Circular Membrane Research Articles

Polymer Conductive Membrane-Based Circular Capacitive Pressure Sensors from Non-Touch Mode of Operation to Touch Mode of Operation: An Analytical Solution-Based Method for Design and Numerical Calibration.

Polymer-based conductive membranes play an important role in the development of elastic deflection-based pressure sensors. In this paper, an analytical solution-based method is presented for the design and numerical calibration of polymer conductive membrane-based circular capacitive pressure sensors from non-touch mode of operation to touch mode of operation. The contact problem of a circular membrane in frictionless contact with a rigid flat plate under pressure is analytically solved, and its analytical solution is used for the design of touch mode circular capacitive pressure sensors for the first time. The analytical relationship with input pressure as independent variable and output capacitance as dependent variable is precisely derived and is used for the numerical calibrations of the analytical relationships with input capacitance as the independent variable and output pressure as the dependent variable in order to meet the capacitive pressure sensor mechanism of detecting pressure by measuring capacitance. For the first time, an example showing the design and numerical calibration of a given (given design parameters) polymer conductive membrane-based circular capacitive pressure sensor from non-touch mode of operation to touch mode of operation is provided. Then, the influence of changing several important design parameters on input capacitance–output pressure relationships is comprehensively investigated in order to clarify the desired input–output relationships when changing design parameters.

Analysis of space debris impact source localization based on PVDF piezoelectric film

As the pace of human exploration and utilization of space continues to accelerate, space debris gradually becomes an inevitable problem affecting and threatening human space activities. When space debris strikes the spacecraft bulkhead, determining the impact source location timely and accurately is the foundation of the repair damage, and is also of great importance for the safety of astronauts' life. This paper analyzed the wave propagation law in thin plates, established a lightweight sensor array using PVDF (Polyvinylidene fluoride) circular thin-film sensors, and used a two-stage light-gas gun loading system to conduct hypervelocity collision localization experiments on impacting 2A12 aluminum plates to study the effects of sensor array radius and sensor size on localization results. The results show that the smaller the radius of the PVDF sensor array is, the more accurate the positioning result is under the premise of the same size of the PVDF circular film sensor array. On the premise of the same PVDF sensor array arrangement, the larger the PVDF circular membrane sensor is, the more accurate the positioning result is. ABAQUS finite element software is used to study the stress wave propagation of aluminum ball impacting aluminum plate at high speed, simulating space debris impacting spacecraft. The stress waveform obtained from the simulation is in good agreement with the experiment, which shows the accuracy of the numerical simulation method.

Mechanics of pressurized planar hyperelastic membranes.

The paper examines the mechanics of inflation of incompressible planar hyperelastic membranes that are rigidly fixed at their boundary and subjected to a uniform pressure. Strain energy functions characterized by the neo-Hookean, Mooney-Rivlin and the Ogden forms are used. Fixity is provided along either circular or elliptical boundaries. The computational results indicate that the strain energy function has a significant influence on the pressure versus inflated volume response of the deformed membrane. When the strain energy function corresponds to a Mooney-Rivlin form, the circular membrane displays no tendency to develop any instability. The equivalent circular membranes composed of both the neo-Hookean and Ogden-type strain energy functions developed an initial 'Wrinkling Instability'. For planar membranes with an elliptical planform, the wrinkling instability is more pronounced; membranes composed of hyperelastic materials with a Mooney-Rivlin form of the strain energy function continue to deform without the development of an initial instability point, whereas membranes composed of both the neo-Hookean and Ogden materials exhibit wrinkling behaviour at critical locations at the interior of the fixed boundary region. The dependency of the strain energy function on the second invariant of the Cauchy-Green strain tensor has an influence in the suppression of hyperelastic effects. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation

Essential to the design and development of circular contact mode capacitive pressure sensors is the ability to accurately predict the contact radius, maximum stress, and shape of a laterally loaded circular membrane in frictionless contact with a concentric circular rigid flat plate. In this paper, this plate/membrane contact problem is solved analytically again by simultaneously improving both out-of-plane equilibrium equation and geometric equation, and a new and more refined closed-form solution is given to meet the need of accurate prediction. The new closed-form solution is numerically discussed in convergence and effectiveness and compared with the previous one, showing that it can greatly improve the prediction accuracy of the contact radius, maximum stress, and shape of the circular membrane in frictionless contact with the rigid flat plate.

