logo
    Nonlinear Static Mechanic Couple Analysis of Piezoelectric Laminated Circular Plates for Pressure Sensors
    2
    Citation
    0
    Reference
    20
    Related Paper
    Citation Trend
    Abstract:
    Based on the Von Karman plate theory, the piezoelectricity and the classical laminate theory, the electromechanical coupled characteristics of circular plate pressure sensors with thin piezoelectric layers were quantitatively analyzed. Firstly, a static mechanic coupled model of a piezoelectric laminated sensor was presented, and the general expression of the sensitive charge was given. By means of the series method in expansion, the exact solution of the geometrical nonlinear couple problem was obtained. The characteristic curves of sensitive charge vs pressure and central deflection were obtained, which are the great interest for the signal output of piezoelectric pressure sensors. The influence the secondary piezoelectric effect were quantitatively discussed simultaneously. For piezoelectric pressure sensor, the results of the solved problems can be directly to measure the pressure and the deflection of the laminated plate structures by the output of electric signals.
    Keywords:
    Plate theory
    In order to investigate the problem associated with nolinear bending of pressure sensor of circular thin plate with piezoelectric patches under the action of coupling load of mechanical pressure and applied voltage,based on Von Karman plate theory and basic piezoelectricity equation,the nonlinear bending governing equation is derived and solved using modified iterative method in this study.The nonlinear relation of load,deflection and applied voltage is obtained.Numerical example shows that the bending deflection of the circular plate can be effectively controlled by regulating the magnitude and direction of voltage applied.The study results provide some useful value.
    Plate theory
    Bending of plates
    Citations (0)
    An accurate modeling of the piezoelectric effect of coupled structures is essential to application of piezoelectric materials as sensors and actuators in engineering structures, such as Micro-Electro-Mechanical Systems and Interdigital Transducer for health monitoring of structures. This paper presents a simulation for the shear horizontal wave propagation in an infinite metal plate surface bonded by a piezoelectric layer with open electrical circuit, with focus on the dispersion characteristics of a metal core bonded by a layer of piezoelectric material to be used in health monitoring of structures. The dispersive characteristics and mode shapes of the deflection, electric potential, and electric displacement of the piezoelectric layer are theoretically derived. The results from numerical simulations show that the phase velocity of the piezoelectric coupled plate approaches the bulk-shear wave velocity of the substrate at high wavenumbers. The mode shapes of electric potential and deflection of the piezoelectric layer with steel substrates change from a shape with few zero nodes to one with more zero nodes at higher wavenumbers and with thicker piezoelectric layer. For the coupled plate with gold substrates at higher wavenumbers, the electric potential is found to jump from null at the interface of the piezoelectric layer and the substrate to a constant at the surface of the piezoelectric layer along the thickness direction. These findings are useful to the design of sensors using the piezoelectric coupled structures.
    Piezoelectric motor
    Wavenumber
    Citations (6)
    Piezoelectric material inherently possesses coupling between electrostatics and structural dynamics. Utilizing linear piezoelectric theory results in an intrinsically coupled pair of piezoelectric constitutive equations. One equation describes the direct piezoelectric effect where strains produce an electric field and the other describes the converse effect where an applied electrical field produces strain. The purpose of this study is to compare finite element analysis and experiments of a thin plate with bonded piezoelectric material. Since an isotropic plate in combination with a thin piezoelectric layer constitutes a special case of a laminated composite, the classical laminated plate theory is used in the formulation to accommodated generic laminated composite panels with multiple bonded and embedded piezoelectric layers. Additionally, the von Karman large deflection plate theory is incorporated. The formulation results in laminate constitutive equations that are amiable to the inclusion of the piezoelectric constitutive equations yielding in a fully electro-mechanically coupled composite laminate. Using the finite element formulation, the governing differential equations of motion of a composite laminate with embedded piezoelectric layers are derived. The finite element model not only considers structural degrees of freedom (d.o.f.) but an additional electrical d.o.f. for each piezoelectric layer. Comparison between experiment and numerical prediction is performed by first treating the piezoelectric as a sensor and then again treating it as an actuator. To assess the piezoelectric layer as a sensor, various uniformly distributed pressure loads were simulated in the analysis and the corresponding generated voltages were calculated using both linear and nonlinear finite element analyses. Experiments were carried out by applying the same uniformly distributed loads and measuring the resulting generated voltages and corresponding maximum plate deflections. It is found that a highly nonlinear relationship exists between maximum deflection and voltage versus pressure loading. In order to assess comparisons of predicted and measured piezoelectric actuation, sinusoidal excitation voltages are simulated/applied and maximum deflections are calculated/measured. The maximum deflection as a function of time was determined using the linear finite elements analysis. Good correlation between prediction and measurement was achieved in all cases.
    Plate theory
    Piezoelectric accelerometer
    Piezoelectric motor
    Citations (10)
    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.
    Plate theory
    Citations (0)
    The governing equations were inferred by simplifying laminated piezoelectric plate on the basis of Kichhoff assumption. The laminated piezoelectric beam under the situation of open circuit at both ends was explored. An analytic solution for static electromechanical coupled behavior of laminated piezoelectric beam under the non external voltage situation was also presented. The distributions of voltage and deflection in piezoelectric layer and matrix were provided. The results show that the voltage through thickness can be treated as linear distribution.
    Open-circuit voltage
    Citations (0)
    The actuator of piezoelectric inkjet printhead is analyzed as a rectangular laminated plate for vibrations. With the theory of piezoelectric plates and Rayleigh-Ritz method, an analytical model of laminated piezoelectric rectangular plate was established, and the governing equations were derived and solved for forced vibrations of the thin-plate. The primary resonance of rectangular plate is investigated for the deformation and frequency. The amplitude-frequency response curve and the first-order vibration mode shapes are obtained. The results in the present study is to be used for the improvement of electric driving of printhead structure.
    Plate theory
    Rayleigh–Ritz method
    This paper deals with the vibration analysis of a circular plate surface bonded by two piezoelectric layers, based on the Kirchhoff plate model. The form of the electric potential field in the piezoelectric layer is assumed such that the Maxwell static electricity equation is satisfied. The validation of the theoretical model is done by comparing the resonant frequencies of the piezoelectric coupled circular plate obtained by the theoretical model and those obtained by finite-element analysis. The mode shape of the electric potential obtained from free vibration analysis is generally shown to be non-uniform in the radial direction in contrast to what is commonly assumed. The piezoelectric layer is shown to have an effect on the frequencies of the host structure. The proposed model for the analysis of a coupled piezoelectric circular plate provides a means to obtain the distribution of electric potential in the piezoelectric layer. The model provides design reference for piezoelectric material application, such as an ultrasonic motor.
    Piezoelectric motor
    Piezoelectric accelerometer
    Citations (197)