Mathematical Methods in Interdisciplinary Sciences

12Dynamic Behavior of Nanobeam Using Strain Gradient Model

Subrat Kumar Jena, Rajarama Mohan Jena, and Snehashish Chakraverty

Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, 769008, India

12.1 Introduction

Dynamic analysis of nanostructures is very crucial for engineering design of several electromechanical devices such as nanoprobes, nanooscillators, nanosensors, etc. This analysis is very fundamental as the experimental study in nanoscale is very tedious and expensive. Also, classical mechanics fails to address the nanoscale effect. In this regard, several nonclassical theories have been introduced by researchers to address the small‐scale effect. These theories include strain gradient theory [1], couple stress theory [2], modified couple stress theory [3], micropolar theory, and nonlocal elasticity theory [4]. Investigations related to the dynamical analysis of beams, membranes, nanobeams, nanotubes, nanoribbons, etc., are reported in the literature [5–14].

Akgöz and Civalek [15] analytically studied the static behavior of the Euler–Bernoulli nanobeam under the framework of the modified strain gradient theory and modified couple stress theory. They also investigated the influence of size effect and material parameters on the static response of the beam. Akgöz and Civalek [16] again developed a size‐dependent higher order shear deformation beam using modified strain gradient theory, which can address both the microstructural and shear ...