Dynamic analysis of bi-directional functionally graded Timoshenko nanobeam on the basis of Eringen's nonlocal theory incorporating the surface effect

• Published in: Applied mathematics and computation 2021-04, Vol.395, p.125857, Article 125857
• Main Authors: Lal, Roshan, Dangi, Chinika
• Format: Article
• Language: English
• Subjects: Bi-directional functionally graded nanobeam; Gurtin-Murdoch surface elasticity theory, Eringen's nonlocal theory; Timoshenko's beam theory; Vibration characteristics
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2020.125857

•Surface theory and Eringen's nonlocal theory has been used to capture the size-effect on vibration characteristic of bi-directional functionally graded Timoshenko nanobeam.•A parametric study has been performed to examine the impact of considering surface effect together with bi-directional material distribution, nonlocal parameter, and slenderness ratio.•Effect of surface effect is more noticeable due to bi-directional variation in material properties. In this article, a nonlocal model based on the Timoshenko beam theory has been introduced for vibration response of bi-directional functionally graded moderately thick nanobeam under the influence of surface effect. Surface and nonlocal effects have been accounted using the Gurtin-Murdoch surface elasticity theory and Eringen's nonlocal theory, respectively. The material properties of the beam are changing according to the power-law distribution in both the thickness and length directions. Employing Hamilton's energy principle, the governing equations of motion and corresponding boundary conditions have been extracted. The numerical results for frequency parameter have been obtained using the differential quadrature method for three different combinations of clamped and simply supported edge conditions. The study reveals that the consideration of surface and nonlocal effects in predicting the vibration characteristics of bi-directional functionally graded shear deformable nanobeam plays an important role and can't be ignored in the analysis. The results are validated by comparing with those available in the literature.