Four new species of Arrenurus water mites (Acari, Hydrachnidiae, Arrenuridae) from China

ABSTRACT The paper deals with four new species of Arrenurus (Acari, Hydrachnidiae, Arrenuridae) from standing water habitats in China: Arrenurus (Arrenurus) pseudonemani sp. nov., Arrenurus (Arrenurus) circinatus sp. nov., Arrenurus (Arrenurus) menglaensis sp. nov., and Arrenurus (Megaluracarus) guantingensis sp. nov. Arrenurus (Arrenurus) pseudonemani sp. nov. can be distinguished by the petiole membrane enlarged in the middle, making the middle part significantly wider than the front and rear ends. Arrenurus (Arrenurus) circinatus sp. nov. can be distinguished by petiole bearing a circular petiole membrane at the end. Arrenurus (Arrenurus) menglaensis sp. nov. can be distinguished by petiole with a pair of setae and split down the middle, forming a pair of pointed crescents at the ends. Arrenurus (Megaluracarus) guantingensis sp. nov. can be distinguished cauda slightly convex basally, without lateral extensions, P-2 with 15 small medial setae near distoventral corner. All the type specimens are deposited in GUGC. http://www.zoobank.org/urn:lsid:zoobank.org:act:22E84E7B-2E0A-4E82-8ED4-A617139A4CE0

Polymer Conductive Membrane-Based Non-Touch Mode Circular Capacitive Pressure Sensors: An Analytical Solution-Based Method for Design and Numerical Calibration.

In this paper, an analytical solution-based method for the design and numerical calibration of polymer conductive membrane-based non-touch mode circular capacitive pressure sensors is presented. The accurate analytical relationship between the capacitance and applied pressure of the sensors is derived by using the analytical solution for the elastic behavior of the circular polymer conductive membranes under pressure. Based on numerical calculations using the accurate analytical relationship and the analytical solution, the analytical relationship between the pressure as output and the capacitance as input, which is necessary to achieve the capacitive pressure sensor mechanism of detecting pressure by measuring capacitance, is accurately established by least-squares data fitting. An example of how to arrive at the design and numerical calibration of a non-touch mode circular capacitive pressure sensor is first given. Then, the influence of changing design parameters such as membrane thickness and Young’s modulus of elasticity on input–output relationships is investigated, thus clarifying the direction of approaching the desired input–output relationships by changing design parameters.

Study of hydrodynamics and mass transfer in the bench-scale membrane testing devices

Computational fluid dynamics (CFD) was used to study hydrodynamics and mass transfer in a conventional circular bench-scale membrane testing device, and improved geometry of the device was proposed. The conventional and modified geometries were fabricated for experimental validation of the simulation results. It was observed that the modified cell outperformed the conventional cell in terms of distribution of mass transfer coefficient and shear stress on the membrane surface. Further, the ranges of average shear stress and mass transfer coefficient in the modified membrane testing cell for crossflow rates between 25 and 60 L/h overlaped with the corresponding ranges observed in a spacer-filled membrane channel. Hence, the modified geometry is a better choice for membrane testing and can also be extended to study the performance of antifouling membranes.

Analytical, numerical and experimental study of the finite inflation of circular membranes

Analytical, numerical and experimental study of the finite inflation of circular membranes

Investigation of Achieving Ultrasonic Haptic Feedback Using Piezoelectric Micromachined Ultrasonic Transducer

Ultrasound haptics is a contactless tactile feedback method that creates a tactile sensation by focusing high-intensity ultrasound on human skin. Although air-coupled ultrasound transducers have been applied to commercial products, the existing models are too bulky to be integrated into consumer electronics. Therefore, this study proposes a piezoelectric micromachined ultrasonic transducer (pMUT) with a small size and low power consumption to replace traditional transducers. The proposed pMUT has a resonance frequency of 40 kHz and a radius designed through the circular plate model and finite element model. To achieve better performance, lead zirconate titanate was selected as the piezoelectric layer and fabricated via RF sputtering. The cavity of the pMUT was formed by releasing a circular membrane with deep reactive ion etching. The resonance frequency of the pMUT was 32.9 kHz, which was close to the simulation result. The acoustic pressure of a single pMUT was 0.227 Pa at 70 Vpp. This study has successfully demonstrated a pMUT platform, including the optimized design procedures, characterization techniques, and fabrication process, as well as showing the potential of pMUT arrays for ultrasound haptics applications.

