Einar Halvorsen

Downhole sensing is important for the exploration and production of oil and gas. The development of downhole sensors faces challenges due to remote and harsh environment in oil and gas wells. In addition, real-time monitoring is essential for optimizing well-completion design and production. This paper presents a sensor concept for downhole pressure sensor that provides near real-time measurement, and suitability for remote and harsh environment. The downhole part of the sensor system is a mechanical resonator whose resonant frequency is modulated by pressure. Ambient noise is the energy source for mechanical oscillations, which are converted into phase oscillations of light within an optical fiber. Above the ground, the light signal is processed and analyzed to determine the resonant frequency, and hence the pressure. Optical fiber provides low-loss high-speed transmission and thus enables near real-time measurements. The proposed sensor system was demonstrated in a laboratory setting and showed a comparable accuracy to a commercial pressure gauge.

Patterning the piezoelectric layer of a PMUT plate usually leads to improved performance, however modeling of such PMUT is not as straightforward as its conventional counterpart. This paper presents an electroacoustic model for conventional as well as patterned piezoelectric micromachined ultrasonic transducers (PMUTs) with square shaped membranes. Hamilton’s principle is utilized to formulate the dynamics of the patterned PMUT. The derived mode shape is used to obtain the electrical, mechanical and acoustic parameters to arrive at the complete electroacoustic model. The model is applied to 8 different designs, where 4 are of conventional type with different electrode configurations and the other 4 are patterned designs with different patterning configurations. Using the proposed model, the electrode and patterning geometry for each PMUT design is optimized. Natural frequency, mode shape, the input impedance at the electrical port and the transfer function from the electrical to the acoustic port calculated from this model are shown to be in good agreement with those obtained from finite element analysis for all the studied designs. Moreover, the patterned PMUTs are shown to have superior performance, in terms of volume velocity per unit voltage, over conventional PMUTs operating at a given resonance frequency.

Piezoelectric micromachined ultrasonic transducers (PMUTs) with multiple electrodes can be utilized as multi-frequency transducers by exciting selected vibration modes of the diaphragm providing configurability that may be beneficial in modern ultrasound imaging and therapeutic techniques. This requires judicious arrangement of the electrode configuration to excite the desired modes or combination of modes. Optimization of the electrode pattern can be done using full electroacoustic Finite Element Method (FEM) simulations, but this is computationally intensive and gives limited insight into the underlying physics. This paper presents a simple and efficient approach based on the in-vacuum strain mode shapes of the PMUT diaphragm to optimize the electrode configurations for an arbitrary PMUT cell resonating at any flexural mode. Strain mode shapes are obtained both from an analytical model as well as FEM. The proposed method is compared to and verified by full electroacoustic FEM simulations of PMUTs radiating into water. The optimal electrode patterns for the first few flexural modes are found for rectangular PMUTs with three different length-to-width aspect ratios, and examples of configurable PMUTs are given by combining the optimal electrodes at two different modes.

Silicon-based kinetic energy converters employing variable capacitors, also known as electrostatic vibration energy harvesters, hold promise as power sources for Internet of Things devices. However, for most wireless applications, such as wearable technology or environmental and structural monitoring, the ambient vibration is often at relatively low frequencies (1–100 Hz). Since the power output of electrostatic harvesters is positively correlated to the frequency of capacitance oscillation, typical electrostatic energy harvesters, designed to match the natural frequency of ambient vibrations, do not produce sufficient power output. Moreover, energy conversion is limited to a narrow range of input frequencies. To address these shortcomings, an impacted-based electrostatic energy harvester is explored experimentally. The impact refers to electrode collision and it triggers frequency upconversion, namely a secondary high-frequency free oscillation of the electrodes overlapping with primary device oscillation tuned to input vibration frequency. The main purpose of high-frequency oscillation is to enable additional energy conversion cycles since this will increase the energy output. The devices investigated were fabricated using a commercial microfabrication foundry process and were experimentally studied. These devices exhibit non-uniform cross-section electrodes and a springless mass. The non-uniform width electrodes were used to prevent pull-in following electrode collision. Springless masses from different materials and sizes, such as 0.5 mm diameter Tungsten carbide, 0.8 mm diameter Tungsten carbide, zirconium dioxide, and silicon nitride, were added in an attempt to force collisions over a range of applied frequencies that would not otherwise result in collisions. The results show that the system operates over a relatively wide frequency range (up to 700 Hz frequency range), with the lower limit far below the natural frequency of the device. The addition of the springless mass successfully increased the device bandwidth. For example, at a low peak-to-peak vibration acceleration of 0.5 g (peak-to-peak), the addition of a zirconium dioxide ball doubled the device’s bandwidth. Testing with different balls indicates that the different sizes and material properties have different effects on the device’s performance, altering its mechanical and electrical damping.

