2nd Reading September 10, 2022 12:7 WSPC-255-IJAM S1758-8251 2250069 International Journal of Applied Mechanics Vol. 14, No. 5 (2022) 2250069 (24 pages) © World Scientific Publishing Europe Ltd. DOI: 10.1142/S1758825122500697 A New Theoretical Framework for Couple Stress Analysis of Reddy–Levinson Micro-Beams H. Golbakhshi * , M. R. Dashtbayazi †,§ and A. R. Saidi ‡ Department of Mechanical Engineering Faculty of Engineering Shahid Bahonar University of Kerman Kerman, Iran * golbakhshi@ujiroft.ac.ir † dashtbayazi@uk.ac.ir ‡ saidi@uk.ac.ir Received 10 April 2022 Accepted 14 July 2022 Published In this paper a new scheme, other than the modified couple stress theory (M-CST) and consistent couple stress theory (C-CST), is proposed for the analysis of micro-beams and based on the main kinematical assumptions in the beam theories, the couple-stress tensor is constrained to be skew-symmetric. This new consideration also makes it possible to revise the governing equations and boundary conditions, derived from Hamilton’s principle into a more convenient form. Then according to the third-order Reddy–Levinson beam theory, a revised couple stress model similar to the classical Timoshenko beam theory is presented in the current study. The validity of the model is demonstrated by static bending and free vibration investigations of isotropic and FG porous micro-beams subjected to a concentrated load at the mid-span. Keywords : Size effect; microstructure; couple stress theory; Reddy–Levinson beam; vari- ational principle. 1. Introduction In recent years, the micro- and nano-electromechanical systems are widely used as sensors and acutators in various applications. Among them, beam-type struc- tures are well-known for easy manufacturing, low energy consumption and very good compatibility with integrated circuits [Ferreira and Aphale, 2010]. Various characteristics of material properties and mechanical behaviors are used to develop micro-sensors and micro-acutators. As an example, the frequency shift of buckled micro-beams is used in highly sensitive pressure and gas sensors [Hajjaj et al., 2017, 2019]. It is noted that the magnetic fields create uniform transverse force on heated structures and change the stiffness. So, by evaluating the frequency shift of these § Corresponding author. 2250069-1