34. Vibration Reduction of a Structure by Using Nonlinear Tuned Vibration Absorbers

Tuned Vibration Absorbers (TVA) are commonly used in reducing undesirable vibrations of mechanical structures. However, TVAs work in a very limited frequency range and if the excitation frequency is outside of this range, they become ineffective. In order to solve this problem, researchers started to consider nonlinear TVAs for vibration attenuation. In this study, dynamic behavior of a linear Euler-Bernoulli beam coupled with a nonlinear TVA is investigated. The system is subjected to sinusoidal base excitation. Parameters of the nonlinear TVA is optimized to minimize vibration amplitudes of the primary system. Assumed modes method is used to model the Euler-Bernoulli beam. Nonlinear differential equations of motion are converted to a set of nonlinear algebraic equations by using Harmonic Balance Method (HBM). The resulting set of nonlinear algebraic equations is solved by Newton’s Method with Arc-Length continuation. Nonlinearities used in the TVA are cubic stiffness, cubic damping and dry friction damping. Hill’s method is used to evaluate stability of the solutions obtained. Results of the system with optimum nonlinear TVAs are compared with that of optimum linear TVA. Although, NES show to exhibit good vibration reduction performance – which is in parallel with the results given in literature, due to instability of the frequency domain solutions, it is observed that, actually, it is not as effective as other nonlinear TVAs.