Nonlocal vibration of carbon/boron-nitride nano-hetero-structure in thermal and magnetic fields by means of nonlinear finite element method

Abstract

Hybrid nanotubes composed of carbon and boron-nitride nanotubes have manifested as innovative building blocks to exploit the exceptional features of both structures simultaneously. On the other hand, by mixing with other types of materials, the fabrication of relatively large nanotubes would be feasible in the case of macroscale applications. In the current article, a nonlinear finite element formulation is employed to deal with the nonlocal vibrational behavior of carbon/boron-nitride nano-hetero-tubes in the presence of magneto-thermal environment. Euler–Bernoulli beam model in conjunction with the Eringen’s nonlocal theory of elasticity is adopted to derive the governing equation of motion. In order to conduct a nonlinear frequency analysis, the von-Kármán nonlinearity associated with moderate rotations is also considered. It is well known that temperature gradients can significantly change the dynamic behavior of nanotubes. On the other hand, the coefficients of thermal expansions of carbon and boron-nitride nanotubes are quite different that may affect the structural stability of hybrid nanotubes. Hence, to explore the vibration characteristic of such composite structures, the influence of magneto-thermal environment is also taken into account. Finally, the eigenvalue analysis is performed to exhibit the nonlinear mode shapes and natural frequencies of the system due to initial displacement. It is expected that the recognition of dynamic behavior of such hybrid nanotubes may open the doors to the creative design of next-generation nano-devices.

A review on recent research studies on vibration analysis of fluid-conveying nanotubes

“…As a result, at smaller deflection values, there may be no need to adopt the higher-order non-local strain gradient theories [60]. Sedighi et al [61] simultaneously considered the impacts of length ratio, size dependence, magnetic field, and temperature environment on the nonlinear vibrational properties of composite CNT/BNNT. Figure 4 depicts a doubly clamped nano-heterostructure composed of two different types of tubular materials.…”

“…As a result, the effect of the magneto-thermal environment is also considered while investigating the vibration characteristics of such composite structures. Sedighi et al [61] demonstrated that when the contribution of the boron-nitride section is dominant, the location of the greatest amplitude would shift to the left when considering larger temperature gradients. In addition, they found that the configurations of the non-linear mode forms are substantially influenced by the high-temperature environment.…”

A new eigenvalue problem solver for thermo‐mechanical vibration of Timoshenko nanobeams by an innovative nonlocal finite element method

“…The studies on the static and dynamic analyses with nonlocal elasticity of beams [31][32][33][34][35][36][37][38][39][40][41][42][43][44] and rods [45][46][47][48][49][50][51] have led to an understanding of the mechanical behaviors of atomic-scaled structures. Moreover, the thermal vibration 52 and buckling 53 of Euler-Bernoulli beams, thermal vibrations of Timoshenko beams, 54,55 and vibration of Rayleigh beam axially loading and lying on two-parameter elastic foundation 56 are studied.…”

On the nonlocal bending problem with fractional hereditariness

“…Small-scale devices [1][2][3][4], biological and bioinspired materials [5][6][7], advanced porous nanostructures [8,9], self-healing matter [10], hierarchical and periodic structures [11,12], new-generation of complex composites [13][14][15] require sophisticated methodologies and advanced models to predict their mechanical behavior. Usually, classical models of local continuum elasticity are not accurate enough to simulate the mechanical behavior of these nonconventional structural elements.…”