# Nonlinear Vibration Isolation via a NiTiNOL Wire Rope
## 1 Introduction
Wire ropes produce nonlinear damping due to inner frictions, and the damping is rate-independent. The wire ropes have been adopted in nonlinear dampers. [PERSON] et al. [33] studied an asymmetric Stockbridge damper and the steel wire ropes are utilized as cantilever beams. [PERSON] et al. [34] proposed a tuned mass damper using steel wire ropes with both ends clamped, and the nonlinear damping force was characterized with a Bouc-Wen model. Compared to steel wire ropes, NiTiNOL wire ropes are more efficient in energy dissipation due to the phase transitions of the material. [PERSON] et al. [35; 36] proposed a vibration absorber accomplished with NiTiNOL-steel wire rope assemblies and revealed a pinching effect derived from NiTiNOL. [PERSON] et al. [37] integrated a NiTiNOL wire rope with a nonlinear energy sink to improve energy dissipation. [PERSON] et al. [38] adopted a NiTiNOL wire rope for structural vibration suppression. With the wire ropes styled as a ring, the load capacity was enhanced and showed promise for vibration isolation. [PERSON] et al. [39] studied the shear cyclic behavior of polycal wire rope isolators. [PERSON] et al. [40] attached a NiTiNOL wire rope to a ring-type isolator and enhanced the isolation performances. [PERSON] et al. [41] investigated a compact nonlinear isolator with initially curved wire ropes. The ring-type or semi-ring-type isolator presented an asymmetric restoring force, and it was not conducive to vibration isolation. We [42] have proposed a nonlinear isolator with compliant mechanisms and straight steel wire ropes with a linear spring enhancing the load capacity and verified the superiority of the symmetric restoring force for vibration isolation. An isolator with straight NiTiNOL wire ropes showed promise for exhibiting a symmetric restoring force and stronger damping effects. The pinching effect of NiTiNOL endowed the isolator with more nonlinear behaviors. It is essential to perform a comprehensive comparison of the nonlinear characteristics and the isolation performances between the isolators with steel wire ropes and those with NiTiNOL wire ropes. Furthermore, the stiffness and damping of the isolators with wire ropes are not only nonlinear but also non-monotonically varying. This leads to the unique issue of \"the most suitable excitation amplitude\" for the isolators. The aim of this research was to reveal the parameter influences on the most suitable excitation amplitude. In this paper, we propose an isolator with a NiTiNOL wire rope with both ends and the middle part clamped. The isolator exhibited nonlinear stiffness and nonlinear damping due to geometric constraints, frictions, and phase transitions of the material. The isolator was modeled with a modified Bouc-Wen model and analyzed with a harmonic balance method. A comparison was made between isolators with steel and those with NiTiNOL wire rope. The most suitable excitation amplitude and the parameter influences were revealed. The paper is organized as follows. The nonlinear isolator and its dynamic model are introduced in Section 2. The harmonic balance analysis and the stiffness and damping ratio analysis are presented in Section 3. The numerical simulation results are presented in Section 4 with further discussion. Conclusions are drawn in Section 5.