The dynamic instability of single-walled carbon nanotubes (SWCNT), double-walled carbon nanotubes (DWCNT) and triple-walled carbon nanotubes (TWCNT) embedded in an elastic medium under combined static and periodic axial loads are investigated using Floquet–Lyapunov theory. An elastic multiple-beam model is utilized where the nested slender nanotubes are coupled with each other through the van der Waals (vdW) interlayer interaction. Moreover, a radius-dependent vdW interaction coefficient accounting for the contribution of the vdW interactions between adjacent and non-adjacent layers is considered. The Galerkin’s approximate method on the basis of trigonometric mode shape functions is used to reduce the coupled governing partial differential equations to a system of extended Mathieu-Hill equations. Applying Floquet–Lyapunov theory, the effects of elastic medium, length, number of layers and exciting frequencies on the instability conditions of CNTs are investigated. Results show that elastic medium, length of CNTs, number of layer and exciting frequency have significant effect on instability conditions of multi-walled CNTs. پرونده مقاله

In this paper, based on the nonlocal Timoshenko beam theory, a nonlinear model is presented for the vibrational behavior of carbon nanotubes (CNTs) embedded in elastic medium in thermal environment. Using the Timoshenko beam theory and nonlocal elasticity of Eringen, the influences of rotary inertia, transverse shear deformation and small scale effect are taken into account. To model the interaction forces between walls, whether adjacent or non-adjacent, the van der Waals interlayer interactions are considered. The harmonic balance method (HBM) is used for the solution of the set of nonlinear governing equations and the frequency function of the system for the simply-supported boundary conditions is derived. Compared to the incremental harmonic balance method which has been employed in the previous studies, the HBM is simpler and has a reasonable accuracy. The effects of geometrical parameters of nanotubes such as the number of walls, the ratio of length to outer diameter and environmental conditions such as elastic medium modulus, temperature and also the effect of nonlocal parameter on the nonlinear frequency are investigated. The presented nonlinear vibration analysis is of a general form, so that they are applicable for CNTs with arbitrary number of walls. The obtained results for single-, double- and triple-walled CNTs indicate that with an increase in the number of walls, elastic medium modulus, aspect ratio and temperature, the value of nonlinear frequency tends to that of its linear counterpart. Also, a comparison between the results of the Timoshenko beam theory and those of Euler-Bernoulli beam theory shows that the difference between the frequency responses of these theories is significant for short CNTs, but, as the length increases, the difference between the results becomes negligible. پرونده مقاله

In this paper, natural frequency and response of forced vibration of composite laminated conical shells under different boundary conditions are investigated. To this end, equations of Donnell's thin shell theory are used as governing equations. The analytical Galerkin method together with beam mode shapes as weighting functions is employed to solve the problem. Due to importance of boundary conditions upon the mechanical behavior of conical shells, the analysis is carried out for all possible boundary conditions. The response of forced vibration is calculated via the modal participation factor method. Numerical comparisons of free vibration with the results in the open literature are made to validate the present methodology. پرونده مقاله

In the present research, the elastic buckling of composite cross-ply elliptical cylindrical shells under axial compression is studied through finite element approach. The formulation is based on shear deformation theory and the serendipity quadrilateral eight-node element is used to study the elastic behavior of elliptical cylindrical shells. The strain-displacement relations are accurately accounted for in the formulation in local coordinate system. The contributions of the work done by applied load are also incorporated. The obtained governing equations by the principle of minimum potential energy is solved through eigenvalue approach. The influence of elliptical cross-sectional parameters on the critical buckling loads of elliptical cylindrical shells is examined .Results show that changes in the elliptical cross-sectional parameters significantly change critical buckling loads of the elliptical cylindrical shells. پرونده مقاله

The Existence of crack in a structure leads to local flexibility and changes the stiffness and dynamic behavior of the structure. The dynamic behavior of the cracked structure depends on the depth and the location of the crack. Hence, the changes in the dynamic behavior in the structure due to the crack can be used for identifying the location and depth of the crack. In this study the first three natural eigenfrequencies of a cantilever beam having a transverse open crack have been computed for 10 different depths and 30 different locations by the finite element method. These natural eigenfrequencies have been used as input data for GMDH-type neural networks and adaptive neuro-fuzzy inference system, ANFIS, for crack location and depth modeling. پرونده مقاله