FINITE ELEMENT MODELING OF MODERATELY THICK COMPOSITE PLATE WITH PIEZOELECTRIC SENSORS AND ACTUATORS

A rectangular finite element for laminated plate with bonded and/or embedded piezoelectric sensors and actuators is developed based on the variational principle and the first order shear deformation theory. The element has four-node, 20-degrees-of-freedom with one potential degree of freedom for each piezoelectric layer to represent the piezoelectric behavior. The higher order derivation of deflection is obtained by using the normal rotation expressions to take the effects of transverse shear deformation into considerations. The finite element can accurately simulate the deformation of both thin and moderately thick plates. A Fortran program is written and a number of benchmark tests are exercised to verify its effectiveness. Results are compared well with the existing data. The unbalanced composite with piezoelectric layers is then analyzed by using the model. Results show that the changes of the ratio between the thickness of positive angle layers and the negative angle layers have an effect on the deformation of the structure under the same electric loading.

ANALYSIS OF NONLINEAR PIEZOELECTRIC CIRCULAR SHALLOW SPHERICAL SHELLS BY DIFFERENTIAL QUADRATURE ELEMENT METHOD

The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect is considered. Detailed formulations and procedures are given for the first time. Several examples are analyzed and accurate results are obtained by the DQEM. Based on the results in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions of structural elements. It can be seen that the shell shape may be theore tically controlled and snap through may occur when the applied voltage reaches a critical value even without mechanical load for certain geometric configurations.

Theoretical Analysis and Experimental Verification on Flow Field of Piezoelectric Pump with Unsymmetrical Slopes Element

Regular valveless piezoelectric pumps have rectifying elements outside their chambers to produce net flow. These rectifying elements outside the chamber will increase the overall volume of the pump and prevent its minimization. Valveless piezoelectric pump with unsymmetrical slopes elements（USE）, proposed in this paper, differs from other valveless pumps in that it is easy to be minimized by developing the chamber bottom as such a rectifying element. In this research, the working principle of the proposed pump was analyzed first. Numerical models were thereby established and numerical simulation was conducted to the chamber flow field with the method of time-dependent velocity. The effects of the USEs on the flow field in the chamber were shown clearly in simulation. And the particular feature of flow field in the chamber was discovered. It behaves a complex flow field, in which strong turbulent occurs companying a lot of vortexes in different directions and different sizes. This feature is just opposite to what regular piezoelectric pumps expect： a moderate flow field. The turbulent flow could be used to have different liquids stirred and well mixed in the chamber to produce homogeneous solution, emulsion or turbid liquid. Meanwhile, numerical simulation also presents the effect of the angles difference of the two slopes upon the flow field, and upon the flow rate of the pump, which fits to the theoretical analysis. Experiments with the proposed pump were also conducted to verify the numerical results. In these experiments, six USEs with different slope angles were used for efficiency tests, which proved the validity and reliability of the numerical analysis. The data obtained from numerical analysis agree well with that from the experiments. The errors ranged from 4.4% to 14.8% with their weighted average error being 9.7%.

Analysis on Flow Field of the Valveless Piezoelectric Pump with Two Inlets and One Outlet and a Rotating Unsymmetrical Slopes Element

