Vibration analysis of constrained layered beams with multiple damping layers

With an increasing demand for light, continuous, and high strength structures, multi-layered systems with viscoelastic materials have gained major importance over the years. Viscoelastic layered systems provide a simple and flexible solution for damping vibration of sheet metal panels. They also help to effectively eliminate noise from resonant structures and surfaces. There has been a lot of work done on active and passive layered sandwich beams based on the theoretical models proposed by Kerwin (1959) and extended by Ditaranto (1965), Mead and Markus (1969), and other researchers. This work presents an analytical formulation to predict the stiffness and damping of constrained layered beams that have multiple viscoelastic damping layers. The model was derived for symmetrical setups using variational methods. The equations to evaluate the stiffness and damping were derived in closed form and can be evaluated for different boundary conditions. The complex modulus approach was used to model the elastic and shear modulus of the viscoelastic material. The equations of motion for multi-layer system in this research were compared with Mead's three layer beam model. Equations derived in this dissertation match well with Mead's equation for symmetric system. A parametric analysis has been conducted to study the effects of different parameters on the damping and stiffness of the system under simply supported boundary conditions.; In addition, another analytical model was developed for the unsymmetrical setups with two different viscoelastic materials adjacent to each other. Experiments were conducted on simply supported three-layered beams at different temperatures to validate theoretical results. The experimental results show good agreement with the modal frequencies estimated by theory. The first four modes were considered in the computation and experiment validation. The multi-objective optimization procedure to obtain optimum structural and material parameters corresponding to given temperature and frequency range for maximizing system damping and minimizing the system mass was also obtained. Using an illustrative example, it was shown that it is possible to arrive at a configuration that has maximum damping without sacrificing stiffness and weight requirements.