S. D. Hu

Flexoelectric Responses of Circular Rings

Dynamic sensing is essential to effective closed-loop control of precision structures. In a centrosymmetric crystal subjected to inhomogeneous deformation, when piezoelectricity is absent, only the strain gradient contributes to the polarization known as the “flexoelectricity.” In this study, a flexoelectric layer is laminated on a circular ring shell to monitor the natural modal signal distributions. Due to the strain gradient characteristic, only the bending strain component contributes to the output signal. The total flexoelectric signal consists of two components respectively induced by the transverse modal oscillation and the circumferential modal oscillation. Analog to the signal analysis, the flexoelectric sensitivity is also studied in two forms: a transverse sensitivity induced by the transverse modal oscillation and a transverse sensitivity induced by the circumferential modal oscillation. Analysis data suggest that the transverse modal oscillation dominates the flexoelectric signal generation and its magnitude/distribution shows nearly the same as the total signal. Furthermore, voltage signals and signal sensitivities are evaluated with respect to ring mode, sensor segment size, ring thickness, and ring radius in case studies. The total signal increases with mode numbers and sensor thicknesses, decreases with sensor segment size and ring radii, and remains the same with different ring thicknesses.

Comparison of flexoelectric and piezoelectric dynamic signal responses on flexible rings

Piezoelectric materials have been widely used for structural sensing due to the linear electromechanical coupling effect. Flexoelectricity, generally existing in all dielectrics, describes the linear inhomogeneous electromechanical coupling phenomena. Previous studies have shown that the direct flexoelectric effect is sensitive to the bending deformation. This study focuses on comparison and differences between two sensing mechanisms, that is, the flexoelectric and the piezoelectric effects, and explores their distinctive characteristics and potential applications. Based on the direct flexoelectric/piezoelectric effects, flexoelectric/piezoelectric materials treated as flexoelectric/piezoelectric sensors are applied to two ring models with identical dimensions. The mathematical models of thin elastic rings laminated with flexoelectric/piezoelectric sensors are established. Open-circuit sensing signals are derived for further evaluation and comparison. Sensing capabilities of these two materials and mechanisms are compared with respect to ring thickness, sensor thickness, and ring radius in case studies. Results show that the piezoelectric sensing signal appears to be sensitive for both bending-dominant and membrane-dominant vibrations, while the flexoelectric signal is much more prominent than the piezoelectric one for sensing of bending-dominant vibrations. For a flexible structure performing transverse vibration, the bending behavior is usually dominant. Thus, the flexoelectric effect could provide an effective alternative for structural sensing.

PVDF energy harvester on flexible rings

In this paper, the elastic ring is laminated with a convolving PVDF layer on the rings inner surface for energy harvesting. With the segmentation technique, the piezoelectric layer is uniformly segmented into several energy harvesting patches. The generated energy is the function of electric signal and the capacitance of energy harvesting patch. For each harvester, the circumferential vibration induced modal energy, the transverse vibration induced modal energy and the total energy is evaluated. By discussing different case studies (e.g., harvester thickness and segment size), the maximum magnitudes of modal energies are plotted, compared and evaluated. When the segment size increases, the maximum energies exhibit the deficiency because of signal average and cancellation. This study is to serve as a design guideline to achieve a higher energy harvesting efficiency for practical applications.

Modal signal analysis of conical shells with flexoelectric sensors

Flexoelectricity is known as the electromechanical coupling effect between the strain gradient and the polarization. In this study, a flexoelectric sensor is laminated on conical shells to monitor the natural modal signal distributions. The sensing mechanism of a generic flexoelectric sensor patch is presented first. Then, the spatially distributed microscopic sensing signal with respect to coordinates is evaluated in detail to reveal the modal signal distributions. Due to the gradient effect, the bending strain component is the only contribution to the total sensing signal. The total signal consists of two components resulting from the circumferential and longitudinal bending strain components. Analytical results show that the flexoelectric sensing signal induced by the longitudinal bending strain is the dominant contribution to the total signal for lower order modes; the contribution of the circumferential bending strain components increases while increasing the circumferential mode number. In lower modes, the optimal location of flexoelectric sensor is at the minor end and shifts to the middle for shallow shells. In higher modes, the optimal location is at the middle of the shell, but first shifts to the major end and then shifts to the minor end while increasing the semi-apex angle.

Electromechanical coupling and energy harvesting of circular rings

Ring shell structures often exhibit oscillatory behaviors during their operations. It is a crucial challenge to extract vibration energy, which is always wasted, to convert to useful electric energy. In this study, the concept of energy harvesting based on a circular ring laminated with a piezoelectric patch is established to achieve this purpose. The electrical device is assumed to be an equivalent resistance in the close-loop circuit as a simplified energy harvesting system. Due to the direct piezoelectric effect, the electromechanical coupling mechanism of the energy harvesting system is analyzed. Then, the electric power on the resistance is obtained. Case studies with respect to different system parameters, such as the equivalent resistance, excitation frequency, and the ring size, are conducted to optimize the modal power. Results show that the maximal modal power output is related to the equivalent resistance, the excitation frequency, as well as the ring radius. The optimal modal parameters are evaluated to maximize the energy harvesting effectiveness and provide a design guideline of ring-type energy harvesters for practical applications.

