Size-Dependent Torsional Dynamics of Rectangular Microrods: A Modified Couple Stress Theory Approach

Articles in Press

Document Type : Original Article

Authors
Farshad Khosravi 1
Seyed Amirhosein Hosseini 2
Babak Alizadeh Hamidi 3
1 Department of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran
2 Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University, Buein Zahra, Iran
3 Department of Mechanical Engineering, University of Bonab, Bonab, Iran
10.22034/ijicmes.2025.547353.1002
Abstract
This study presents a comprehensive investigation into the torsional vibration behavior of rectangular microrods using modified couple stress theory (MCST) to capture size-dependent effects. Unlike previous studies focused on circular cross-sections, we develop a novel analytical model for noncircular microrods with clamped-clamped (C-C) and clamped-disk (C-D) boundary conditions. The governing equations are derived via Hamilton’s principle and solved using Galerkin’s method, incorporating the material length scale parameter to account for microscale effects. Key findings reveal that: Increasing the material length scale parameter enhances torsional stiffness, raising natural frequencies by up to 35% for C-C boundary conditions. Aspect ratio significantly influences vibrational response: horizontal configurations exhibit 20% higher frequencies than vertical ones. Attached disk mass reduces frequencies by 50% under C-D boundary conditions, demonstrating critical design implications for MEMS/NEMS applications. Validation using silicon microrods confirms theoretical predictions, bridging the gap between continuum mechanics and microscale behavior. This work provides a foundational framework for optimizing microrod-based sensors and actuators in nanotechnology and biomedical devices.
Keywords
Modified couple stress theory
Torsional vibration
Rectangular microrods
Size effect
MEMS/NEMS
Analytical modeling
International Journal of Innovative Computational Methods in Engineering Sciences

Articles in Press, Accepted Manuscript
Available Online from 02 October 2025