Pendulum tuned mass damper (PTMD) with geometric nonlinear dampers for seismic response control

In engineering applications, the geometric nonlinear (GN) arrangement of pendulum-tuned mass dampers (PTMDs) may induce the damping force to deviate from its intended state. Therefore, this study extends the scope of the structural control strategy by introducing a pendulum-tuned mass damper considering geometric nonlinear dampers (GND). Specifically, the damper developed in this study, termed PTMD with GND, is an inconspicuous pendulum-type tuned mass damper with different GN settings in the initial state. A nonlinear mathematical model of the PTMD with GND is developed, identifying its significant nonlinear characteristics, particularly the "unavailable" locations. The stochastic linearization method (SLM) is adopted to simplify the nonlinear model using the Kanai-Tajimi modified spectrum. The SLM agrees well with the numerical results obtained using the Monte Carlo simulation method. Furthermore, the control strategy of PTMD with GND is proposed with the consideration of filtered random excitation. Several numerical cases have been conducted to investigate the availability of PTMD with GND and the proposed optimal design strategy under 178 real seismic excitations. The results show that the PTMD with GND is nearly as effective as the ideal transitional TMD in mitigating the seismic response of the primary structure and more effective than the inverted rough linear adjustment. It can be concluded that the proposed optimal design strategy for the PTMDs with GND efficiently suppressed the structural vibration through multiple performance indices and used the nonlinearity of the damping mechanism of the GND to provide a sufficient damping energy dissipation effect adaptively.