Finite element modeling of embedded piezoelectric sensors

Abstract

Proving Ground, MD 21 005-5069, USA 1.Introduction Thin film piezoelectric transducers, fabricated with PVDF or P(VDF-TrFE) may be embedded in material structure for identification of damages and control of mechahical stress [ 1-81: The piezoelectric behaviour of a transducer (ie sensor) is governed by the electrical and mechanical properties, via dielectric tensor, dielectric displacement, electric field, stress and strain tensors and the elastic stiffness tensor. These properties and their inter-relations may be expressed thus, T = cS -e T E and D = eS + EE where T and S are the stress and strain tensors respectively, D the dielectric displacement, E the electric field, e the piezoelectric tensor and e' is its transpose, c the elastic stiffness tensor at a constant electric field and E the dielectric tensor at a constant mechanical strain. A suitable mathematical model of the polymer behaviour as a fbnction of fiequency may provide a theoretical basis with which experimental results can be compared. The present work reports the development of a finite element method to determine theoretically the first resonance frequency of a P (VDF-TrFE) transducer.(1)(2) 2. Finite Element Method (FEM)The finite element method has been used in many engineering simulation problems to obtain approximate solutions of differential equations and it is particularly usefbl in the analysis of stress related problems. Its main advantage over other methods is in the modelling of complex geometries, such as diphasic semicrystalline polymers containing both the crystalline and amorphous phases. All structure in the real world are discrete and three dimensional. The basic principle in the finite element method is to divide a region in which the values of a variable parameter is required, into an assembly of elements which are interconnected at nodes. The magnitude of the variable at each element is exuressed by a set of linear algebraic equations instead of the partial differential equations. The sblution of these linear equations is a vector whose components are the values of the unknown variable at the nodal prints [9]. The number of equations becomes very large when the size of the elements is reduced in order to obtain a satisfactory approximation. With the knowledge of the nodal values of the variable it is then possible to evaluate the frequency response of the transducer. In the present work the solution of the system equations has been obtained using the Numerical Algorithm Group (NAG) finite element library routine.Id" International Symposium on Electrets, I999 0-7803-5025-1/99/$10.00 01999 IEEE

Characterization and Evaluation of Smart Concrete Modules Embedded with Piezoelectric Devices

“…Hailu [10] embedded a piezo-platelet interdigital transducer (IDT) into a 3.4mm thick plate of Ciba-Geigy Hard-set (CY13O1/HY1300) epoxy resin and generate ultrasonic lamb waves to proceed structural health monitoring. Ledda [11] established a finite element model of embedded PVDF for identification of damages and control of mechanical stress. In the research of Blanas [12], the PTCa/Epoxy and PTCa/P(VDF-TrFE) composite materials are employed as embedded sensors in composite laminates to detect elastic waves propagating in such structures and to monitor transient applied loads.…”

Finite element modeling of a plate with localized piezoelectric sensors and actuators

“…Other engineering applications using finite element model of smart structures have been reported. Ledda et al (1999) presented the development of a finite element method to determine theoretically the first resonance frequency of a PVDF-TrFE transducer and Lopes et al (2000) used the finite element formulation in order to generate the training data for a neural network to correlate the frequency response function (FRF) and the electrical impedance of smart structures.…”