# Vortex-Induced Micro-Cantilever Vibrations with Small and Large Amplitudes in Rarefied Gas Flow
## 1 Introduction
The implications of VIV are profound, as they not only affect structural integrity but also pose risks to safety and environmental sustainability, particularly in offshore oil and gas operations [17; 11]. Recent advancements in numerical simulations and experimental studies have enhanced the understanding of VIV, enabling engineers to develop effective suppression strategies or to use this phenomenon. Techniques such as the use of vortex generators and dynamic vibration absorbers have shown promise in mitigating the adverse effects of VIV on structures [18; 19]. Furthermore, ongoing research continues to explore the influence of various parameters, including flow conditions and structural characteristics, on the vibration response, thereby contributing to the development of more resilient designs [20; 21]. As the field progresses, the integration of these findings into engineering practices will be crucial for ensuring the safety and longevity of structures exposed to vortex-induced vibrations. More specifically, this is the case when VIVs are connected with micro-structures. When a micro-cantilever is placed in a flow field where vortex shedding occurs, the resulting oscillations can be harnessed for energy-harvesting applications. Studies have shown that piezoelectric materials integrated into cantilever structures can convert the mechanical energy from VIV into electrical energy, demonstrating the potential for practical applications in energy harvesting from ambient flows [22; 23]. Overall, the interaction of rarefied gas flow with micro-cantilevers presents significant challenges spanning theoretical modelling, experimental validation, and practical implementation. An important part of our approach is using the DSMC method to model the rarefied gas flow around the micro-elastic beam. Our group was the first to adopt the DSMC method for accurately capturing non-equilibrium phenomena in micro-cantilever fluid-structure interactions, as first demonstrated in our works [4; 5; 6]. More recently, [PERSON] et al. [24] applied DSMC-based FSI to atmospheric ice particles in post-shock hypersonic conditions, where dynamic, brittle fracture necessitates modelling beyond the continuum regime. They specifically emphasized the importance of DSMC in capturing non-continuum effects that current continuum-based FSI approaches cannot reproduce. These recent innovative studies highlight DSMC's critical role in bridging the gap where conventional continuum methods fail, such as Navier-Stokes equations, and continued progress in this domain promises further micro-cantilever design and performance innovations. Our previous study [6] investigated a rarefied gas flowing past a cantilever beam oriented normally to the free stream, forming a Karman vortex street. Using a linear beam model, we found that if the vortex-shedding frequency is close to the natural frequency of the cantilever, large body motions are observed, and the structure undergoes near-resonance vibration resonance. These findings suggest opportunities to develop micro-devices, especially in scenarios where measuring or experimenting with extremely small, fast processes is challenging. In this new paper, we expand that work by comparing linear and nonlinear cantilever models in the same resonance zone. The aim is to investigate the sensitive region where differences between linear and nonlinear models are expected to become more notable. This work will provide deeper insight into nonlinear and non-equilibrium phenomena and models at the micro-scale, thus advancing the development of precise vibrational dynamics in micro-devices operating under rarefied gas flows.