Typically,liquid pump and liquids mixer are two separate devices.The invention of piezoelectric pump makes it possible to integrate the two devices.Hower,the existing piezoelectric mixing-pumps are larger because the need the space outside the chamber,and another shortcome of them is that they cannot adjust the mixing ratio of two liquids.In this paper,a new piezoelectric pump being capable of integrating mixer and pump is presented,based on the theory of the piezoelectric pump with the unsymmetrical slopes element（USE）.Besides the features of two inlets and one outlet,the piezoelectric pump has a rotatable unsymmetrical slopes element（RUSE）.When the pump works,two fluids flow into the inlet channels respectively.Then the RUSE controls the ratio of the two flows by adjusting the flow resistances of the two inlet channels.The fluids form a net flow due to the USE principle,while they are mixed into a homogeneous solution due to strong turbulence flow field and complex vortices generated by RUSE in the chamber.And then the solution flows through the outlet.Firstly,the theoretical analysis on this pump is performed.Meanwhile,the flow field in the chamber is calculated and simulated.And then,the relationship between the flows of the two channels and the rotating angle of the RUSE is set up and analyzed.Finally,experiment with the proposed pump is carried out to verify the numerical results.A RUSE with 20° slope angle is used in the experiment.Four sets of data are tested with the RUSE at the rotating angles of 0°,6°,11°,and 16°,respectively,corresponding to the numerical models.The experimental results show that the empirical data and the theoretical data share the same trend.The maximum error between the theoretical flow and the experimental flow is 11.14%,and the maximum error between the theoretical flow ratio of the two inlets and the experimental one is 2.5%.The experiment verified the theoretical analysis.The proposed research provides a new idea for integration of micro liquids mixer and micro liquids pump.

Finite Element Analysis of Smart Structures with Piezoelectric Sensors/Actuators Including Debonding

In vibration active control of composite structures, piezoelectricsensors/actuators are usually bonded to the surface of a host structure. Debonding of piezoelectricsensors/actuators can result in significant changes to the static and dynamic response. In thepresent paper, an novel Enhanced Assumed Strain(EAS) piezoelectric solid element formulation isdeveloped for vibration active control of laminated structures bonded with piezoelectric sensors andactuators. Unlike the conventional brick elements, the present formulation is very reliable, moreaccurate, and computationally efficient and can be used to model the response of shell structuresbesides thin plates. Delaminations are modeled by pairs of nodes with the same coordinates butdifferent node numbers, and numerical results demonstrate the performance of the element and theglobal and local effects of debonding sensors/actuators on the dynamics of the adaptive laminates.

Two-scale finite element method for piezoelectric problem in periodic structure

The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.

Active Vibration Control of a Railway Vehicle Carbody Using Piezoelectric Elements

In recent years and according to modem trans- portation development, rail vehicles are manufactured lighter to achieve higher speed and lower transportation costs. On the other hand, weight reduction of rail vehicles leads to increase the structural vibration. In this study, Active Vibration Control of a rail vehicle using piezo- electric elements is investigated. The optimal control employed as the control approach regard to the first two modes of vibration. A simplified Car body structure is modeled in Matlab using the finite element theory by considering six DOF beam element and then the Eigen functions and mode shapes are derived. The surface roughness of different classes of rail tracks have been obtained using random vibration theory and applied to the secondary suspension as the excitation of the structure; Then piezoelectric mounted where the greatest moments were captured. The effectiveness of Piezoelectric in structural vibrations attenuation of car body is demon- strated through the state space equations and its effect on modal coefficient.

Indentation behavior of a semi-infinite piezoelectric semiconductor under a rigid flat-ended cylindrical indenter

This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flatended cylindrical indenter.The contact area and other surface of the PSC half-space are assumed to be electrically insulating.By the Hankel integral transformation,the problem is reduced to the Fredholm integral equation of the second kind.This equation is solved numerically to obtain the indentation behaviors of the PSC half-space,mainly including the indentation force-depth relation and the electric potential-depth relation.The results show that the effect of the semiconductor property on the indentation responses is limited within a certain range of variation of the steady carrier concentration.The dependence of indentation behavior on material properties is also analyzed by two different kinds of PSCs.Finite element simulations are conducted to verify the results calculated by the integral equation technique,and good agreement is demonstrated.

Control model for experiments on piezoelectric and electrostrictive elements

As an ideal micro displacement actuator, piezoelectric and electrostrictive elements are in wide use in many fields, but their further application is restricted because of its shortages such as hysteresis, creep and non linearity. Through the analysis of the polarization mechanism of piezoelectric and electrostrictive elements, a new normalization model was proposed, analysis and experiments are run with the model, and the linearity of voltage displacement curve is analyzed as well.

