Dynamic Analysis and Performance Evaluation of Inerter Fractional Nonlinear Quasi-Zero Stiffness Isolator on a Multi-Span Bridge Under Moving Load

In this paper we propose a new vibration isolator system, which combines the advantagesof a quasi-zero stiffness (QZS) isolator, a damper exhibiting fractional propertiesand an inerter, to reduce the vibrations of a multi-span continuous beam bridge excitedby moving loads. The inerter produces a fictitious mass amplification effect toimprove the controller performance and the fractional order takes into account the previousstate of the viscoelastic material. After formulating the dynamics equation usingbeam theory, the amplitude response is determined analytically using the averagingmethod. The results obtained from the analytical study are validated using the directnumerical simulation method (Newton-Leipnik method). By comparing the isolationperformance of the FQZS (fractional quasi-zero stiffness) isolator and the IFQZS (inerterfractional quasi-zero stiffness) isolator, it is shown that the addition of inertancecan significantly suppress the tendency of the curve to slope to the right, allowing us tohave a wider isolation frequency range on force transmissibility while improving theeciency of the isolator. One also shows that increasing the fractional parameter contributesto a decrease in the vibration amplitude of the structure, the amplitude of theforce transmitted and the area in which unstable solutions appear. However, beyond acertain value of the fractional parameter, we observe an increase in the latter. In orderto further extend the study, bifurcation diagram, phase portrait, time history and powerspectral density are explored.