Bending, buckling, and vibration analysis of functionally graded nanobeams using an inverse trigonometric beam theory

Authors

• Atteshamuddin Shamshuddin Sayyad ¹
• Yuwaraj Marotrao Ghugal ²

1. Department of Civil Engineering, SRES’s Sanjivani College of Engineering, Savitribai Phule Pune University, Kopargaon-423601, Maharashtra, India.
2. Department of Applied Mechanics, Government College of Engineering, Karad-415124, Maharashtra, India.

Abstract

In this study, an inverse trigonometric nanobeam theory is applied for the bending, buckling, and free vibration analysis of nanobeams using Eringen’s nonlocal theory. The present theory satisfies zero shear stress conditions at the top and bottom surfaces of the nanobeam using constitutive relations. Equations of motion are derived by applying Hamilton’s principle. The present theory is applied for the analysis of functionally graded material nanobeams. All problems are solved by using the Navier technique. For the comparison purpose, the numerical results are generated by using the third shear deformation theory of Reddy, first-order shear deformation theory of Timoshenko, and classical beam theory of Bernoulli-Euler considering the nanosize effects. The present results are found in good agreement with those of higher order theories.

Keywords

• Vibration
• Bending
• Buckling
• Eringen’s Nonlocal Theory
• FG Nanobeam
• Trigonometric Nanobeam Theory