Optimum addition of inerter element to tuned mass dampers for seismic control of steel structures by particle swarm algorithm

tuned mass dampers are a combination of mass, spring and dampers. tuned mass dampers are set on a specific frequency range, when the structure is subjected to external force in the desired frequency range, TMD reduce the responses of the structure by creating a force against the movement direction of the structure. The most important limitation of TMD is providing a sufficient mass ratio in order to optimally control the structure. The inerter element is an element with two terminals that can produce a force proportional to the acceleration difference created in its two terminals. One of the distinguishing features of this element compared to other structural control tools is the possibility of changing the mass matrix of the structure. Nowadays, extensive research is being done in order to combine the inerter element with structural control systems. Adding an inerter element to conventional tuned mass dampers significantly increases the efficiency of TMD and removes the limitation of TMD to provide a suitable mass ratio. The placement position of the inerter element in the control system is very important. If the inerter element is placed between two inappropriate levels in the system, it will disrupt the function of absorbing dynamic vibrations and cause the responses to intensify. In this research, the optimization of the parameters of the inerter element combination with tuned mass dampers is done using the particle optimization algorithm and with the ability to generalize to all structures