## 1 Introduction  
The global transition toward green energy solutions has driven offshore wind power installations into increasingly deeper and more remote marine environments [1]. While this expansion promises greater energy yields, it introduces significant engineering challenges, particularly concerning low-frequency vibrations induced by extreme wave conditions and complex hydrodynamic interactions [2]. These vibrations not only compromise platform stability and energy conversion efficiency but also pose long-term structural integrity risks through fatigue accumulation [3]. Effective vibration mitigation strategies are therefore critical for ensuring the reliability and longevity of offshore renewable energy infrastructure [1, 2, 3, 4]. Various vibration control approaches have been developed to meet different mitigation requirements, including passive [5], semi-active [6], and active control methods [7]. While semi-active and active strategies can generate substantial control forces and achieve superior performance, they demand significant energy input (e.g., piezoelectric materials or electromagnetic components) and involve costly mechatronic systems with high maintenance requirements. In contrast, passive vibration control offers superior stability and cost-effectiveness, making it particularly attractive for engineering applications [5, 8]. The three primary passive methods include dampers for energy dissipation [9; 10; 11; 12], tuned mass dampers for energy transfer [13], and isolation platforms for energy isolation [14]. Among these, vibration isolation systems stand out for their broad effective frequency range and exceptional high-frequency attenuation performance. These advantages have established isolation platforms as the predominant passive control solution in practical offshore applications. Vibration isolation systems serve dual critical functions in this context, protecting sensitive equipment from environmental vibrations and preventing machinery-induced vibrations from propagating through supporting structures [5]. The fundamental challenge lies in attenuating transmitted forces while maintaining system stability, particularly in the low-frequency range characteristic of ocean wave excitations [2]. Conventional linear isolation systems face inherent limitations in this regard, as achieving sufficient low-frequency attenuation typically requires reducing system stiffness, which in turn compromises static load-bearing capacity. This trade-off has motivated the development of advanced isolation technologies capable of simultaneously providing high static stiffness for structural support and low dynamic stiffness for effective vibration isolation [14]. Recent advances in quasi-zero stiffness (QZS) isolators have demonstrated particular promise for ultra-low frequency vibration isolation in floating platforms [7]. By incorporating negative stiffness elements with carefully tuned linear springs, these systems achieve high-static-low-dynamic stiffness (HSLDS) characteristics that effectively decouple static and dynamic performance requirements [15]. [PERSON] et al. [16] summarized the recent advancements in QZS-based vibration isolators and isolation platforms, while also categorizing and synthesizing the various approaches to achieving QZS characteristics. Theoretical and experimental studies have validated various implementations, including oblique springs or pre-buckled beam configurations that provide tunable negative stiffness [17; 18; 19; 20; 21], magnetic arrangements offering contactless stiffness modulation [6; 22; 23], bio-inspired designs mimicking natural vibration-damping structures [24; 25; 26; 27; 28; 29; 30; 31], cam mechanisms [32; 33], and metamaterials [34]. The effectiveness of QZS isolators stems from their nonlinear stiffness characteristics, which enable significant extension of the effective isolation bandwidth, maintenance of high static load capacity, and improved stability compared to conventional low-frequency isolators.