This article presents a variational model for the geometrically nonlinear behaviour of the piezoelectrically actuated MEMS tunable lenses. Residual stresses during fabrication and larger actuation voltages cause large deflections such that a linear model would provide less accurate approximation. This presses the need for a nonlinear model that can explain the softening and hardening effects exhibited by the lens during its operation and affect its optical performance. Thus, in the view of von Kármán’s plate theory, the presented nonlinear model predicts the lens displacement after solving a cubic nonlinear system of equations. The chosen displacement ansatz fits the problem under study by satisfying the mechanical boundary conditions, and simplifying calculation of the variational integrals and optical representation of the lens’ sag. The model also shows good agreement with FEM simulations over various combinations of tensile and compressive residual stresses. Moreover, it succeeds in fitting measurements when used in a constrained optimization scheme in which the layers’ residual stresses and the e-form piezoelectric coupling coefficient are the fitting parameters.

In bending of a purely elastic beam or plate, it is well established that the cross-sectional shape changes character with decreasing bending radius-of-curvature and that the transition can be characterized by the Searle parameter. In a piezoelectric structure, the cross-sectional deformation is affected by the opposite anticlastic and electromechanical bending curvatures. The behavior is consequently more complicated and it is an open question how the cross-sectional shape develops with increasing bending. In this paper, analytical solutions are used to study the cross-sectional deformation of piezoelectric cantilever-actuators taking both anticlastic and electromechanical bending effects into account. We consider unimorph and bimorph actuators. In the case of electrical actuation, as for the purely mechanical case, we find that the Searle parameter is an important parameter characterizing the shape of the cross-section. A load scaling rule gives a criterion for fixed cross-section-deflection for different actuator widths. Using this scaling rule, the Searle parameter is kept unchanged. The analytical results are verified by non-linear finite element analysis using electric potential and mechanical moment as applied loads.

Interdigitated electrodes (IDEs) on dielectric films is an important electrode design in electrical components such as transducers and sensors. Further development and use of IDEs for characterization of the in-plane properties of dielectric films requires models for the capacitance, particularly when used in a multilayer stack. Previous models for the capacitance have permitted erroneous boundary conditions between layers with associated limitations to accuracy. In this work we present a new model based on fulfilling the boundary conditions between layers with different dielectric constant. We further demonstrate how the model can be used to calculate the in-plane dielectric constant and polarization of BaTiO₃ films. The model is shown to outperform previous models using both the experimental data from BaTiO₃ films on SrTiO₃ substrates and finite element method simulations of the corresponding case. One important advantage compared to previous work is that the new model provides good results regardless of film thickness.

Inductive and capacitive impedance matching are two different techniques optimizing power transfer in magnetic resonance inductive wireless power transfer. Under ideal conditions, i.e., unrestricted parameter ranges and no loss, both approaches can provide the perfect match. Comparing these two techniques under non-ideal conditions, to explore fundamental differences in their performance, is a challenging task as the two techniques are fundamentally different in operation. In this paper, we accomplish such a comparison by determining matchable impedances achievable by these networks and visualizing them as regions of a Smith chart. The analysis is performed over realistic constraints on parameters of three different application cases both with and without loss accounted for. While the analysis confirms that it is possible to achieve unit power transfer efficiency with both approaches in the lossless case, we find that the impedance regions where this is possible, as visualized in the Smith chart, differ between the two approaches and between the applications. Furthermore, an analysis of the lossy case shows that the degradation of the power transfer efficiencies upon introduction of parasitic losses is similar for the two methods.