Vibration isolation systems using hysteretic multiple tuned mass damper oscillators

The subject of this study is the vibration isolation effect of linear and nonlinear hysteretic single degree of freedom oscillators attached to a structure. The system of oscillators, attached to the main structure, reduce the amplitude of its structural response, over a wide frequency band excitation. This is achieved by distributing the natural frequencies of the attachments over an a priori specified frequency interval, which is related to the excitation power spectrum density. In order to introduce hysteretic restoring force to the oscillators and study its effect to the vibration reduction on the main structure the Bouc-Wen differential model of hysteresis is used. The introduction of hysteresis to the oscillators is observed to increase the vibration isolation efficiency of the attachments in certain cases. The study of the vibration isolation system behavior is conducted using the Monte Carlo technique. An explicit matrix formulated Newmark integration scheme is used for the linear attachment case. In the case of hysteretic attached oscillators, the system of equations of motion is integrated by an iterative decoupled Newmark integration technique both for the computation of the restoring force as well as the total response of the system. This scheme improves significantly the efficiency of the numerical integration of the equations of motion and accelerates the computational intensive Monte Carlo method. Further, statistical linearization of the hysteretic system is conducted. The agreement of the statistics of the nonlinear system response computed by the Monte Carlo method with those computed by the statistical linearization method enables the use of the latter as an efficient method for the computation of the nonlinear system response statistics in the frequency domain