An Analytical Study on Surface Energy Effect on Free Longitudinal Vibration of Cracked Nanorods

Journal of Solid Mechanics

مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 04 شهریور 1402

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2023.1987288.1778

نویسندگان

H Shokrollahi^{* 1}؛ R Nazemnezhad²

¹Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

²School of Engineering, Damghan University, Damghan, Iran

چکیده

The present work analytically studies the free longitudinal vibration of nanorods in the presence of cracks based on the surface elasticity theory. To this end, governing equations of motion and corresponding boundary conditions are obtained using Hamilton’s principle. Due to considering the surface stress effect, as well as the surface density and the surface Lamé constants, the obtained governing equations of motion become non-homogeneous. The non-homogeneous governing equations are solved using appropriate analytical methods, and the natural frequencies are extracted. To have a comprehensive research, the effects of various parameters such as the length and radius of the nanorod, the crack severity, the crack position, the type of boundary condition, and the values of surface and bulk material properties on axial frequencies of the nanorod are investigated. Since this work considers the effects of all surface energy parameters, it can be claimed that it is a comprehensive study in this regard.

کلیدواژه‌ها

Cracked nanorod؛ Longitudinal vibration؛ Surface energy