Electromechanical Finite Element Analysis Research Articles

Piezoelectric resonant ice protection systems – Part 1/2: Prediction of power requirement for de-icing a NACA 0024 leading edge

This paper proposes a numerical method to analyze the ice protection capability and predict the power requirements of a piezoelectric resonant de-icing system. The method is based on a coupled electro-mechanical finite element analysis which enables the fast computation of the modes of resonance of interest to de-ice curved surfaces and the estimation of the input voltage and current required for a given configuration (defined by its mode, actuator location, ice deposit, etc.). Eventually, the electric power to be supplied can be also assessed. The method is applied to a NACA 0024 leading edge equipped with piezoelectric actuators. First, two extension modes are analyzed and compared with respect to their efficiency and power requirements. Then, tests are carried out in an icing tunnel to verify the effectiveness of the piezoelectric ice protection system and the predictions of the maximal required power. The system allows de-icing the leading edge in less than 2 s for a glaze ice deposit.

Numerical Modeling and Experimental Verification for High-Speed Forming of Al5052 with Single Current Pulse

Application of electric current pulses during plastic deformation changes the mechanical behavior owing to the electro-plastic effect. The effect of electric current pulses on the Al5052 alloy is investigated in this study. In order to demonstrate the advantages of passing electric current pulses through a metal sheet during the forming process, a uniaxial tensile test with an electric current pulse was carried out using a self-designed device; this device can apply a 2-kA electric current pulse to the specimen for a short period (>100ms). The electric current increases the temperature of the specimen due to Joule heating. It is, therefore, necessary to decouple the thermal effect from the overall behavior to understand only the contribution of electric current in the mechanical behavior. Firstly, an electro-thermo-mechanical finite element study of an electrically assisted uniaxial tensile test of Al5052 alloy is performed to isolate the thermal effect. The simulated results yielded the thermal effect due to the electric current. By comparing the experimental and simulated results, the contribution of electric current is decoupled from that of thermal effect. The electric current-dependent material model is implemented into the commercial FEM code LS-DYNA using user-defined material(UMAT) subroutine. The electric current-dependent material model was used to simulate the electro-mechanical finite element analysis of the high-speed forming of an aluminum sheet with electric current pulse. Simulation results were compared with experimental results at several applied electric currents to evaluate the accuracy of the UMAT. The present work can be utilized to develop simpler constitutive models for the mechanical behavior of metals subjected to a pulsed electric current.

Optimal Sensors/Actuators Placement in Smart Structure Using Island Model Parallel Genetic Algorithm

Determination of optimal placements of sensors/actuators in large structures is a difficult job as large number of possible combinations leads to a very high computational time and storage. Therefore, this kind of optimization problem demands a parallel implementation of the optimization schemes. Island model genetic algorithm (GA) being inherently parallel has been used for searching optimal placements of collocated sensors/actuators. Numerical simulations have been done for determination of optimal placements of collocated PZT sensors and actuators in smart fiber reinforced shell structures using island model parallel GA (IMPGA) in conjunction with electro-mechanical finite element analysis with an objective of maximizing the controllability index. It has been observed that the present IMPGA-based formulation (due to its migration scheme) not only makes it possible to determine optimal sensors/actuators locations for large structures but also leads to a better solution at a much reduced and achievable computational time. Results from scalability analysis also show that the efficacy of the present method of using IMPGA for determination of optimal sensors/actuators location based on FEA will be more pronounced when actually used for real life problems requiring large number of sensors and actuators.

Intrinsic electromechanical dynamic equations for piezoelectric power harvesters

This paper discusses, compares and contrasts two important techniques for formulating the electromechanical piezoelectric equations for power harvesting system applications. It presents important additions to existing literature by providing intrinsic formulation techniques of the harvesting system for the two different electromechanical dynamic equation-based voltage and charge-type systems associated with the standard AC–DC circuit interface developed using the extended Hamiltonian principle. The derivations of the two analytical methods rely on the fundamental continuum thermopiezoelectricity concepts of the electrical enthalpy energy and Helmholtz free energy. The benefit of using analytical charge-type modelling is that the technique shows more compact formulation for developing simultaneous derivations by coupling the mechanical and electromechanical systems of the piezoelectric devices and electronic system so that the frequency response functions (FRFs) and time wave form systems can be formulated. On the other hand, the analytical voltage-type modelling is obviously convenient but can show tedious derivation process for joining with the electronic circuit part. To tackle this situation, the analytical voltage type with mechanical and electromechanical forms of the piezoelectric structure can be derived separately from the electronic system where they can be combined together after applying further derivations to formulate the FRFs. In this paper, the two analytical techniques also show particular benefit and even further development of how to model the power harvesting scheme with the combinations of piezoelectric structure and electronic system. Moreover, validations of the two analytical methods show good agreement with previous authors’ electromechanical finite element analysis and experimental works. Further parametric electromechanical energy harvesting behaviours have been explored to study the system responses.

