Free out-of-plane vibrations of a rotating beam with non-linear elastomeric constraints

Free out-of-plane vibration of a rotating beam with a non-linear, elastomeric constraint has been investigated. The elastomer is modelled as a parallel combination of spring and damper elements. The stiffness and damping parameters are evaluated by using the previous experimental data. The linear analysis is performed by two techniques, one based on a power series expansion and the other based on the Rayleigh-Ritz principle. The results are found to be in excellent agreement. In the non-linear analysis, a numerical-perturbation technique is applied to determine the frequency-amplitude relationship. A parametric study revealing the influence of the non-linear constraint is presented