Large Amplitude Free Vibration Analysis of Isotropic Curved Nano/Microbeams Using a Nonlocal Sinusoidal Shear Deformation Theory-Based Finite Element Method

Abstract

In this investigation, the nonlinear flexural free vibration characteristics of size dependent curved isotropic nano/microbeams are studied using the nonlocal elasticity theory along with the sinusoidal shear deformation theory (SSDT). Based on Hamilton’s principle, the governing equations are derived in terms of generalized displacements using finite element approach. The formulation by extending the von-Karman model accounts for both large deflections and rotations in the strain displacement definition. Direct iterative procedure is used to solve the nonlinear problem through eigenvalue procedure. This investigation aims to study the effect of various design parameters like slenderness ratio of the beam, curved beam included angle, nonlocal parameter, and boundary conditions on the amplitude–frequency response obtained from the free vibration behavior of curved nano/microbeams. This study is very useful to designers for optimal design of nano/microsystem involving structural elements of the beam type.