Raman Spectroscopic Probe for Nonlinear MoS2 Nanoelectromechanical Resonators.

Resonant nanoelectromechanical systems (NEMS) enabled by two-dimensional (2D) semiconductors have been actively explored and engineered for making ultrascaled transducers toward applications in ultralow-power signal processing, communication, and sensing. Although the transduction of miniscule resonant motions has been achieved by low-noise optical or electronic techniques, direct probing of strain in vibrating 2D semiconductor membranes and the interplay between the spectroscopic and mechanical properties are still largely unexplored. Here, we experimentally demonstrate dynamical phonon softening in atomically thin molybdenum disulfide (MoS2) NEMS resonators by directly coupling Raman spectroscopy with optical interferometry resonance motion detection. In single-layer, bilayer, and trilayer (1L to 3L) MoS2 circular membrane NEMS resonators, we show that high-amplitude nonlinear resonances can enhance the Raman signal amplitude, as well as introduce Raman modes softening up to 0.8 cm-1. These results shall pave the way for engineering the coupling and control between collective mechanical vibrations and Raman modes of the constituent crystals in 2D transducers.

Theoretical and experimental study on the effect of plane diaphragm tension on hydroelastic coupled vibrations in a hemispherical tank

In this study, to simulate liquid sloshing in a spacecraft fuel tank, the effect of tension of a plane diaphragm on the hydroelastic coupled vibration of the liquid in a hemispherical tank was investigated both analytically and experimentally. In the theoretical analysis, the liquid was assumed to be incompressible, non-viscous, and irrotational, and the plane diaphragm corresponded to a clamped circular membrane. The influence of tension of the diaphragm on the natural frequency was investigated. In addition, its natural frequencies and vibration modes were compared with those of a liquid in a cylindrical tank. The comparison revealed that the natural vibration characteristics of a liquid in a hemispherical tank approximate those of a liquid with the same volume in a cylindrical tank. In the experiment, two silicon test membranes with diameters of 500 mm, one 0.22 mm thick and the other 0.34 mm thick, were used as plane diaphragms. Each test membrane was uniformly tensioned in the radial direction at ten points that were uniformly spaced along the circumference of the edge of the membrane. The natural frequencies were measured by tapping the test membranes with a finger and conducting an FFT analysis of the response. The vibration modes were measured by exciting the membranes acoustically and measuring their responses using a scanning laser Doppler vibrometer. A comparison between the experimental and theoretical results showed that they were in good agreement, even in the case of an empty tank. This demonstrates the validity of the theoretical analysis and accuracy of the experimental results.

Unusual nonlinear frequency response in circular dielectric elastomer membranes excited by fluctuating through-thickness voltages

This work demonstrates novel nonlinear vibration behavior in circular dielectric elastomer membranes that are excited by low nominal voltages with moderate-to-large-amplitude sinusoidal fluctuations. Low nominal voltages are those where the membrane has only one equilibrium stretch, and snap-though instability is not possible. The dynamic stretches therefore can be extremely large, and are limited only by the locking stretch of the elastomer. Because extremely large stretches are possible without snap-through instability, resonances in the frequency response transition from softening nonlinearity at moderate stretches to hardening nonlinearity at large stretches. Two types of atypical frequency response that depend on the amplitude of voltage fluctuations that dynamically excite the membrane are reported here for the first time. First, for moderate-amplitude voltage fluctuations, three steady-state vibrations (corresponding to small, moderate, and extreme stretches) are possible within a frequency band near resonance. Second, for large-amplitude voltage fluctuations, a frequency band occurs near resonance where only one steady-state vibration is possible, and this vibration corresponds to extreme dynamic stretches. Because of these unique steady-state solutions near resonance, new atypical jump-phenomenon may occur during frequency sweeps through resonance. The new, previously unreported vibration and jump phenomena demonstrated in this paper may be leveraged for improved performance in applications like resonators, energy harvesters, actuators, and sensors.

