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

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 impli