A Free Vibration Analysis of Microbeams by Modified Strain Gradient Theory

Abstract

The paper presents a model based on the modified strain gradient theory for the free vibration analysis of isotropic microbeams. The analysis includes the effects of rotatory inertia and shear deformation on natural frequencies. It takes into account the dependence of the mechanical properties of the material on the size of the microbeams. The model is sensitive to the Poisson´s ratio and its effect can be observed on the natural frequency coefficients. The numerical results developed in this paper include Timoshenko and Bernoulli - Euler microbeams considering different boundary conditions: simply supported-simply supported, clamped-free, clamped-simply supported, clamped-clamped, simply supported-free, free-free. The effects that boundary supports of the microbeams have on the natural non-dimensional frequencies are also studied. Numerical solutions are obtained using the Ritz method with sets of admissible functions that best model the boundary conditions of the microbeam. Additionally, results obtained with the classical theory and with the modified couple stress theory are also presented.