Active vibration suppression of payloads with a conical isolator

This article focuses on active vibration isolation of a rigid payload using a conical shell isolator laminated with piezoelectric sensors and actuators. The payload is mounted on the top (minor end) of the conical shell isolator. The piezoelectric sensor is laminated on the inner surface, and the piezoelectric actuator is laminated on the outer surface of the conical shell. The macro-fiber composite piezoelectric material is utilized as the actuator to enhance control performance, and polyvinylidene fluoride actuators are used as a comparison. The mathematical model of the conical isolator and the payload is derived in terms of the sensing signal equation and the actuation equation. Then, the modal equations are transformed into the state-space form with sensing signal as the system output and modal control force as the system input. Linear quadratic controllers are designed for each independent mode. In case studies, axial vibration isolation of the payload is performed to characterize the performance of the conical isolator and the optimal controller.

Energy Harvesting Characteristics of Conical Shells

Piezoelectric energy harvesting has experienced significant growth over the past few years. Various harvesting structures have been proposed to convert ambient vibration energies to electrical energy. However, these harvester’s base structures are mostly beams and some plates. Shells have great potential to harvest more energy. This study aims to evaluate a piezoelectric coupled conical shell based energy harvester system. Piezoelectric patches are laminated on the conical shell surface to convert vibration energy to electric energy. An open-circuit output voltage of the conical energy harvester is derived based on the thin-shell theory and the Donnel-Mushtari-Valsov theory. The open-circuit voltage and its derived energy consists of four components respectively resulting from the meridional and circular membrane strains, as well as the meridional and circular bending strains. Reducing the surface of the harvester to infinite small gives the spatial energy distribution on the shell surface. Then, the distributed modal energy harvesting characteristics of the proposed PVDF/conical shell harvester are evaluated in case studies. The results show that, for each mode with unit modal amplitude, the distribution depends on the mode shape, harvester location, and geometric parameters. The regions with high strain outputs yield higher modal energies. Accordingly, optimal locations for the PVDF harvester can be defined. Also, when modal amplitudes are specified, the overall energy of the conical shell harvester can be calculated.Copyright

Experimental study of a piezoelectric ring energy harvester

Vibration energy harvesting is becoming an important issue in engineering applications. Energy harvesters based on shell and non-shell structures have been proposed. In this paper, laboratory experiments are conducted to validate the theory of a circular ring shell energy harvester. With the experimental natural frequencies and damping ratios testing in the experiments, energy harvesting experiments are conducted. Output voltage across the external resistor in the closed-circuit condition is measured. Comparing experiment results with theoretical ones, the errors between them are under 10% for the output voltage. Laboratory experiments demonstrate that energy harvesting theory based on the ring is practical in practical applications.

Size optimization of conical piezoelectric energy harvester

This research focuses on the size optimization of the piezoelectric patches. The origin of the patch is fixed at an optimal location. Three parameters are chosen to define the size of piezoelectric patch, i.e., the circumferential width, the length from the origin to the minor end, and the length from the origin to the major end. Origin and sizes are derived according to the modal voltage. Next, solving the extremum of energy equation with respect to the three parameters yields the optimal size of the piezoelectric patch. Case studies are given to evaluate the energy outputs of the optimal piezoelectric energy harvester. The results prove that with origin located at the optimal location, the output energy of the piezoelectric patch firstly increases with the width as well as the length till the maximum, and then decreases with the spatial width and length parameters. The optimal width is always 75% of the half wave length.

Static Nano-Control of Cantilever Beams Using the Inverse Flexoelectric Effect

Flexoelectricity, an electromechanical coupling effect, exhibits two opposite electromechanical properties. One is the direct flexoelectric effect that mechanical strain gradient induces an electric polarization (or electric field); the other is the inverse flexoelectric effect that polarization (or electric field) gradient induces internal stress (or strain). The later can serve as an actuation mechanism to control the static deformation of flexible structures. This study focuses on an application of the inverse flexoelectric effect to the static displacement control of a cantilever beam. The flexoelectric layer is covered with an electrode layer on the bottom surface and an AFM probe tip on the top surface in order to generate an inhomogeneous electric field when powered. The control force induced by the inverse flexoelectric effect is evaluated and its spatial distribution resembles a Dirac delta function. Therefore, a “buckling” characteristic happens at the contact point of the beam under the inverse flexoelectric control. The deflection results of the cantilever beam with respect to the AFM probe tip radius indicate that a smaller AFM probe tip achieves a more effective control effect. To evaluate the control effectiveness, the flexoelectric deflections are also compared with those resulting from the converse piezoelectric effect. It is evident that the inverse flexoelectric effect provides much better localized static deflection control of.flexible beams.Copyright