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This study investigates influence of fringing field effect on the voltage dependent behavior of electrostatically actuated micro-beams. For this purpose, the size dependent beam model is used. Strain gradient formulation is utilized to consider size effects. The effect of fringing field effect on the beam's behavior is investigated and it is shown that lack of considering the fringing field effect in the formulation of the problem may lead to considerable error in predicting the size dependent micro-beams behavior under the effect of electrostatic actuation. The results of this research can be used for safe and stable design of electrostatically actuated micro-beams  

This paper presents a nonlocal strain gradient theory for capturing size effects in buckling analysis of Euler-Bernoulli nanobeams made of threedimensional functionally graded materials. The material properties vary according to any function. These models can degenerate to the classical models if the material length-scale parameters is assumed to be zero. The Hamilton's principle applied to drive the governing equation and boundary conditions. Generalized differential quadrature method used to solve the governing equation. The effects of some parameters, such as small-scale parameters and constant material parameters are studied. © 2022 PAGEPress Publications. All rights reserved  

Conventional continuum theory does not account for contributions from length scale effects which are important in modeling of nano-beams. Failure to include size-dependent contributions can lead to underestimates of deflection, stresses, and pull-in voltage of electrostatic actuated micro and nano-beams. This research aims to use nonlocal and strain gradient elasticity theories to study the static behavior of electrically actuated micro- and nano-beams. To solve the boundary value nonlinear differential equations, analogue equation and Gauss–Seidel iteration methods are used. Both clamped-free and clamped–clamped micro- and nano-beams under electrostatical actuation are considered where... 

In this paper, a size-dependent formulation is presented for vibration analysis of micro-end mill tool. The formulation is developed based on the strain gradient elasticity theory in order to enhance the modeling capability of micro-size structures. Due to stubby geometry of micro-tool, the shear deformation and rotary inertia effects are considered in the derivation of equations. Hence, based on the strain gradient Timoshenko beam theory, the extended Hamilton's principle is used to formulate a detailed dynamical model of the rotating micro-tool. The dynamical model includes a set of partial differential equations with gyroscopic coupling produced due to the spindle rotation. The governing... 

In this paper, a size-dependent formulation is developed for Timoshenko beams made of functionally graded materials (FGMs). The developed formulation is based on the strain gradient theory; a non-classical continuum theory able to capture the size-effect in micro-scaled structures. Five new equivalent length scale parameters are introduced as functions of the constituents' length scale parameters. It is shown that the size-dependent static and dynamic behavior of FG micro-beams can be described using these equivalent length scales. The governing differential equations of motion and both classical and non-classical sets of boundary conditions are derived for the proposed strain gradient FG...