Pull-in Instability Research Articles

Pull-in instability and nonlinear vibration of microbeam with piezoelectric patch driven by electrostatic force using modified couple stress theory

The static and dynamic pull-in characteristics of electrostatically and piezo-electrically actuated microbeam are investigated. The static pull-in voltage is evaluated using analytical methods based on MCST, CCMT and validated through the use of FE based COMSOL multiphysics tools. The dynamic pull-in voltage obtained from numerical technique and verified with existing literature, lower than the static pull-in voltage. The piezoelectric patch has a significant influence on the pull-in voltage and an effect on the aspect ratio. Moreover, the pull-in band and instability zone of the microbeam with weak and hard forcing function have been investigated using multiple scale method.

A scaling law approach to rate fabrication tolerances of double-sided electrostatic actuators

Abstract Symmetric double-sided electrostatic actuators in push-pull configuration are particularly suitable for linear actuation with low harmonic distortion. However, their motion still is largely determined by pull-in instabilities that are sensitive to geometry variations. A considerable simulation effort is therefore required when assessing manufacturing tolerances during the design process or determining the optimal operating point. Recently, an accurate method was demonstrated, allowing for the numerically inexpensive and experimentally non-destructive extraction of the full quasi-static performance of a clamped-free beam-like electrostatic micro-mechanical actuator with complex 3D design. The key step was to determine the voltage scaling related to the pull-in voltage based on data collected far away from pull-in conditions. This relates a dimensionless ansatz to the physical input voltages as well as the output like e.g. the actuator’s tip deflection. For the chosen approach, however, the relationship between the model and the geometry parameters is unknown. In this paper we propose a method to enable quantifying the impact of geometry parameter variations. In particular, we adapt the model equation for the case of symmetry-breaking tolerances on the basis of few FEM-simulations. The quasi-static pull-in instability, as well as the nonlinear deflection, are consistently reproduced over the full range of relevant combinations of signal and bias voltages. Our analysis was developed in the context of a specific electro-acoustic transducer. However, we find indications that the underlying method is in fact applicable to a much broader range of micro-mechanical actuators.

Exploiting Nonlinearities of Electrostatic MEMS Resonators for Tunable Low Pressure Sensing

In this paper, we demonstrate the potential functionalization of inherent nonlinearities associated with electrostatic MEMS resonators for low air pressure applications, with operating ranges as low as 0.65-295 mbar. The proposed pressure sensor is made of a polysilicon microplate subject to electrostatic actuation via an underneath electrode and attached to two cantilever microbeams. The pressure sensing mechanism relies on the motion-induced current method, a transduction mechanism that converts the dynamic alteration of the microplate due to pressure variations into an electrical signal detected via a lock-in amplifier. The experimental study showed evidence of the possible tunability of the pressure sensor via the deployment of different detection mechanisms to achieve superior performance in terms of sensitivity and low pressure operating range. These mechanisms rely on nonlinear dynamic features that result from the strong coupling between the microplate and the surrounding fluid along with the electrostatic actuation. These include dynamic pull-in instability, bifurcation and softening behavior associated with the elastic effect of the squeeze-film damping. The experimental results revealed that tracking the bifurcation frequency allows for the detection of low pressure levels, in the range of a few millibars. This capability is not provided by the resonance frequency shift method, which, while offering higher sensitivity, does not achieve the same low-pressure detection.

Investigation of surface roughness effects on the dynamic performance of electromagnetic nano-resonators

Here, we expose the influence of surface roughness on the dynamics of electromagnetic nano-resonators. To this end, the continuum field equations of an electromechanical nano-resonator subjected to an external magnetic flux are formulated. The developed model considers surface integrity, including surface roughness, waviness, and altered layer. Also, the influence of residual stresses of the extreme surfaces of the resonator is incorporated in the proposed model. It was revealed that the surface roughness significantly tailors the dynamic stability of the resonator, as the voltage that onsets the pull-in instability of the resonator decreases as the surface roughness increases, which thus indicates the necessity of particular calibrations of nano-resonators for surface roughness. To investigate the problem and the effect of factors such as magnetic field intensity, roughness, and beam surface thickness on the pull-in voltage, we have performed an analysis using the Taguchi method and analysis of variance. The results show that the intensity of the magnetic field has the most significant effect on pull-in voltage. Also, the more accurate results show on the resonance frequency; with the increase of the input voltage to the beam, the impact of increasing the intensity of the magnetic field and other factors increases. The rest of the paper proposes a linear and non-linear model to express the pull-in voltage according to the investigated factors.

