Nonlinear flexural free vibrations of size-dependent graphene platelets reinforced curved nano/micro beams by finite element approach coupled with trigonometric shear flexible theory

Abstract

In this work, the nonlinear flexural free vibration behavior of size-dependent curved nano/micro beams with reinforcement of graphene platelets is studied using the nonlocal elasticity theory along with a trigonometric shear flexible beam theory. The governing equations through the finite element model are derived in terms of displacements using the dynamic version of principle of virtual work. The formulation extends the von-Karman model to account for both large deflections and rotations in the strain displacement relationship. Direct iterative procedure is used to solve the nonlinear eigenvalue problem. This methodological study aims to analyze the influence of various design parameters like slenderness ratio of the beam, curved beam included angle, distribution pattern of porosity and graphene platelets, nonlocal parameter, and boundary conditions on the free vibration behavior of curved nano/micro beams by studying the amplitude frequency response curves. The present work also highlights the variation in modeshapes with reference to axial/transverse directions.

Keywords:

• Finite element
• graphene platelets reinforced nanobeam
• nonlinear flexural vibration
• nonlocal analysis
• sinusoidal shear deformable theory
• size-dependent

Disclosure statement

The authors have no financial/proprietary interests in any material discussed in this article.

Additional information

Funding

The authors have no relevant financial or non-financial interests to disclose. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.