A review and critique of theories for piezoelectric laminates

A review and critique of different laminate theories used for the modeling and analysis of laminated composite beams or plate structures is presented. Many finite-element models use classical laminate theory (CLT), also known as first-order shear deformation theory (FSDT), for the numerical simulation of active structures. The basic assumptions of this model have evolved from those proposed for composite laminate models and are based on thin-plate theory with resulting approximations for the elastic displacement, stress and strain components. In the case of piezoelectric laminates, the approximations spill over into the electric potential and electric field components. No studies and simulations have been documented for the dynamical electromechanical field variations through the thickness of the laminate structure at the resonant frequencies of the structure. This is essential to the understanding of the validity and range of applicability of thin-plate assumptions for active vibration control of structures. On the one hand, thin-plate models result in a computationally tractable model for smart structures, but they should not compromise on the electromechanical coupling effect, which is at the basis of active control. This paper first presents a three-dimensional (3D) complete field solution for active laminates based on a modal, Fourier series solution approach that is used to compute all the through-thickness electromechanical fields near the dominant resonance frequency of a beam plate with two piezoelectric (sensor and actuator) and one structural layers. Then a detailed review of the extant laminate models used for piezoelectric laminates, emphasizing the underlying assumptions in each case, is presented. The non-zero, through-thickness field components are computed under these assumptions. The results of the 3D model and FSDT model are compared for two aspect ratios ((ARs) - thickness-to-width of the layers). An AR of 20 is at the limit of the FSDT and an AR of 50 well within the assumptions of the FSDT. It is concluded that for moderate ARs, several of the approximations of the FSDT are questionable at resonance frequencies. A detailed set of pertinent and general references to papers dealing with piezoelectric laminates is also included. It is hoped that this study will be a reference source for those who want to use FSDT and for those want to understand the dynamical behavior of the internal fields in a smart laminate.