Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model.pdf

Appl. Math. Mech. -Engl. Ed., 35(7), 875–886 (2014) Applied Mathematics DOI 10.1007/s10483-014-1835-9 and Mechanics c Shanghai University and Springer-Verlag Berlin Heidelberg 2014 (English Edition) Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model∗ 1 2 1 B. AMIRIAN , R. HOSSEINI-ARA , H. MOOSAVI (1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran; 2. Department of Mechanical Engineering, Payame Noor University, Tehran 19395-3697, Iran) Abstract This paper deals with the free vibration analysis of circular alumina (Al O ) 2 3 nanobeams in the presence of surface and thermal effects resting on a Pasternak foun- dation. The system of motion equations is derived using Hamilton’s principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equa- tions which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams wit