Electrostatically Actuated X-Band Mesh Reflector with Bend-Formed Support Structure

Increasing the size of radio frequency (RF) reflectors in space can enhance gain and spatial resolution in applications such as space-based communication and remote sensing. The size of current passive deployable reflectors is limited by a tradeoff between diameter and surface precision, which causes RF performance to degrade as size increases. A promising approach to overcome this tradeoff is to combine in-space manufacturing, which enables large structures, with distributed embedded actuation, which enables precise control over the reflector surface. Here we demonstrate a reflector antenna system that integrates these two technologies, using a candidate in-space manufacturing process, termed “Bend-Forming,” with embedded electrostatic actuators. We design and fabricate a 1-m-diam prototype of an electrostatically actuated X-band reflector with a knitted gold-molybdenum mesh as the reflector surface, carbon-fiber-reinforced plastic booms as electrodes, and a truss support structure fabricated with Bend-Forming. We characterize the RF performance of this reflector, successfully demonstrating i) control over a wide range of focal lengths by suppressing a pull-in instability and ii) beam steering over an angular range of 4.2° via asymmetric electrostatic actuation. This work lays the foundation for future space communication and remote sensing technologies, offering a scalable solution to enhance RF performance through in-space manufacturing and precision control.

A self-centering and stiffness-controlled MEMS accelerometer

This paper presents a high-performance MEMS accelerometer with a DC/AC electrostatic stiffness tuning capability based on double-sided parallel plates (DSPPs). DC and AC electrostatic tuning enable the adjustment of the effective stiffness and the calibration of the geometric offset of the proof mass, respectively. A dynamical model of the proposed accelerometer was developed considering both DC/AC electrostatic tuning and the temperature effect. Based on the dynamical model, a self-centering closed loop is proposed for pulling the reference position of the force-to-rebalance (FTR) to the geometric center of DSPP. The self-centering accelerometer operates at the optimal reference position by eliminating the temperature drift of the readout circuit and nulling the net electrostatic tuning forces. The stiffness closed-loop is also incorporated to prevent the pull-in instability of the tuned low-stiffness accelerometer under a dramatic temperature variation. Real-time adjustments of the reference position and the DC tuning voltage are utilized to compensate for the residue temperature drift of the proposed accelerometer. As a result, a novel controlling approach composed of a self-centering closed loop, stiffness-closed loop, and temperature drift compensation is achieved for the accelerometer, realizing a temperature drift coefficient (TDC) of approximately 7 μg/°C and an Allan bias instability of less than 1 μg.

Applying numerical control to analyze the pull-in stability of MEMS systems

The micro-electro-mechanical system is widely used for energy harvesting and thermal wind sensor, its efficiency and reliability depend upon the pull-in instability. This paper studies a micro-electro-mechanical system using He-Liu [34] formulation for finding its frequency-amplitude relationship. The system periodic motion, pull-in instability and pseudo-periodic motion are discussed. This paper offers a new window for security monitoring of the system reliable operation.

Modeling pull-in instability of CNT nanotweezers under electrostatic and van der Waals attractions based on the nonlocal theory of elasticity

This work investigates the electromechanical response and pull-in instability of an electrostatically-actuated CNT tweezer taking into consideration a TPNL constitutive behavior of the CNTs as well as the intermolecular forces, both of which provide a significant contribution at the nanoscale. The nonlocal response of the material introduces two additional parameters in the formulation, which are effective in capturing the size effects observed at the nanoscale. The problem is governed by a nonlinear integrodifferential equation, which can be reduced to a sixth-order nonlinear ODE with two additional boundary conditions accounting for the nonlocal effects near to the CNT edges. A simplified model of the device is proposed based on the assumption of a linear or parabolic distribution of the loading acting on the CNTs. This assumption allows us to formulate the problem in terms of a linear ODE subject to two-point boundary conditions, which can be solved analytically. The results are interesting for MEMS and NEMS design. They show that strong coupling occurs between the intermolecular forces and the characteristic material lengths as smaller structure sizes are considered. Considering the influence of the nonlocal constitutive behavior and intermolecular forces in CNT tweezers will equip these devices with reliability and functional sensitivity, as required for modern engineering applications.

