Vibration Analysis of Elastic Beams With Unconstrained Partial Viscoelastic Layer

Material damping treatments, such as adding viscoelastic layers (VEL) to engineered structures, are commonly used for vibration attenuation. Study of the VEL geometry, shape, location (in case of partially adding), and arrangement (in composites), are of engineering interest to optimize the damping effect versus the weight and cost. In order to show the possibility of higher damping characteristics for shorter VEL, this paper aims for a two-step vibration analysis of an elastic cantilever beam with an unconstrained partial VEL. The governing equations are developed based on Euler-Bernoulli beam theory and Kelvin-Voigt viscoelastic model. In order to answer how the VEL length and thickness affect the modal parameters and dynamic response, both free and forced vibration problems are solved analytically, and the results are manipulated to achieve a much more applicable size range with higher damping characteristic. A non-uniform trend and inconsistent behaviour in both frequency and amplitude changes is observed versus increasing the VEL length, which addresses the necessity of an optimization challenge and gives a good insight to take into account the concept of VEL critical length.