Electric potential approximations for an eight node plate finite element

The aim of this work is to develop a computational tool for multilayered piezoelectric plates: a low cost tool, simple to use and very efficient for both convergence velocity and accuracy, without any classical numerical pathologies. In the field of finite elements, two approaches were previously used for the mechanical part, taking into account the transverse shear stress effects and using only five unknown generalized displacements: C⁰ finite element approximation based on first-order shear deformation theories (FSDT) [Polit O, Touratier M, Lory P. A new eight-node quadrilateral shear-bending plate finite element. Int J Numer Meth Eng 1994;37:387–411] and C¹ finite element approximations using a high order shear deformation theory (HSDT) [Polit O, Touratier M. High order triangular sandwich plate finite element for linear and nonlinear analyses. Comput Meth Appl Mech Eng 2000;185:305–24]. In this article, we present the piezoelectric extension of the FSDT eight node plate finite element. The electric potential is approximated using the layerwise approach and an evaluation is proposed in order to assess the best compromise between minimum number of degrees of freedom and maximum efficiency. On one side, two kinds of finite element approximations for the electric potential with respect to the thickness coordinate are presented: a linear variation and a quadratic variation in each layer. On the other side, the in-plane variation can be quadratic or constant on the elementary domain at each interface layer. The use of a constant value reduces the number of unknown electric potentials. Furthermore, at the post-processing level, the transverse shear stresses are deduced using the equilibrium equations.Numerous tests are presented in order to evaluate the capability of these electric potential approximations to give accurate results with respect to piezoelasticity or finite element reference solutions. Finally, an adaptative composite plate is evaluated using the best compromise finite element.     

A piezoelectric solid shell element based on a mixed variational formulation for geometrically linear and nonlinear applications

The paper is focused on a piezoelectric solid shell finite element formulation. A geometrically nonlinear theory allows large deformations and includes stability problems. The formulation is based on a variational principle of the Hu–Washizu type including six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The element has eight nodes with displacements and the electric potential as nodal degrees of freedom. A bilinear distribution through the thickness of the electric field is assumed to obtain correct results in bending dominated situations. The presented element is able to model arbitrary curved shells and incorporates a 3D-material law. Numerical examples demonstrate the ability of the proposed model to analyze piezoelectric devices.     

Electro-mechanical behavior and direct piezoelectricity of cellulose electro-active paper

This study focuses on investigating the piezoelectric effects of cellulose-based electro-active paper (EAPap) using quasi-static direct piezoelectricity. Mechanical properties were investigated first and then electro-mechanical behavior was studied by applying electric field during the pulling test. In-plane piezoelectric charge constant (d₃₁) of EAPap was quantified by the quasi-static relation between induced charge and applied stress. Strong shear electro-mechanical coupling was observed and 45° sample provided the largest in-plane piezoelectric charge constant. The measured piezoelectric charge constant was in the range of 8–28.2 pC/N, which are similar to those of piezo polymer. Cellulose EAPap provides promising potential as biodegradable and cheap piezoelectric polymer material.     

A refinement of Ambartsumian multi-layer beam theory

One of the current problems connected with multi-layer composite structures concerns the analysis of the distribution of the stresses around peculiarities (free edge and loaded edge) and at the interfaces of each layer. This work presents a new shear stress function in the form of the exponential function, to predict the mechanical behaviour of multi-layered laminated composite structures. As a case study, the mechanical behaviour of a laminated composite beam (90°/0°/0°/90°) is examined. The results are compared with the model “Sinus” and 2D finite element method studied. Results show that this new model is more precise than older ones as compared to the results obtained by the finite element analysis [Abaqus]. To introduce continuity on the interfaces of each layer, the kinematics defined by Ossadzow is used with the new exponential model. The equilibrium equations and natural boundary conditions are derived by the principle of virtual power.     

GaAs-based tuning fork microresonators: A first step towards a GaAs-based coriolis 3-axis Micro-Vibrating Rate Gyro (GaAs 3-axis μCVG)

This paper presents the design of a piezoelectric MEMS Coriolis Vibrating Gyroscope (CVG) based on a single gallium arsenide vibrating structure allowing the measurement of rotation rate along 3 orthogonal sensitive axes. Based on a theoretical and FEM study, we demonstrate that the achieved sensitivities reached for each axis is about 1.6 × 10⁻¹⁶ C/(°/s). We then demonstrate the feasibility of the realization of simple MEMS structures from C-doped Gallium Arsenide (GaAs) using standard micromachining processes. Finally, we show the fabrication and characterization of GaAs-based tuning fork microresonators as a first step towards a complete 3-axis GaAs MEMS CVG. These resonators show a resonance frequency of 42 350 Hz, a quality factor of 122 000 and a frequency temperature coefficient of 24 ppm/°K, validating the high potential of GaAs as a structural material for 3-axis MEMS CVGs.     