The Large Deflection Solution of Circular Elastic Membrane under Composite Loads

In this paper, the large deflection problem of axisymmetric isotropic elastic membranes subjected to the composite loads is studied. The Hencky transformation is extended and the general solution of large deflection of the membranes under the composite loads is obtained. The general solution is given in different forms in different values of loads. The obtained results of the numerical values of elastic characters can be applied in practice.

Locomotion of magnetoelastic membranes in viscous fluids

The development of multifunctional and biocompatible microrobots for biomedical applications relies on achieving controllable locomotion. Here we describe the conditions that allow homogeneous magnetoelastic membranes composed of superparamagnetic particles to swim through viscous fluids. By solving the equations of motion, we find the dynamical modes of circular membranes in precessing magnetic fields, which are found to actuate in or out of synchronization with a magnetic field precessing above or below a critical precession frequency ${\ensuremath{\omega}}_{c}$, respectively. For frequencies larger than ${\ensuremath{\omega}}_{c}$, synchronized transverse waves propagate on the membrane along the rotational (perimeter) and radial directions. Using the lattice Boltzmann approach, we show how these waves give rise to locomotion in an incompressible fluid at low Reynolds numbers. Nonreciprocal motion resulting in swimming is achieved by breaking the morphological symmetry of the membrane, attained via truncation of a circular segment. The membrane translation can be adapted to a predetermined path by programming the external magnetic field. Our results lay the foundation for achieving directed motion in thin, homogeneous magnetoelastic membranes with a diverse array of geometries.

Analytical, numerical and experimental study of the finite inflation of circular membranes

In the present work we derive an analytical expression for the pressure–deflection curve of circular membranes subjected to inflation. This problem has been studied mostly from a numerical point of view and there is still a lack of accurate closed-form solutions in nonlinear elasticity. The analytical formulation is developed with a semi-inverse method by setting a priori the kinematics of deformation of the membrane. A compressible Mooney–Rivlin material model is considered and a pressure–deflection relation is derived from the equilibrium. The kinematics is approximated and therefore the obtained solution is not exact. Consequently, the formulation is adjusted by introducing an additional polynomial function in the pressure–deflection equation. The polynomial is calibrated by fitting numerical solutions of the exact system of differential equilibrium equations. The calibration is done over a wide range of constitutive parameters that covers the response of all rubber materials for technological applications. As a result, a definitive and accurate expression of the applied pressure as a function of the deflection of the membrane is obtained. The formula is validated with finite element (FE) simulations and compared with other solutions available in the literature. The comparison shows that the present model is more accurate. In addition, unlike the other models, it can be applied to compressible materials. Experimental uniaxial and bulge tests are carried out on rubber materials and the model proposed is used to characterize the Mooney–Rivlin constitutive parameters. Since the pressure–deflection formula is accurate and easy-to-use, it is an innovative tool in engineering applications of inflated membranes.

In-plane nonlinear vibration of circular dielectric elastomer membranes with extreme stretchability

This work investigates large in-plane stretches in thin circular membranes pre-stretched mechanically and dynamically excited by fluctuating voltages applied through their thicknesses. The nonlinear equation of motion is derived using Hamilton’s principle. Nonlinearity arises from the elastomer’s material behavior and electromechanical coupling from applied voltages. Primary and secondary resonances exhibit typical softening nonlinearity characterized by a range of frequencies where two coexisting vibrations, referred to as the upper branch and lower branch response, are possible. Our focus is the upper branch response, where extremely large dynamic stretches in the hundreds of percent are possible. These large stretches have not been fully investigated by prior research. The membrane’s upper branch vibrations can be found by decreasing frequency sweeps through resonance, and may not be captured if only increasing frequency sweeps are analyzed. Large-amplitude upper branch stretches occur when the membrane vibrates about both small-stretch and large-stretch equilibria. In addition to larger amplitudes, the upper branch dynamic stretches near secondary resonances have dominant frequencies different from the excitation frequency. Whether the dielectric elastomer membrane vibrates on the lower or upper branch depends on its initial conditions, and the initial conditions that result in each case are quantified. A technique is demonstrated to switch the membrane’s vibration from the lower to upper branch using impulse-like voltages superposed on the nominal sinusoidal component. The large-amplitude nonlinear dynamic stretches highlighted in this work, and the strategies we propose for accessing and controlling them, could be leveraged for improved performance in existing soft transducer technologies.

