Linear equivalence for motion amplification devices in earthquake engineering

Motion amplification devices utilized to amplify the motion of dampers can effectively improve the energy dissipation performance of dampers to reduce seismic responses of engineering structures. This study systematically develops a linear equivalence theory for motion amplification devices based on the proposed equivalent Maxwell model. This equivalent model accurately predicts the supplemental damping effect provided by motion amplification devices without approximation. Also, the equivalent model is capable of quantifying the amplification effect of motion amplification devices by means of deriving the analytical expressions of the equivalent damping and stiffness coefficients, which reveal that motion amplification devices simultaneously enhance the original damping and stiffness coefficients by ${\overline{\alpha }}^2$, where $\overline{\alpha }$ is the proposed rigidity motion amplification factor. The representative value of member stiffness $k_p$ is developed to comprehensively evaluate the supporting stiffness of motion amplification devices. All the achieved results strongly support that the proposed linear equivalence theory provides a generic paradigm to explain, measure and compare different types of motion amplification devices in terms of their supplemental damping effects, and hence helps researchers and engineers gain valuable insight into the dynamic properties of motion amplification devices.