Cylindrical bending of piezoelectric laminates with a higher order shear and normal deformation theory

An analytical solution, based on a higher order shear and normal deformation theory, is presented for the cylindrical flexure of piezoelectric plates. The primary displacement terms are expanded in thickness coordinate and an exact nature of electric potential is obtained in actuator and sensing layers. The electric potential function is evaluated by solving a second order ordinary differential equation satisfying electric boundary conditions along thickness direction of piezoelectric layer. A unidirectional composite plate attached with distributed actuator and sensor layers is analyzed under electrical and mechanical loading conditions and comparison of results with exact solution is presented. Results for non-piezoelectric plates are also compared with elasticity and other solutions of cylindrical bending.     

Piezoelectric linear motor with unimorph structure by co-extrusion process

A new piezoelectric linear motor was developed using a ring-shaped, unimorph stator composed of a piezoelectric active layer (0.3PZN–0.7PZT/Mn) and a conductive passive layer (0.3PZN–0.7PZT/Mn/Ag). The stator was prepared by co-extrusion followed by the thermoplastic green machining (TGM) process. After co-extruding the piezoelectrically active and passive layers together, they were machined into a ring shape and then sintered at 930 °C for 4 h. The stator was poled in the thickness direction and operated in radial vibration mode. A glass rod was used as the moving shaft. When a saw-tooth electric field was applied, the shaft moved linearly as a result of the stator's bending motion. When an inverted saw-tooth electric potential was applied, the shaft moved linearly in the opposite direction. The velocity of the piezoelectric linear motor was about 4 mm/s at an applied voltage of 80 V_p–p and a resonance frequency of 36.5 kHz.     

Effects of internal electrode composition on the reliability of low-firing PMN–PZT multilayer ceramic actuators

We investigated the effects of internal electrode composition on the reliability of low-firing multilayer ceramic actuators using Ag internal electrodes. Ag–ceramic composite pastes were prepared by adding Pb(Mg_1/3Nb_2/3)O₃–Pb(Zr_0.475,Ti_0.525)O₃ (PMNZT) ceramic powders to a commercial Ag paste at concentrations in the range of 0–60 vol%. PMNZT multilayered laminates were fabricated using tape casting, and then cofired at 925 °C for 10 h. The fatigue behaviors of multilayer actuators with Ag internal electrodes having different PMNZT concentrations were compared by applying a 2 kV/mm ac electric field at 50 °C under a relative humidity of 30%. The failure data were analyzed using Weibull statistics. The addition of PMNZT ceramics enhanced the mean time to failure by reducing the densification mismatch between the piezoelectric ceramic and internal electrode layers during the cofiring process.     

Langasite based surface acoustic wave sensors for high temperature chemical detection in harsh environment: Design of the transducers and packaging

This work presents the design and the thermal behavior characterization of an innovative self-test portable surface acoustic wave platform for chemical detection under high temperature. Before the forthcoming deposition of the sensitive coating, the thermal behavior of the bare LGS acoustic platform has been focused on. The system includes a (0°, 140°, 25°) crystallographic cut langasite (LGS) piezoelectric substrate, a ceramic heater, and a platform with RF connections for remote measurements. The packaging consists in a hermetic stainless steel cell, which enables safe gas detection. Its thermal behavior was successfully investigated in the temperature range 25-500 °C thanks to the integrated heater, without using an external furnace. Finite element modeling aided the development of this platform structure by predicting the thermal behavior of each of its parts and their cross-influences. The structure of the platform was specifically designed so that 500 °C could be reached on the LGS acoustic device while the temperature on the PCB connections should not exceed 50 °C. Then, the temperature-dependence on the waves generated by the acoustic transducers has been investigated through numerical modeling by resolving the wave propagation equations with several sets of LGS constants. Corresponding simulations showed good agreement with experiments, Thermal cycling up to 350 °C highlighted satisfactory hardiness and response-reproducibility of the system towards thermal stress, after a first burn effect.     

