The purpose of this research is to present new methods of active and passive vibration control for flexible structures. The study includes: 1) passive viscoelastic damping treatment; 2 ) active vibration control using layered shape memory alloy (SMA); 3) combined application of viscoelastic damping treatment and SMA; 4) experiments.In order to maximize damping and save weight of the structure and cost, a partially covered double sandwich cantilever beam model has been presented. It is shown that the double sandwich beam is better than single sandwich beam for some conditions. To take into account of end loads effect of elastic structures such as robot arm or manipulator, a model of partially covered double sandwich cantilever beam with mass at free end is given and discussed. Also a more accurate model (Timoshenko model) is discussed. The experiments were done to verify the theoretical results.The active vibration control by means of layered shape memory alloy actuator is discussed. The layered structure is easy to implement in real application, especially for the existing structures. The control results are compared and discussed. The temperature effects are discussed.Also a model with combined application of viscoelastic damping treatment and shape memory alloy layer is presented. Both the vibration characteristics and control results are obtained and discussed. The vibration control results for different control schemes are compared and discussed. The temperature effects are also discussed
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