Analytical modeling of sandwich beam for piezoelectric bender elements

Piezoelectric bender elements are widely used as electromechanical sensors and actuators, An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory （FSDT）, which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simplysupported bender elements was carried out and the numerical results showed that, solutions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.

BUCKLING AND POST-BUCKLING OF PIEZOELECTRIC PLATES USING FINITE ELEMENT METHOD

The finite element equations considering the geometrical nonlinearity of piezoelectric smart structures are derived based on the total Lagrange method under the assumption of weak coupling between electricity and mechanics. Buckling and post-buckling of piezoelectric-plate with various boundary conditions are investigated. The calculated results show that piezoelectric effects and external voltage can hardly affect the buckling and post-bucking characteristics of piezoelectric-plate under uniaxial pressure while the buckling caused by displacement in-plane has much to do with the electric field.

Energy Harvesting Strategy Using Piezoelectric Element Driven by Vibration Method

This study demonstrates a method for harvesting the electrical power by the piezoelectric actuator from vibration energy. This paper presents the energy harvesting technique using the piezoelectric element of a bimorph type driven by a geared motor and a vibrator. The geared motor is a type of PWM controlled device that is a combination of an oval shape cam with five gears and a speed controller. When using the geared motor, the piezoelectric element is size of 36L×13W×0.6H. The output voltage characteristics of the piezoelectric element were investigated in terms of the displacement and vibration. When using the vibrator, the electric power harvesting is based on piezoelectric effect and piezoelectric vibrator consists of a magnetic type oscillator, a cantilever, a bimorph actuator and controllers. Low frequency operating technique using piezoelectric vibrator is very important because normal vibration sources in the environment such as building, human body, windmill and ship have low frequency characteristics. We can know from this study results that there are many energy sources such as vibration, wind power and wave power. Also, these can be used to the energy harvesting system using smart device like piezoelectric element.

Enhancing Stress Intensity Factor Reduction in Cracks Originating from a Circular Hole in a Rectangular Plate under Uniaxial Stress through Piezoelectric Actuation

Circular holes are commonly employed in engineering designs;however, they often serve as locations where cracks initiate and propagate. This paper explores a novel approach to structural repair by utilizing piezoelectric actuators. The primary focus of this study is to investigate the influence of an adhesively bonded piezoelectric actuator patch placed above a circular hole on the stress intensity factor (SIF) in an aluminium plate. The plate is subjected to uniaxial tensile stress, while the piezoelectric actuator is excited with varying voltage levels. The analysis is conducted using the finite element method (FEM), a powerful numerical technique for simulating complex structures. The study assesses the stress distribution and employs the SIF as an adequate criterion for evaluating the impact of different patch configurations. The results indicate a strong correlation between the applied voltage and the SIF. Whether the SIF increases or decreases depends on the polarization of the piezoelectric actuator. Particularly noteworthy is the finding that rectangular patches in a horizontal orientation significantly reduce the SIF compared to other patch geometries. Moreover, double-sided patches exhibit a pronounced decrease in the SIF compared to single-sided patches. In summary, this research underscores the potential of piezoelectric actuators in mitigating stress intensity in structures with circular hole with crack initiation. It offers valuable insights into the influence of applied voltage, patch geometry, and patch placement on the SIF, thereby contributing to developing effective strategies for enhancing structural integrity.

Piezoelectric and dielectric properties of Cr-doped PSN-PZN-PZT qua-ternary piezoelectric ceramics

PSN-PZN-PZT + x wt. %Cr2O3, X = 0.0-0-9, were prepared by conventional mixed oxide techniques at sintering temperatures of 1220 degrees C-1300 degrees C for 2 h. The effect of sintering temperature on the microstructure and the piezoelectric properties was investigated by XRD, SEM, and other conventional measurement. The result indicated that with temperature increasing, the valence of Cr ion from Cr5+ or Cr6+ changes into C3+, and the piezoelectric properties turn hard. With increasing Cr2O3 content, the amount of rhombohedral phases increases and the morphotropic boundary phase is correspondingly shifts to rhombohedral phase. A uniform microstructure and excellent comprehensive properties were obtained at 1240 degrees C as the amount of Cr2O3 is 0.5 wt.%.