Demonstration of optimizing piezoelectric polarization in the design of a flextensional actuator

Much effort has gone into amplifying the displacements of actuators built around piezoelectric materials (PZTs). Some researchers have used topology optimization to design compliant mechanisms that best magnify either the geometric or mechanical advantage of piezoelectric wafers or “stack” actuators. PZTs are generally poled through the “thin” direction, so actuation by an electric field in that direction only induces eigenstrains normal to the free edges. Some researchers have shown advantages of “shear mode” actuation, and material scientists have demonstrated the ability to pole a PZT in an arbitrary direction. This work attempts to justify the inclusion of the PZT polarization vector as a design variable in the design of a flextensional actuator. We present two examples based on the “cymbal” actuator: one using a simplified model to justify off-angle polarization and another using the polarization vector as a design variable to optimize the topology of a compliant mechanism.     

A finite element formulation for composite laminates with smart constrained layer damping

A composite laminate with active constrained-layer damping treatment is studied. The interface element for viscoelastic damping layers has been developed based on the relative displacements between composite plates and piezoelectric constraining layers. As an example, the problem of forced oscillations of the laminated composite structure with a smart constrained damping treatment is solved and the vibration response of the composite plate with smart damping layers is calculated using the presently developed procedure.     

Structural response of composite plates equipped with piezoelectric actuators

We propose the modelling of piezoelectric elements perfectly bonded on an elastic structure. The study aims at predicting the static and dynamic (vibration) electromechanical responses of the structure. The model is mostly based on the kinematic assumption of the Love–Kirchhoff thin plate theory including shear function with a quadratic variation of the electric potential along the thickness direction of the piezoelectric parts. A variational formulation of piezoelectricity leads to the equations of motion for an elastic plate equipped with piezoelectric elements. An important feature of the present investigation is that the stiffness and inertial contributions of the piezoelectric patch is not neglected. Moreover, the numerical simulations demonstrate the influence of the actuator position on the global and local responses of the elastic plate for two situations (i) bilayer and (ii) sandwich configurations. A number of benchmark tests are considered in order to characterize the plate deformation when applying an electric potential to the piezoelectric patch faces. Plate vibration problem is also presented and the frequencies for the axial and flexural modes are obtained. The spectra of vibration for the plate with a time-dependent electric potential are computed.     

Fracture analysis of plane piezoelectric/piezomagnetic multiphase composites under transient loading

The transient response of cracked composite materials made of piezoelectric and piezomagnetic phases, when subjected to in-plane magneto-electro-mechanical dynamic loads, is addressed in this paper by means of a mixed boundary element method (BEM) approach. Both the displacement and traction boundary integral equations (BIEs) are used to develop a single-domain formulation. The convolution integrals arising in the time-domain BEM are numerically computed by Lubich’s quadrature, which determines the integration weights from the Laplace transformed fundamental solution and a linear multistep method. The required Laplace-domain fundamental solution is derived by means of the Radon transform in the form of line integrals over a unit circumference. The singular and hypersingular BIEs are numerically evaluated in a precise and efficient manner by a regularization procedure based on a simple change of variable, as previously proposed by the authors for statics. Discontinuous quarter-point elements are used to properly capture the behavior of the extended crack opening displacements (ECOD) around the crack-tip and directly evaluate the field intensity factors (stress, electric displacement and magnetic induction intensity factors) from the computed nodal data. Numerical results are obtained to validate the formulation and illustrate its capabilities. The effect of the combined application of electric, magnetic and mechanical loads on the dynamic field intensity factors is analyzed in detail for several crack configurations under impact loading.     

High temperature dynamic viscosity sensor for engine oil applications

This paper presents a new high temperature dynamic viscosity sensor for in situ condition monitoring of engine lubricants. The sensor is used to measure the variation in the quality factor of a vibrating piezoelectric cantilever beam due to viscous damping. The sensor was used to measure the dynamic viscosity of various single and multi-grade engines oils up to 180 cP from 25 °C to 60 °C. The sensor is capable of detecting degradation and dilution of engine oil for both new and used samples of 5W-30 and 10W-40 and diluted SAE 30 engine oils. All of the viscosity measurements presented are within 0.13-9.8% of the results obtained using the standard Walther equation at various temperatures. An equation relating dynamic viscosity of an oil sample to the quality factor of the beam is presented. The quality factor measurement circuit presented in this research can be implemented in automotive applications for in situ condition monitoring of lubricant viscosity.     

