a nonlocal beam model based on the bernoulli–euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (swcnts) in thermal environment under combined static and periodic axial loads. the dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. the equation of motion is...

We propose two methods to find analytic periodic approximations intended for differential equations of Hill type. Here, we apply these methods on the simplest case of the Mathieu equation. The former has been inspired in the harmonic balance method and designed to find, making use on a given algebraic function, analytic approximations for the critical values and their corresponding periodic sol...

The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker–Hill equations in the first approach. When the two centers have the same ...

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 d...

Let us consider the Dirac operator L = iJ d dx + U, J = ( 1 0 0 −1 ) , U = ( 0 a cos 2πx a cos 2πx 0 ) , where a 6= 0 is real, on I = [0, 1] with boundary conditions bc = Per, i.e., F (1) = F (0), and bc = Per−, i.e., F (1) = −F (0), F = ( f1 f2 ) ∈ H(I). Then σ(Lbc) = −σ(Lbc), and all λ ∈ σPer+(L(U)) are of multiplicity 2, while λ ∈ σPer−(L(U)) are simple (Thm 15). This is an analogue of E. L....

A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD o...

the forging model for cold rolling is one of rolling models that is used in rolling calculations. in this model,the final rolling pressure is an average value and it is not an accurate model.also by using this model,the firction hill curves are plotted due to the central point of the rolling bite length while frictional stresses intersect at the neutral point.in this study, a new model based on...