An improved analytical method to design CMUTs with square diaphragms

A highly accurate mathematical method has been presented for analytical characterization of capacitive micromachined ultrasonic transducers (CMUTs) built with square diaphragms. The method uses a new two-dimensional polynomial function to more accurately predict the deflection curve of a multilayer square diaphragm subject to both mechanical and electrostatic pressure and a new capacitance model that takes into account the contribution of the fringing field capacitances. Both of the models have been experimentally verified by comparing the models predicted values with measurement results and are found to be in excellent agreement with a maximum deviation of less than 2% for experimentally measured capacitance values. 3-D electromechanical finite element analysis (FEA) for a wide range of material properties, geometric specifications, and loading conditions show that the presented method is highly consistent in accuracy over the typical square-diaphragm CMUT design space.

Fabrication and measurements of dynamic response of an SOI based non-planar CMUT array

An SOI based hyperbolic paraboloid geometry capacitive micromachined ultrasonic transducer (CMUT) array has been fabricated to realize a frequency independent constant beamwidth broadband beamforming capability. Detailed fabrication and packaging techniques are presented along with measurement results on individual CMUT cells for transient and steady-state response using a Polytec laser Doppler vibrometer. The measurement results are compared with analytical and 3-D electromechanical finite element analysis using IntelliSuite™. The measured results are in excellent agreement with analytical and FEA results. Measurement results also show that the CMUTs exhibit a flat bandwidth within the specified frequency range. SEM inspection also shows very close agreement between mask features and fabricated geometry that ensures reproducibility of the device with a high degree of fidelity. The CMUT array has been designed for automotive blindspot detection application and works in the 113–167 kHz range.

Design, implementation and testing of electrostatic SOI MUMPs based microgripper

This paper presents a detail modeling, finite element analysis and testing results of MEMS based electrostatically actuated microgripper. Interdigitated lateral comb pairs have been used to actuate the microgripper. The microgripper is optimized using standard SOI-MUMPs technology in L-Edit of MEMS-Pro with dual jaws actuation at low voltages. Coupled electromechanical finite element analysis performed in COVENTOR-WARE shows total displacement of 15.5 μm at jaws tip at 50 V, which is quite comparable to experimental result of 17 μm displacement at the tip of gripper jaw for the same voltage. Micromanipulation experiments have successfully demonstrated the gripping, holding micro-objects between 53 and 70 μm in size. The simulated model is used to study detail profile of Von Mises stresses and deformations in the model. It is noted that maximum stress in microgripper is 200 MPa which is much smaller than yield stress of 7 GPa. The slight difference between finite element analysis and experimental results is because of small variations in process material parameters. The total size of gripper is 5.03 × 6.5 mm2.

A Highly Accurate Pull-in Voltage Model for an Atomic Force Microscope Probe

A readily usable closed-form model has been developed to determine the pull-in voltage of an atomic force microscopy (AFM) cantilever probe under electrostatic actuation. The analytical model is derived based on the Euler-Bernoulli beam theory, Taylor series expansion of the nonlinear electrostatic force, and deflection function of the first natural mode of a cantilever beam. The model takes account of the electrostatic force associated with the fringing field capacitances between the cantilever probe and the substrate to predict a more accurate pull-in voltage. The developed closed-form model has been verified by comparing the model predicted values with published experimental results with a maximum deviation of 3.36%. The model has also been compared with a published closed-form model and 3-D electromechanical finite element analysis (FEA) carried out by the authors. The results are found to be in excellent agreement.

