OICC Press Journal of Solid Mechanics 2008-7683 15 5 2024 09 21 An Analytical Study on Surface Energy Effect on Free Longitudinal Vibration of Cracked Nanorods 449 468 EN Hassan Shokrollahi Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran Reza Nazemnezhad School of Engineering, Damghan University, Damghan, Iran Journal Article 2024 09 21 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.