Effective machine learning pull-in instability estimation of an electrostatically nano actuator under the influences of intermolecular forces

Effective machine learning pull-in instability estimation of an electrostatically nano actuator under the influences of intermolecular forces

Variational iteration method for the nanobeams-based N/MEMS system

The nano/microelectromechanical system (N/MEMS) has triggered worldwide concern, and its applications have revolutionized technologies in various advanced fields from wearable sensors, 5 G communication technology, to energy harvesting, to aerospace. However, when the applied force is sufficiently large, the pull-in instability arises, and reliable operation is forbidden. Therefore, it is extremely important to insight fast and accurately into the periodic motion of the system to prevent the system from its pull-in motion. The basic aim of this study is to demonstrate the applicability of the well-known variational iteration method (VIM) for predicting the dynamic behavior of N/MEMS. For this, a nanobeam-based microstructure with van der Waals force for actuation is used as an example to reveal its periodic properties. The governing equation for the oscillation of the microsystem is obtained from the Euler-Bernoulli beam principle, considering the midplane stretching effect. We then employ the Galerkin technique to transform the governing partial differential equation into an ordinary differential equation, which is highly nonlinear, making it extremely difficult to solve by some traditional analytical methods, however, the VIM shows its ability to elucidate accurately the basic properties of the N/MEMS by simple calculation. This paper offers a new road for fast and accurate prediction of the microsystem's properties, and the result can be used for optimizing the N/MEMS.•A nanobeam-based N/MEMS system with van der Waals force is considered.•A strongly governing equation without a linear term is obtained.•The variational iteration method is applied to figure out the basic properties of the system.

Effect of Electrode on the Dynamics of Electroactive Membrane

Abstract The dynamics of the electroactive membranes are being studied extensively due to their vast application at the current time. However, the effect of the mechanical behavior of the compliant electrode needs to be addressed. This article presents the nonlinear analysis of an electrically actuated membrane, considering the inertia of the electrode. The membrane is modeled as a hyperelastic material and is assumed to be incompressible, homogeneous, and isotropic. The proposed analysis is discussed in a generalized way for both the compression and suspension phases. Since the membrane is vulnerable to pull-in instability, the conditions to prevent electromechanical instability are defined. Further, an analytical relation is established for breakdown voltage and is validated with experimental data. The analytical solution of axial vibration is presented in the form of elliptic integrals and by the use of multiple scale method in a generalized way for both the phases. The resultant motions and their various physical aspects under suspension and compression phases for general initial conditions are described through graphical results to comprehend the proposed analysis. Also, parameter values are quantified analytically, for which the system executes reverse behavior in a given configuration.

Nonlinear dynamics of a piezoelectrically laminated initially curved microbeam resonator exposed to fringing-field electrostatic actuation

In this paper, the nonlinear dynamics of a piezoelectrically sandwiched initially curved microbeam subjected to fringing-field electrostatic actuation is investigated. The governing motion equation is derived by minimizing the Hamiltonian over the time and discretized to a reduced-order model using the Galerkin technique. The modelling accounts for nonlinearities due to the fringing-field electrostatic force, initial curvature and mid-plane stretching. The electrostatic force is numerically computed using finite element simulation. The nonlinear dynamics of the microbeam in the vicinity of primary resonance is investigated, and the bifurcation types are determined by investigating the location of the Floquet exponents and their configuration with respect to the unit circle on the complex plane. The branches on the frequency–response curves, which originate from the period-doubling bifurcation points, are introduced, and the transition from period-1 to period-2 response is demonstrated by slight sweep of the excitation frequency over the time. The effect of DC and AC electrostatic excitation and the piezoelectric excitation on the response of the system are examined, and their effect on the bifurcation types is determined. The force response curves assuming the AC voltage as the bifurcation parameter are also introduced; it is illustrated that in contrast to in-plane electrostatic excitation, in fringing field-based resonators the resonator is not limited by pull-in instability, which is substantially confining the amplitude of the motion in in-plane resonators.

