On dynamic analysis of nanorods

In the present study, longitudinal free vibration behaviors of one-dimensional nanostructures with various boundary conditions are investigated based on Eringen's nonlocal theory. The governing differential equation of motion is analytically solved for a number of different boundary conditions like clamped, free, attached mass and/or spring. It is noted that some of these solutions for the nonlocal frequencies of nanorods with attachments ones are the first in the literature. Effects of nonlocal parameter, attachments, boundary conditions, and length on the natural frequencies of nanorods are studied in detail. It can be emphasized that the inclusion of attachments decreases the longitudinal frequencies of nanorods, especially in higher modes.