Vibration analysis of functionally graded porous nano-beams: A comparison study

Abstract

Porous nano-beams has been widely used in macro as well as nano and micro-sized systems and devices such as biosensors, nano actuators, and nano-electro-mechanical systems. Presence of porosity in the nano-beams significantly affects the material properties and consequently the structural behavior of the nano-beams. Hence it is very important to take care of porosity effects during the modelling of nanostructures. In the present article, vibration characteristics of porous nano beams has been studied along with a comparative study between the two porosity models by taking the cosine type porosity distribution. One porosity model is based on the incorporation of porosity by reducing the average material properties of the constituents in the same amount. While second model is based on the open cell type porosity theory. The effective material properties of the nanobeams are obtained by modifying the power law model according to the different methods of porosity incorporation. The Reddy’s beam theory in conjunction with Eringen’s nonlocal elasticity theory is used to define the displacement field by taking care of size effects. Further, governing equations are derived using the Lagrange’s equation. Finite element method by considering the three noded beam element with four degrees of freedom at each node is used to solve the governing equation. In addition, the influence of porosity co-efficient, the porosity incorporation techniques, and power law index on the effective material properties and vibration characteristics of the functionally graded nano-beams has been studied. A significant influence of porosity incorporation technique on the effective material properties and non-dimensional fundamental frequency of nanobeams has been found for higher values of porosity fraction. For 20% volume of porosity, maximum 6.68% difference between the frequency is found for the considered power law index by using different porosity incorporation methods. While this difference is found 35.74% for 80% volume of porosity with the considered power law index.