Modulation of the dynamic response and stability of dielectric balloon by stretch-dependent dielectric permittivity

The dynamic response of dielectric elastomers is widely used in many functional devices, but current research has neglected the effect of varying dielectric permittivity on their dynamic oscillations and stability. This paper studies the thin-walled dielectric balloon in which the stretch-dependent dielectric permittivity is considered. We obtain the dynamic equation of motion by Hamilton’s principle. Based on the principle of no energy dissipation in conservative systems, we establish energy conservation at the maximum stretching position and at the initial moment, then we investigate the stability in the dynamic case. It is found that a stretch-related dielectric permittivity can increase the critical electric field of the balloon and can also change the mode of electric field instability and modulate the critical stretch value. In the dynamic case, the stretch-dependent permittivity increases the critical electric field by 4% when the balloon is only subjected to electric force; moreover, it increases the critical stretch value by 316.68% by changing the unstable mode from pull-in instability to snap-through instability. It is hoped that this work will provide new thinking in designing functional devices by using the dynamical response and stability of dielectric elastomers.

NONLINEAR VIBRATION RESPONSE OF PIEZOELECTRIC NANOSENSOR: INFLUENCES OF SURFACE/INTERFACE EFFECTS

In the present work, surface/interface energy effects for pull-in instability analysis on dimensionless natural frequency (DNF) and nonlinear dynamics response (NDR) of piezoelectric nanosensor (PENS) subjected to nonlinear electrostatic excitation and harmonic force are studied using Gurtin–Murdoch (GM) surface/interface energy approach. To achieve this purpose, the Hamilton’s approach, assumed mode and Lagrange–Euler’s theories and also arc-length continuation and complex averaging methods are used to investigate influences of surface/interface parameters of PENS such as Lame’s constants, residual stress, piezoelectric constants and mass density for analysis of pull-in instability voltage.

THE GREEN-RVACHOV QUASI-FUNCTION METHOD IN THE NUMERICAL ANALYSIS OF MICROELECTROMECHANICAL SYSTEMS USING TWO-SIDED APPROXIMATIONS

The work is devoted to developing a bilateral iterative method of numerical analysis of one electrostatic microelectromechanical system based on the use of the Green – Rvachev quasi-function. Microelectromechanical systems are miniature devices that combine electronic and mechanical components of micron size. Electrostatically activated microelectromechanical systems have certain disadvantages that limit the range of their operation. One of these is the pull-in instability of the functional components of the system, which occurs if the applied voltage difference is above a particular critical value. The mathematical model of the system under consideration in the work is a semi-linear elliptic equation with the Laplace operator and the Dirichlet condition. To construct an approximate solution of the problem, it is proposed to use the methods of nonlinear analysis in semi-ordered spaces, particularly the results of V. I. Opoitsev on the solvability of nonlinear operator equations with a heterotonic operator. The boundary value problem simulating the most straightforward microelectromechanical system under the action of external pressure is reduced to the Urison integral equation using the Green – Rvachev quasi-function method, which makes it possible to expand the application of the method of two-sided approximations for problems in areas of somewhat arbitrary geometry. The paper substantiates the possibility of constructing iterative sequences with two-sided convergence to a positive solution of the problem: the computational scheme is given, the conditions for its convergence to the desired solution are obtained, and the a posteriori error estimate is derived. The method is illustrated by a computational experiment for a problem considered in a rectangular area. The computational experiment results are presented in the form of the surface and lines of the level of the approximate solution, and the two-sided nature of the convergence of the proposed method is also graphically illustrated.

Size dependent pull-in instability of functionally graded microbeams using a finite element formulation

The size dependent static pull-in instability of functionally graded (FG) microbeams in micro-electromechanical systems (MEMS) is studied, considering the influence of the axial force. The material properties of the microbeams are varied in the beam thickness by a power-law function, and they are calculated by the rule of mixture. To account for the microsize effect, the classical Euler-Bernoulli beam theory is employed in combination with the modified couple stress theory to describe the microbeams deformation. Based on Von Kármán nonlinear relationship, a beam element is derived and employed to establish the discretized governing equation for the microbeams. Newton-Raphson iterative procedure is adopted to compute frequencies and pull-in voltages for the microbeam with clamped ends. Numerical result reveals that the pull-in voltage is increased by the increase of the power-law exponent and the microscale parameter. The effects of the material distribution, the axial force as well as the microstructural parameter on the pull-in instability of the FG microbeams are investigated in detail.

