An improved finite element model for vibration and control simulation of smart composite structures with embedded piezoelectric sensor and actuator
This thesis details a study conducted to investigate the dynamic stability of an existing active control model (ACFl) of a composite structure embedded with a piezoelectric sensor and actuator for the purpose of vibration measurement and control. Criteria for stability are established based on the second method of Lyapunov which considers the energy of the system. Results show that ACFl is asymptotically stable although piezoelectric control effects persist when the feedback gain is set to zero. Meanwhile, it is required that there should be no control effects occurring through the piezoelectric actuator when the gain is set to zero. In this study, a new active control model (ACF2) is developed to satisfy the stability criteria, which satisfies the requirement of no piezoelectric control effects when the gain is set to zero. In ACF2 - as well as ACFl - the displacement and potential fields are discretised using the finite element method. In light of the locking phenomena associated with discrete displacements - which is expected to be pronounced in the case of discrete potentials due to their element geometry, ACF2-mixed is developed. ACF2 and ACF2-mixed control methodologies are similar except that in ACF2 both the displacement and potential field are discretised whereas in ACF2-mixed, only the displacement field is discretised and the potential field is continuous. Consequent to ACF2 and ACF2-mixed, stability analysis of the resulting time integration scheme is investigated as well. The results show that the damping forces due to the piezoelectric effect do not add energy to the structure. Hence, asymptotic stability is achieved. The time integration scheme yielded a small error, consistent with the literature. Numerical results revealed that ACFl exhibits a high degree of locking which is relaxed in ACF2 whereas ACF2-mixed exhibits envisaged results when compared with the other two models. Therefore, the ACF2 and ACF2-mixed will provide engineers with an alternative simulation model to solve actively controlled vibration problems hitherto.