed in the stress terms should be carefully examined.

Design and jump phenomenon analysis of an eccentric ring energy harvester

This paper presents the development of a wheel-mounted eccentric ring energy harvester that is driven by centripetal and gravitational forces during wheel rotation. The natural frequency of the eccentric ring matches the wheel rotation frequency at any car speed because its character length is designed equal to the wheel radius. Consequently, the eccentric ring oscillates with a relatively large swing angle at the wheel speed to generate high levels of power. The nonlinear dynamic behavior of the eccentric ring is investigated to ensure that the proposed design produces steady swing angles, especially at high wheel speeds. Herein, the jump phenomenon of the dynamic motion of the eccentric ring is analyzed by using the Duffing equation and the linearization process. The discriminant value obtained from the analysis confirms that no jump phenomenon occurs at all wheel speeds if the eccentric ring is properly designed. In the experiment, the eccentric ring is integrated with magnets and a coil set to generate 318?442??W at constant wheel speeds between 300 and 500?rpm. This shows that the proposed device is a potential power source for low-power wheel-mounted electronics, such as pressure sensors, accelerometers, and thermometers.

Two-axis MEMS scanning mirror driven by a single PZT actuator

In this paper, a novel design for two-axis MEMS scanning mirror driven by a single PZT is presented. For fast scan, the bending moment of the actuator is transferred to torque of the fast torsion bars. An offset is introduced in the present design so that the torsional vibration of the slow scan can be excited by a vertical displacement of the actuator. A vibration analysis reveals that there exists an optimum offset to maximize the slow scanning angle. A simple MEMS process is presented and then a scanning angle test validates the analytical results.