Vibrations of defected local/nonlocal nanobeams surrounded with two-phase Winkler–Pasternak medium: non-classic compatibility conditions and exact solution

Abstract

Dynamics of cracked nanobeams surrounded by size-dependent Winkler –Pasternak medium are investigated utilizing the two-phase local/nonlocal elasticity, as a paradox-free form of the nonlocal theory, in order to considering the nonlocal effect on both of the defected nanobeam and the two-parameter elastic medium. To this aim, governing equations as well as all boundary and compatibility conditions including the constitutive ones corresponding to the two-phase cracked nanobeam and the two-phase medium are derived. The exact solution is presented by combining the governing equations and satisfying all higher order boundary conditions. To confirm the validity of the present formulation and results, several comparison studies are established in detail. The influences of different parameters such as local phase fraction factor, crack characteristics and nonlocal parameter on vibration frequencies are discussed. The present results reveal that applying size dependency on the Winkler –Pasternak medium surrounding the nanobeams leads to significant changes in the vibration frequencies of both intact and defected nanobeams. Also, impact of nonlocal effects can increase or decrease in the defected nanobeams depending on the crack characteristics. This research can be useful to achieve more accurate predictions in vibration analysis of defected nanostructures embedded in two-parameter medium.

KEYWORDS:

• Two-phase local/nonlocal elasticity
• vibration analysis
• cracked nanobeam
• exact solution
• constitutive compatibility conditions
• size-dependent Winkler–Pasternak medium

Disclosure statement

No potential conflict of interest was reported by the author(s).