Longitudinal Vibration Analysis of a Stepped Nonlocal Rod Embedded in Several Elastic Media

Abstract Purpose Mechanical properties of 1D nanostructures are great importance in nanoelectromechanical systems (NEMS) applications. The free vibration analysis is a non-destructive technique for evaluating Young's modulus nanorods and detecting defects nanorods. Therefore, this paper aims to study the longitudinal stepped nanorod embedded several elastic media. Methods based on Eringen’s nonlocal theory elasticity. governing equation obtained using Hamilton’s principle then transformed into analysis. dynamic stiffness matrix (DSM) method used assemble rod segments equations. case two-segment two media deeply investigated. Results effect changing stiffness, ratio, boundary conditions parameter examined. nano-rod spectrum dispersion relations also Conclusion results show that increasing segment ratio increases natural frequencies. Furthermore, reduces frequencies slightly at lower modes significantly higher modes.