In this article, curvature effects on elastic thermal buckling of double-walled carbon nanotubes under Axially compressed force are investigated using cylindrical shell model. Also, the small scale effect is taken into account in the formulation. The dependence of the interlayer van der Waals (vdW) pressure on the change of the curvatures of the inner and outer tubes at that point is considered. The effects of the surrounding elastic medium, curvature and the vdW forces between the inner and outer tubes increase the critical buckling load under thermal and Axial compression loads, while small scale effect decreases it.

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under Axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differential equation. Then Homotopy Analysis Method is employed to obtain an analytic expression for nonlinear natural frequencies. Effects of design parameters including Axial force and slenderness ratio on nonlinear natural frequencies are studied. Moreover, effects of factors of nonlinear terms on the general shape of the time response are taken into account. Combined Homotopy-Pade technique is used to reduce the number of approximation orders without affecting final accuracy. The results indicate increased speed of convergence as Homotopy and Pade are combined. The obtained analytic expressions can be used for a vast range of data. Comparison of the results with numerical data indicated a good conformance. Having compared accuracy of this method with that of the Homotopy perturbation analytic method, it is concluded that Homotopy Analysis Method is a very strong method for analytic and vibration analysis of structures.

In recent years, different damage indexes have been introduced in engineering literature. The most prominent one among other counterparts is the 1985 Park and Ang's damage index (DIPA), which demonstrates well calibration against experimental results. Hence, it has traditionally had broad application in the field of structural engineering. Commonly, in DIPA relevant parameters are assessed based on plastic-hinge approach, which is not well suited to consider the coupled response between stress resultants (Axial force and flexural moment) especially in grossly nonlinear domain. The reason is that named approach is utilized constant shape plastic moment-curvature curve, which is not capable of varying the shape throughout loading history. Another drawback of plastic-hinge method is the difficulty of representing precisely partial yielding of the cross-section. To remedy the situation, the fiber discretization technique is used in this paper. Based on the fiber discretization strategy, not only have the stiffness and strength degradation been characterized more accurately, but also the distribution of plasticity along the plastic zone has been considered. Besides, the multi-directional effect of Axial force and flexural moment is considered to assess DI parameters. Additionally, this strategy directly incorporates the effect of transverse confinement into cross sectional constitutive behaviour.

Rotor vibrations and its control is an important subject in many industries such as power plants and gas stations. When lateral vibrations of rotors during operation exceeds allowable level, a huge damage will be occurred. Surge and stall may be some common reasons of these vibrations. This paper aims to present a simple model for surge and stall and assumes that its effect as a concentrated force acting on a rotor- disk system. This is a basic and conceptual model for future investigations in this area. Therefore, the effect of a concentrated Axial force exerted on an assembled disk on a rotating shaft is investigated theoretically. Equations of motion are derived using Timoshenko beam theory. This governing equations consist of four coupled partial differential equations. Since these equations are complex, coupled and have time- varying coefficients, they are solved using a combination of Galerkin and Newmark methods. Numerical examples are analyzed as well. The accuracy of these equations is verified for a simple beam. Results indicate that the Axial load has a considerable effect on the lateral vibration amplitude of the rotor and this simple proposed model can be improved for next studies in this area.