A Highly Accurate Closed-Form Model for Pull-in Voltage of Circular Diaphragms under Large Deflection

A simple easy to use highly accurate closed-form model to determine the pull-in voltage of electrostatically actuated circular diaphragms subject to large deflection has been developed. The model takes account of the nonlinear stretching of the diaphragm during large deflection, effects of residual stress, bending stress, and the effects of fringing field capacitances. At first a linearized uniform model of the nonlinear non-uniform electrostatic force has been derived that includes the effects of the fringing field capacitances. This model is then used in conjunction with the load-deflection model of a circular diaphragm subject to large deflection to derive the closed-form model for the pull-in voltage based on the condition that at unstable equilibrium, the electrostatic force is just balanced by elastic restoring force. The model has been verified by extensive 3-D electromechanical finite element analysis (FEA) using IntelliSuite. The model is in excellent agreement with 3-D electromechanical FEA with a maximum deviation of 1.6% for a wide range of residual stress and pull-in voltage values. The model leads to an integrated design strategy to optimize the electrical and mechanical design variables for MEMS-based capacitive type sensors having circular diaphragms. The model can be used to determine pull-in voltages of MEMS capacitive type pressure sensors, capacitive micromachined ultrasound transducers (CMUT) for medical diagnostic imaging, MEMS based microphones, touch mode pressure sensors, and other application areas where electrostatically actuated circular diaphragms are used. Keywords: MEMS, electrostatic, sensor, circular diaphragm, pull-in voltage

Genetic algorithm based optimal design for vibration control of composite shell structures using piezoelectric sensors and actuators

The present article deals with the design of optimal vibration control of smart fiber reinforced polymer (FRP) composite shell structures using genetic algorithm (GA) based linear quadratic regulator (LQR) and layered shell coupled electro-mechanical finite element analysis. Open loop procedure has been used for optimal placement of actuators considering the control spillover of the higher modes to prevent closed loop instability. An improved real coded GA based LQR control scheme has been developed for designing an optimal controller in order to maximize the closed loop damping ratio while keeping actuators voltages within limit. Results show that increased closed loop-damping has been achieved with a large reduction of control effort considering control spillover.

Design of a MEMS discretized hyperbolic paraboloid geometry ultrasonic sensor microarray

Design of a discretized hyperbolic paraboloid geometry beamforming array of capacitive micromachined ultrasonic transducers (CMUT) has been presented. The array can intrinsically provide a broadband constant beamwidth beamforming capability without any microelectronic signal processing. A mathematical model has been developed and verified to characterize the array response. A design methodology has been presented that enables determination of the array's physical dimensions and CMUT modeling in a straightforward manner. Developed methodology has been used to design two discretized hyperbolic paraboloid geometry beamforming CMUT arrays: one in the 2.3 MHz to 5.2 MHz frequency range and another in the 113 kHz to 167 kHz frequency range. CMUTs have been designed using a cross-verification method that involves lumped element modeling, 3-D electromechanical finite element analysis (FEA), and microfabrication simulation. The developed array has the potential to be used in real-time automotive collision-avoidance applications, medical diagnostic imaging and therapeutic applications, and industrial sensing.

Fatigue crack growth driven by electric fields in piezoelectric ceramics and its governing fracture parameters

Fatigue crack growth test for piezoelectric ceramics was performed under cyclic electric loading. Double cantilever beam specimen, which was made of two different piezoelectric ceramics, with a through notch was used. The specimens were, varying the amplitude and the mean value, subjected to various cyclic electric fields. It was found that crack growth behavior is greatly dependent on the amplitude and mean value of cyclic electric field and materials. Crack growth rate decreased as electric field increased and finally stopped. Crack growths under the positive, the negative and the shifted electric field were very slow compared to that under fully reversed electric field. However, threshold for the crack propagation did not depend greatly on materials. Then, as possible governing fracture parameters, CED and electric displacement intensity factor were chosen based on the results of electromechanical finite element analysis within linear framework and their closed form equations were also obtained considering the influences of electric boundary conditions inside the notch. Finally, the parameters were correlated with crack growth rate measured experimentally by employing Paris law type equation.

On a vector potential formulation for 3D electromechanical finite element analysis

AbstractA vector potential for the electric induction is applied to static three‐dimensional fully coupled electromechanical problems. A Coulomb gauge condition imposed on the electric vector potential improves the convergence behaviour of nonlinear problems, and in combination with a discrete set of Dirichlet boundary conditions, it can enforce unique vector potential solutions. Based on a spectral analysis of the stiffness matrix, the Coulomb gauge is compared with other gauge conditions. A penalized version of the weak vector potential formulation with Coulomb gauge is proposed and tested on some numerical examples in electrostatics, piezoelectricity and ferroelectricity. Copyright © 2005 John Wiley & Sons, Ltd.