Nonlinear vibration and control of fiber metal laminates

In this dissertation, we first studied the linear and nonlinear vibration of cantilever beams made of Fiber Metal Laminates (FMLs). An inextensible beam model with nonlinear damping was adopted to explore the nonlinearities of cantilever beams. Approximate solutions were obtained by solving an integro-differential equation via Multiple Scales method and Harmonic Balance Method. For the single-mode response, a large discrepancy in the nonlinear coefficient was found between theory and experiment. For different excitation level, a small variation in the linear natural frequency was detected. A beam model with a nonlinear spring-hinged end and the other end free was applied to tune the inextensible cantilever beam theory. While this modified mode can reasonably explain the natural frequency difference, its ability to resolve the discrepancy in the nonlinear coefficient is limited.; Then we studied the efficiency problems of using PZT patches in negative feedback control of beam. Uniform beam model was applied when the mass and stiffness of PZT patches were ignored. Stepped beam model was then derived to describe the beam-actuator structure when the effect of patches was taken into consideration. It is found that the use of PZT patches for active vibration control may degrade the control efficiency by modifying the configuration of the structure. It is also found that the optimal positions from stepped beam model are similar to those from the uniform beam model. The ratio of control efficiency from the stepped beam model to that from the uniform beam model is associated with material properties and structural dimensions. Because the factor is a constant when the structure is determined, we propose a modified model to estimate the control efficiency. Several experiments on vibration control of a beam were conducted to verify our efficiency estimate.; Finally we extended our control efficiency estimation method to the vibration of plates. It is found that the structural modification caused by attaching PZT patches may degrade the control ability while the optimal positions are not sensitive to these structural alterations. Our proposed efficiency estimation method works well for the vibration control of plates.