FINITE ELEMENT MODELS OF PIEZOELECTRIC COMPOSITE LAMINATES

Abstract

Structures which are able to sense, respond and control their own characteristics and states are termed smart structures. These structures can be applied to vibration suppression, shape control, noise attenuation and damage monitoring. Among many smart materials, piezoelectric materials have been widely used as sensors and actuators in smart structures, due to their two characteristics, i.e. direct and inverse piezoelectric effects. These structures are complicated and analytical solutions are hard to obtain. The finite element method has been shown to be a powerful tool for analysing the piezoelectric sensors and actuators as well as whole structures. In this thesis, finite element models and programs based on different theories have been developed for simulating mechanically and thermally induced vibration suppression of piezoelectric composite structures using active feedback control. The models are developed based on the classical plate theory (CPT), the first-order shear deformation theory (FSDT) and the third-order deformation theory (TSDT), respectively, and are used to study the dynamic as well as static responses of piezoelectric composite plates subjected to thermal, mechanical and electrical loading. The finite element models developed are then applied to implement the simulation of active shape control and vibration suppression of laminated composite structures with piezoelectric sensors and actuators. First, the finite element model and program based on the CPT and the principle of virtual displacements have been developed. This model shows its validity in the shape control and active vibration suppression by comparing its results with those available in the literature. However, applications are limited to thin piezoelectric composite laminates within the framework of the Kirchhoff-Love hypothesis, which neglects transverse strains. For moderately thick or thick composite laminates, the CPT model fails to give an accurate prediction due to the strong presence of the transverse strains. To overcome this shortcoming of the CPT model, an alternative model is developed based on the FSDT. Because of consideration of the transverse shear strains m the composite laminates, the finite element model based on the FSDT gives much more accurate results in stress and displacement predictions for moderately thick or thick piezoelectric composite plates. However, the model yields a constant value of the transverse shear strain through the thickness of the plate and requires shear correction factors which are difficult to determine. To achieve better estimations, higher-order expansions of the displacement field need to be used. Therefore, the finite element model based on the TSDT has been established. It accommodates the vanishing of transverse shear strains (and hence stresses) on the top and bottom surfaces of a laminate. By comparing the results obtained from the above three finite element models, it is found that the CPT can give accurate results only for thin piezoelectric composite plates, that the FSDT can give better results than the CPT for moderately thick ones, and that the TSDT can give accurate results both in deflections and stresses for thick ones.