A photopatternable superparamagnetic nanocomposite: Material characterization and fabrication of microstructures

A superparamagnetic nanocomposite obtained by dispersing superparamagnetic magnetite nanoparticles in the epoxy SU-8 is used to fabricate microstructures by photolithography. The dispersion of the nanoparticles and the level of agglomerations are analyzed by optical microscopy, TEM (transmission electron microscope), SAXS (small-angle X-ray scattering), XDC (X-ray disc centrifuge) and XRD (X-ray diffraction). Two different phosphate-based dispersing agents are compared. In order to obtain a high-quality nanocomposite, the influence of particle concentration 1-10 vol.% (4-32 wt.%) on composite fabrication steps such as spin coating and UV exposure are systematically analyzed. Features with narrow widths (down to 1.3 μm) are obtained for composites with 5 vol.% particle concentration. Mechanical, magnetic and wetting properties of the nanocomposites are characterized. These nanocomposites exhibit superparamagnetic properties with a saturation magnetization up to 27.9 kA m⁻¹ for10 vol.%. All nanocomposites show no differences in surface polarity with respect to pure SU-8, and exhibit a moderate hydrophobic behavior (advancing dynamic contact angles approximately 81°). Microcantilevers with particle concentrations of 0-5 vol.% were successfully fabricated and were used to determine the dynamic Young's modulus of the composite. A slight increase of the Young's modulus with increased particle concentration from 4.1 GPa (pure SU-8) up to 5.1 GPa (for 5 vol.%) was observed.     

Accuracy and uncertainty of thermal-infrared remote sensing of stream temperatures at multiple spatial scales

Stream temperature is an important indicator of water quality, particularly in regions where endangered fish populations are sensitive to elevated water temperature. Regional assessment of stream temperatures from the ground is limited by sparse sampling in both space and time. Remotely sensed thermal-infrared (TIR) images are able to make spatially distributed measurements of the radiant skin temperature of streams. We quantify and discuss the accuracy and uncertainty limits to recovering stream temperatures in the Pacific Northwest for a range of stream widths (10-500 m), and TIR pixel sizes (5-1000 m) from remotely sensed airborne and satellite TIR images. Among locations with more than three pixels across the stream, the image temperature overestimated the in-stream temperature on average by 1.2 °C, which is 7% of the in-stream temperature (standard error (SE) of 0.2 °C, n = 21). The corresponding uncertainty (band weighted standard deviation in image temperature) for these locations averaged ± 0.3 °C (SE < 0.1 °C, n = 21) which is 2% of in-stream temperatures. This overestimation by the image temperatures is likely to be due to thermal stratification between the stream surface and the location of the in-stream temperature measurements deeper in the water column. For streams with one to three pixels across, mixing with bank elements increased the overestimation by image temperatures to 2.2 °C (SE = 0.3 °C, n = 23) on average (13% of in-stream temperatures), and the uncertainty increased to ± 0.4 °C (SE = 0.1 °C, n = 23) which is 2% of in-stream temperatures. For a fraction of a pixel across the stream the overestimation by image temperatures was 7.6 °C (SE = 1.2 °C, n = 23) on average (45% of in-stream temperatures), and the uncertainty was ± 0.5 °C (SE = 0.1 °C, n = 23) which is 3% of in-stream temperatures. These results show that reliable satellite TIR measurement of stream temperatures is limited to large rivers (∼180-m across for Landsat ETM+), unless novel unmixing algorithms are used effectively.     

Development and evaluation of piezoelectric-polymer thin film sensors for low concentration detection of volatile organic compounds related to food safety applications

In this study, the regioregular poly (3-hexyl thiophene) (rr-P3HT) based piezoelectric sensors were developed and evaluated to detect alcoholic volatile organic compounds (VOCs) associated with spoiled and Salmonella typhimurium contaminated packaged beef headspace. The drop coating technique was used to deposit thin films of rr-P3HT on both the sides of quartz crystal microbalance (QCM) electrode. The QCM polymer sensors were found to provide repeatable and reproducible sensor response to alcohol VOCs with a fast recovery (<2 min) at room temperature (25 °C). The principal component analysis on the sensors sensitivities was performed to discriminate the sensed alcohol VOCs, namely: 3-methyl-1-butanol from 1-hexanol. The QCM polymer sensors demonstrated selective response to low concentration of 3-methyl-1-butanol (average estimated lowest detection limit (LDL): 4.35 ppm) and to 1-hexanol (average estimated LDL: 3.20 ppm). The 30 days storage study performed on QCM sensors showed identical sensitivity responses for sensing 3-methyl-1-butanol and 1-hexanol at low concentrations.