Buckling of double functionally-graded nanobeam system under axial load based on nonlocal theory: an analytical approach

Buckling treatment of a bonded compressed double-FG nanobeam system (DFGNBS) is studied in this paper based on Eringen’s nonlocal elasticity theory and Euler–Bernoulli beam model. Differential equations and boundary conditions are obtained using Hamilton’s principle, and the nonlocal theory is employed to derive differential equations in small scale. The material properties are assumed to be functionally graded (FG) along the thickness direction. The synchronous, asynchronous and stationary-type buckling are considered in detail. Results reveal that the small-scale effects are higher with increasing values of nonlocal parameter for the case of in-phase (synchronous) buckling modes in compare to the out-of phase (asynchronous) buckling modes. Increasing the stiffness of the coupling elastic medium double-FG nanobeam system decreases the small-scale effects during the out-of-phase (asynchronous) buckling modes. A detailed parametric study is conducted to investigate the influences of nonlocal parameter, higher modes, spring constant and distributed coefficient of DFGNBS. Some illustrative examples are also stated to verify the present formulation and solutions which showed an excellent agreement.