Topological entropy and geometric entropy and their application to the horizontal visibility graph for financial time series

Seismic wave control is very important both in civil and mechanical engineering. Common passive methods for isolating a building or a device include base isolators and tuned mass dampers. In the present paper, a time-varying controllable spring is considered as a vibration isolator for a linear mechanical system. The controller works as follows: When the seismic movement is active, the velocity of the moving mass is monitored as the reference velocity. When such reference velocity is positive, the stiffness is reduced; when it is negative, the stiffness is increased. Numerical investigations show that the controller is capable of filtering seismic excitation close to the natural frequency of the controlled system and reducing the total seismic energy transfer up to 5 times. The role played by the gravity in the active vibration filtering is pointed out by showing that no filtering action can be observed in gravity-free simulations. Moreover, control effectiveness has been proven for a measured seismic signal, showing its robustness in presence of noise.