Dynamic Characterization and Design of Scotch Yoke Inerter with Adjustable Inertance for Seismic Isolation

Abstract

The scotch yoke inerter (SYI) is a new geometrically nonlinear vibration isolator with a smaller maximum transmissibility than linear inerter systems. The influence of internal friction and the damping effect on the response of the SYI system for seismic isolation can be significant and needs to be studied. In this study, a small-scale SYI is designed and tested, and an accurate model of SYI is developed for describing its dynamic behavior. Then, the motion equation of the coupled structure-SYI system is established, and several dynamic analyses are studied, including the amplitude-frequency response, the critical excitation amplitude, the backbone curve, the peak response, the starting frequency, and the linearization design, and many fitting expressions for engineering applications are proposed. Finally, the vibration isolation performance of SYI is investigated when friction and damping effects are considered or not, using a single-degree-of-freedom system and a building structure as examples. For harmonic excitations, the maximum transmissibility of the SYI system is superior to that of the linear inerter system, and its advantage becomes more obvious as the excitation amplitude increases. Its seismic isolation effect is slightly better than that of a linear inerter for seismic excitations, where the SYI considering friction and damping effects is better. A scotch yoke inerter is a geometrically nonlinear inerter that is simple to construct, easy to implement, and has the advantage of variable inertance. The variation of inertance is reflected in two aspects: first, its nominal inertance can be changed by adjusting the location of the pin; second, its dynamic inertance is related to its deformation, which can provide greater negative stiffness effects for larger external excitations. The precise and simplified output force model of the scotch yoke inerter is provided, which can be applied to the calculation and verification of the output force in the design of scotch yoke inerters. Fitting expressions for the critical excitation amplitude, starting frequency, and linearization design are proposed, which can provide a theoretical basis for the application of scotch yoke inerters in base-isolated structures. Compared with traditional linear inerters, scotch yoke inerters have a better isolation control effect, and this control effect can be further improved by making reasonable use of the internal friction and the damping in SYI.