Mohammad Sina Taki (Sept. 2012 - Nov. 2014)
Thesis Title: Dynamic Modeling of a Bistable Composite Plate with Piezoelectric Layer (Co-Supervised by Prof. Ziaei-Rad)
Some important advantages of composite materials such as their high weight to strength ratio, was the cause of their prevalent use in many industrial cases in past decades. Morphing or a shape adaptable structure can be described as a structural system whose shape and structural characteristics can be changed in order to satisfy the operational characteristics alteration morphing structures is so-called the bi-stable structures. Bi-stable composite structures are special kinds of composite structures that their ability to maintain in their stable configurations without any source of energy has made them suitable for morphing structures. It is well known that the asymmetric composite laminates will form curved shapes as their temperature drops from the high curing temperatures to the room temperature. Such curvatures result from the differences between the coefficients of thermal expansion and elastic properties of each layer within the laminate. Therefore, as these structures are exposed to different kinds of loading, large out-of-plane deflection might occur. The two cylindrical stable shapes of such structures cannot be predicted by the classical lamination theory (CLT). A nonlinear mechanism called snap-through is capable of making the change from one stable to another stable configuration. A great amount of research were carried out that focused on the thermal and static behavior of these special plates. The main goal of the present study is dynamic response of [0/90] bi-stable composite plates with piezoelectric layers. Therefore, a specially-written MATLAB code based on the Rayleigh-Ritz technique and minimizing the potential energy is developed to compute statically stable states of the plate. Afterwards, using Rayleigh-Ritz model in conjunction with Hamilton’s Principle the electromechanical equations, short circuit natural frequency and dynamic time responses of plate to the ramp and harmonic electrical fields were computed. The obtained results were in agreement with the results obtained by finite element simulations in ABAQUS software. To eliminate the errors in the results from Rayleigh-Ritz method, biquadratic shape function for the out-of-plane displacement field was proposed and the effect of that was evaluated in the static and dynamic behavior of the plate. Furthermore, the concept of energy harvesting from vibrations of the bi-stable composite plates affected by concentrate forces is investigated. The results revealed that these plates have more ability in producing electrical powers in compared with conventional plates because of having non-linear behavior and snap-through between their stable states.
Keywords: Bi-stable composite plates, Snap-through, Piezoelectric layers, Short circuit natural frequency, Open circuit natural frequency, Energy harvesting