Synthesis of piezoelectric nanocrystalline PZT powder by stearic acid gel method

PZT nanocrystalline powder was prepared by a stearic acid gel method. Thecrystallization process from the precursor was monitored by infrared spectroscopy, differentialthermal analysis, and thermogravimetric analysis. The nano-sized PZT powder was characterized byX-ray diffraction and transmission electron microscopy. It shows that pure single-phase PZT powdercould be obtained at 450 deg C for 1 h, and the particle size is about 20 nm. With an increase inthe calcination temperature, the PZT crystallite size increased.

Finite Element Formulation and Analysis of Fracture Resistance Effected by Near-Tip Nonlinearities in Piezoelectric Solids

Comsidering the fact there are no systematic study on crack effected by large-scale near--tip nonlinearitiesup to now, a nonlinear finite element formulation accounting for nonlinearities and elasticity coupled with piezoelectricity is derived and a finite element program is developed. Numerical examples are presented to show the effect of nonlinear fracture characteristics on fracture resistance. It is found that an electric field may give a negative driving forceto prevent crack propagation.

Study of the Characteristics of Piezoelectric Elements

The piezoelectric effect and electrostrictive effect are analyzed in detail, and the characteristics of piezoelectric elements are studied theoretically. By adopting PD series piezoelectric driver developed by the authors, some experiments have been done with WTDS-I piezoelectric elements, and a conclusion that the electric polar method can reduce the hysteresis and creep of piezoelectric element is drawn. The hysteresis is reduced by 1%. The displacement of piezoelectric element is linearized.

Piezoelectrical－Elements－Driven Worktable and Its Application on the Robotic Precise Assembly

A precise large range worktable with high precision, high resolution and high frequency response, driven by piezoelectrical elements, is presented. The worktable configuration and the control unit are described. Also theoretical analysis and experimental study of the static and dynamic characteristics of the worktable are performed. By combining the worktable with a general purpose robot, a macro/micro manipulator system is built up and the assembly experiments are successfully accomplished.

Finite Element Analysis of Vehicle Load Effect on Harvesting Energy Properties of a Piezoelectric Unit

To realize the goal of harvesting energy from pavement vibration on a large scale, a new type of piezoelectric harvesting units as the energy transducer has been proposed. The piezoelectric harvesting units are paved 40 mm below the asphalt, which is the same as thickness of the top layer of typical asphalt pavement in China. The spacing distance is 2200 mm, which is the same as the one between two tires of a normal vehicle. A mathematical model of the unit is deduced on Meda empirical formula and Hamilton principle and piezoelectric equations. Effects of the external vehicle load on its harvesting energy properties and pavement deformation and stress are analyzed with the finite element method. The results show that the excited voltage is linearly variation with contact pressure while the harvested electrical energy exponential varies with contact pressure. The more the contact pressure is, the larger the harvested electrical energy and the deformation and stress are. The harvested electrical energy also increases with the load frequency. At least 100 mJ of electrical energy can be collected with the proposed piezoelectric harvesting unit. It shows that the technology application of the piezoelectric harvesting energy from pavement is promising.

Modeling of sensor function for piezoelectric bender elements

An analytical sandwich beam model for piezoelectric bender elements is derived based on the first-order shear deformation theory (FSDT), which assumes a single rotation angle for the whole cross-section and a quadratic distribution for coupled electric potential in piezoelectric layers. Shear coefficient is introduced to correct the effect of transverse shear strain on shear force and the electric displacement integration. Static and free vibration analyses of simply-supported bender elements are carried out for the sensor function. The results illustrate the high accuracy of the present model compared with the exact 2D solutions.