Dynamic pull-down theory for the Toda oscillator

The pull-down instability is a newly found phenomenon for oscillators with even nonlinearities. It is a seemingly periodic motion, which will suddenly pull down after some cycles. The phenomenon is similar to the pull-in instability in the micro-electromechanical systems. This paper restudies the well-known Toda oscillator, which is considered to be in periodic motion. Its pseudo-periodic property is studied and the pull-down instability is found for the first time ever. To this end, this paper establishes a variational principle for the Toda oscillator, and the criterion for prediction of the pull-down motion is obtained. A simple formulation to calculate the pull-down instability is proved and verified through examples. Furthermore, an approximate frequency formula is obtained by Li–He modified homotopy perturbation method.

Jump and Pull-in Instability of a MEMS Gyroscope Vibrating System.

Jump and pull-in instability are common nonlinear dynamic behaviors leading to the loss of the performance reliability and structural safety of electrostatic micro gyroscopes. To achieve a better understanding of these initial-sensitive phenomena, the dynamics of a micro gyroscope system considering the nonlinearities of the stiffness and electrostatic forces are explored from a global perspective. Static and dynamic analyses of the system are performed to estimate the threshold of the detecting voltage for static pull-in, and dynamic responses are analyzed in the driving and detecting modes for the case of primary resonance and 1:1 internal resonance. The results show that, when the driving voltage frequency is a bit higher than the natural frequency, a high amplitude of the driving AC voltage may induce the coexistence of bistable periodic responses due to saddle-node bifurcation of the periodic solution. Basins of attraction of bistable attractors provide evidence that disturbance of the initial conditions can trigger a jump between bistable attractors. Moreover, the Melnikov method is applied to discuss the condition for pull-in instability, which can be ascribed to heteroclinic bifurcation. The validity of the prediction is verified using the sequences of safe basins and unsafe zones for dynamic pull-in. It follows that pull-in instability can be caused and aggravated by the increase in the amplitude of the driving AC voltage.

Effect of flexoelectricity on the Pull-in instability of beam-type NEMS

Considering the increasing number of smart materials in advanced industries and technologies, the need to investigate the use of these materials is felt more and more. The flexoelectric effect is one of the most important phenomena created in micro-scale beams, which will have a significant effect on the results and should be investigated. Therefore, in this article, the Pull-in instability in the beam-type microelectromechanical systems has been investigated under the flexoelectric effect. The governing equations of the system have been derived based on the theory that is founded on the strain gradient theory for the Euler-Bernoulli beam model. This beam is under the effect of intermolecular Casimir force and electrostatic force. The equations and boundary conditions related to them have been non-dimensionalized first in direct and indirect flexoelectric effect. With the help of the differential quadrature method, the Pull-in voltage's critical parameters and the system's free-standing behavior have been studied. Among the significant results obtained from this research, it is possible to mention the Pull-in voltage increase due to the flexoelectric effect reduction. Also, in the indirect state of the flexoelectric effect, the increase in the initial applied voltage causes a decrease in the Pull-in voltage.

Photo-induced electrostatic actuators towards micro gap regulator and micro gripper based on lead lanthanum zirconate titanate ceramics

Photo-induced actuators enable potential applications involving soft robots, biomedical engineering, and microelectromechanical system due to the contactless energy supply and high spatial and temporal controllability of light. However, obtaining a fast and reliable photo-induced actuation remains a great challenge. Herein, we report a strategy to realize rapid photo-induced actuation by utilizing a composite actuation mechanism, which combines photoelectric effect and electrostatic actuation mechanism. Novel photo-induced PLZT-based electrostatic actuators (PPEAs) are then proposed towards micro gap regulator (MGR) and micro gripper. Within the electrostatic pull-in point, we demonstrate that the gap of the PPEA regarded as an MGR can be tunable upon light irradiation through simulations. Besides, the pull-in instability enables the PPEA with rapid clamping action to be a micro gripper. Micro grippers with sandwich-like multilayer arms are fabricated using a simplified photolithography process and the fundamental operation and performance of our gripper are demonstrated through a series of experiments. More importantly, the two developed components are driven rapidly and reliably by light, providing great potential to facilitate the current research in photo-induced actuation.