## 1 Introduction  
It is known that CNTs are one of the most promising reinforced materials in many engineering applications, such as satellite antennas, nanoelectronics, nanosensors, automotive, aircrafts, turbine blades, robot arms, and so on. Various models of CNT along with non-classical theories have been proposed in the last years to study vibration, buckling, or bending problems. Composites based on nanotubes offer strength-to-weight ratios. NASA and companies such as Samsung or NEC have invested tremendously and demonstrated product quality devices utilizing CNT for field-emission display. CNTs are remarkably stiff and strong, conduct electricity, and are projected to conduct heat even better than diamond. Also, they can be implanted without trauma at the sites where a drug is needed, slowly releasing a drug over time. Nonlinear vibration, nonlinear bending, and post-buckling were carried out by [PERSON] and [PERSON] [1] for SWCNTs resting on an elastomeric substrate in thermal environments. The governing equation was solved by a two-step perturbation technique in an explicit form that was easy to program and produced full, nonlinear responses. The exact solutions of nonlinear thermal bifurcation buckling behavior of the beams made of a symmetric SWCNT with surface-bonded piezoelectric layers were achieved by [PERSON] et al. [2]. Three types of boundary conditions were assumed for the beam, and the eigenvalue solution was performed to obtain the critical temperature load. By means of the Navier solution method, [PERSON] and [PERSON] [3] analyzed the vibration, bending, and buckling of CNTRC simply supported composite beams resting on a Pasternak elastic foundation. The beams were reinforced by some models of CNT distribution in the polymeric matrix. The generalized differential quadrature method was proposed by [PERSON] and [PERSON] [4] for nonlinear vibration and post-buckling analysis of a variable cross-section composite beam with various symmetric and asymmetric lay-ups. Different combinations of boundary conditions were studied, and natural frequencies were determined by means of the Picard iterative method. The maximum frequency and buckling loads occurred in the case of a clamped-clamped beam, but the minimum took place for a hinged-hinged beam. The finite element method was employed by [PERSON] et al. [5] in the study of the dynamic response of a laminated composite beam with six and ten degrees of freedom. The effects of inertial, Coriolis, and centrifugal forces were evaluated using [PERSON]'s scheme. [PERSON] et al. [6] considered a unified, high-order model for the size-dependent bending and buckling analysis of the nanobeams based on an NSGT. For the buckling and bending problem of a simply supported nanobeam, the [PERSON]'s method was proposed. For Euler-Bernoulli and Timoshenko beam models, it was found to have a remarkable size effect. Based on the first-order shear deformation elasticity theory, [PERSON] et al. [7] found an exact solution for the free vibration of functionally graded CNTRC beams with arbitrary boundary conditions. For the displacements and rotational components of the beams, a linear combination of the standard and modified Fourier series was proposed. The length-scale effect of the nonlinear response of an electrically actuated CNT was used by [PERSON] et al. [8] to examine the interatomic long-range force and the nanostructure deformation mechanism. They derived the differential quadrature method to discretize the governing equations of the nanoactuator and the nonlinear response. Based on the Haar wavelet discretization method, [PERSON] and [PERSON] [9] investigated the nonlinear vibration of the CNTRC beam resting on a nonlinear elastic foundation in a thermal environment. The initial thermal stress due to uniform temperature rise was studied. [PERSON] et al. [10] employed the motion of a Timoshenko beam under the nonlocal elasticity theory, including the free vibration, buckling, and bending behaviors of functionally graded CNT nanobeams, considering the small-scale effect.