Size-dependent nonlinear modal dynamics in MEMS micro rotors

Abstract

Micro-rotor-dynamic systems are vital for rotor-based MEMS technologies, encountering nonlinear dynamics and size-dependent effects due to their small-scale, challenging optimization efforts. This study introduces a novel mathematical model that effectively captures the nonlinear modal dynamics and size-dependent influences in micro rotor-dynamic systems. By employing a non-classical approach-specifically, strain gradient theory-size dependencies are incorporated into the model. The equations of motion is obtained using extended Hamilton’s principle, which is solved using a perturbation technique-method of multiple scales. Extensive numerical simulations and analytical techniques are utilized to explore size-dependent nonlinearities, focusing on dynamic responses, frequency spectra, and phase portraits. In addition to that, parametric analyses of disk location, spin speed, disk mass, and disk mass moment of inertia are conducted to assess their impacts on the modal behavior of micro-dynamic systems. The results are rigorously validated using the Runge–Kutta(4,5) method, ensuring precision and accuracy. This research significantly advances the understanding of nonlinear modal dynamics in micro-scale systems and provides valuable insights for optimizing the design of rotating MEMS devices, effectively addressing scaling challenges.