The effectiveness of a new tuned mass damper to control the dynamics of a mass interacting in a nonsinusoidal Remoissenet-Peyrard potential

This work investigates the ability of a new tuned pendulum mass damper to control the behavior of a structure. A very rich nonlinear dynamics is reached by a mass fixed on a spring and driven by a conveyor belt. That is the stick-slip motion (either regular or chaotic), the chaotic motion and very low amplitude motion. When a control systems like the tuned mass damper are used, the conversion of chaotic stick-slip into regular stick-slip is observed. For certain tuned mass dampers, the regular stick-slip is transformed into a stick-slip with very small amplitude. In addition, the chaotic motion is converted into regular motion, while very low amplitude motion remains unchanged. Very few cases of anti-control have been noted. Thereafter, a comparison on the effectiveness of control systems was made, especially in the case of chaotic motions. For this purpose, the largest Lyapunov exponent is evaluated and the stability map was obtained. It is shown that the best control system depends on the value of the mass ratio between the controller and the structure (which should be as small as possible for civil engineering implementation). In addition, the best control system is closely related to the type of motion considered.