Wave attenuation by a submerged circular porous membrane

Wave action over a submerged circular flexible porous membrane is investigated and the impact of porosity in dampening the far-field wave amplitude is examined in a scattering of incoming waves. The unknown potential for the free surface and the membrane-covered regions are obtained by coupling the respective boundary conditions and Darcy’s law for permeable structure. The associated boundary value problem is solved using the method of expansions of the eigenfunctions as Fourier-Bessel series. To understand the efficiency of the present study, wave force excitation on the circular membrane, far-field scattering wave amplitude, energy dissipation, and flow distribution are computed and examined. The study shows that on the leeward side of the membrane the wave amplitude reduces drastically. In addition, the submergence depth has a significant impact on wave energy dissipation. This model will be beneficial in developing the mechanism to minimize wave force on coastal structures for a variety of marine operations. In addition, this structure has minimal environmental effects on different coastline processes and can therefore be used in a variety of coastal/ocean applications.

Self-assembled silicon membrane resonator for high vacuum pressure sensing

In this paper, a mechanical vacuum gauge based on a circular membrane resonator is proposed and its high responsivity is verified in high vacuum down to a pressure of ∼6 × 10−7 mbar. A silicon-on-nothing (SON) resonator with a self-sealed cavity having a diameter of 150μm and a thickness of 1.55μm is fabricated through a high vacuum annealing process. After the fabricated membrane resonator is placed inside a custom vacuum chamber, its resonant characteristics are measured with a frequency sweep, and the vibration amplitudes are measured by resonance feedback using a laser and photodiodes at various vacuum pressures. Using quality factor (Q factor) measurement, the SON resonator shows a high responsivity (ΔQ/ΔP) of up to ∼3.7 × 108 mbar−1 in the high vacuum range. Both quality factor and amplitude are found to be effective vacuum indicators, and amplitude measurement is specifically useful for real-time vacuum monitoring.

Effect of Rotational Control for Accelerating Water Discharge on the Performance of a Circular Polymer Electrolyte Membrane Fuel Cell

Polymer electrolyte membrane fuel cells are emerging as an important research topic owing to increasingly intensified environmental pollution. The flow field pattern of the fuel cell controls the electrochemically uniform distribution and water flooding in the reaction area between the anode and cathode. Water discharge management in the channel is an important factor influencing the efficiency of the fuel cell. In this paper, we propose a polymer electrolyte fuel cell with a rotatable circular spiral channel set to a constant size. The mass transfer behavior was analyzed numerically according to the number of channel passes. Numerical analysis showed that the production and behavior of water are closely associated with the performance of fuel cells. The circular spiral-pattern fuel cell with the greatest membrane water content was rotated through the experimental device to confirm the performance change of the fuel cell for each rotation speed. The performance improved as the internal water was ejected by the rotational centrifugal force. However, when excessive rotation was applied, the performance decreased because the water was forcibly drained out by a strong centrifugal force.

Localization of travelling and standing waves in a circular membrane coupled to a continuous viscoelastic support

We present an analytical approach for realizing the localization of travelling and standing waves in a circular membrane by means of an interior, continuous, ring-type viscoelastic support when the membrane is subjected to harmonic boundary excitation. This work is a continuation of the wave separation dynamics induced by nonclassical damping in one-dimensional elastic continua. For a two-dimensional azimuthally symmetric configuration, a necessary and sufficient condition is established to realize wave localization, leading to uniformly distributed spring stiffness and damping coefficients for the interior support. A rotating wave localization pattern can also be realized by applying a circumferentially moving boundary excitation. The desired results are shown to depend strongly on the excitation frequency, the circumferential wavenumber, and the radius of the continuous support. For a weakly eccentric configuration with uniformly distributed boundary excitation, non-uniform required distributions of the support properties can be obtained analytically. However, waveform distortion will occur for either non-uniformly distributed boundary excitation with weak support eccentricity or highly eccentric coupling, such that the parameter values of the support have zero crossings on the nodal diameters of the membrane and thus lose physical meaning. The results presented in this work are expected to be useful in the design of mechanical and acoustic systems to localize energy to a sonic bullet by means of the continuous distribution of damping.