Nanomechanical resonators have demonstrated significant potential in sensing technologies due to their exceptional responsiveness to external stimuli. However, in most cases, dynamics of the device for various applications have been studied under high- vacuum conditions to suppress viscous damping and enhance signal fidelity. Furthermore, sensing methodologies have predominantly focused on tracking shifts in fundamental resonance frequency induced by analytical interaction or environmental changes. In this work, we studied the multimodal behavior of cantilever-based resonators under ambient atmospheric conditions, revealing that there exists a critical mode number at which the resonator exhibits maximum $Q$-factor. This optimum mode is shown to be a function of geometric configuration (length), speed of sound in air, and fundamental resonance frequency of the resonator. Furthermore, in our comprehensive assessment of the first three flexural eigenmodes of the resonator, with an emphasis on temperature-dependent variation in $Q$-factor and frequency, we show that the critical mode exhibits the best noise equivalent temperature difference of 4 mK with moderate vibrational amplitude. These findings are further corroborated by rigorous theoretical modeling and numerical simulations, offering insights into multimodal response characteristics of resonators under thermally influenced atmospheric environments.

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• Viscosity
• Direct numerical simulations
• Euler equation
• Homodyne & heterodyne detection
• Lagrangian flow field
• Navier-Stokes equation
• Optical techniques
• Resonance techniques