ASYMPTOTIC NUMERICAL METHOD FOR THE DYNAMIC STUDY OF NONLINEAR VIBRATION ABSORBERS

Abstract

Vibrations are usually undesired phenomena as they may cause discomfort, disturbance, damage, and sometimes destruction of machines and structures. It must be reduced or controlled or eliminated. One of the most common methods of vibration control is the use of the dynamic absorber. The paper is interested in the study of a nonlinear two degrees of freedom (DOF) model. To solve nonlinear equation of motion a high order implicit algorithm is proposed. It is based on the introduction of a homotopy, an implicit scheme of Newmark and the use of techniques of Asymptotic Numerical method (ANM). We propose also a regularization of the contact force to overcome the difficulty of the singularity in this model. A comparison will be presented between the results obtained by the proposed algorithm and those using the classical Newton–Raphson and Newmark time scheme.