The prediction and control of excessive vibration are one the most important concerns in design development geared systems. For any gear set, parametric resonance is main source instability, resulting separation gears mesh chaotic behavior. In many works, modeled with rigid mountings, various analytical numerical approaches have been used to investigate dynamic characteristics system different ...

A simplified isotope dilution method for measurement of the bile acid pool size in normal subjects is described and compared with the traditional method of Lindstedt (Acta Physiol. Scand. 40: 1-9, 1957). Advantages of this simplified method include a four- to eightfold reduction of isotope dose, facilitation of analytical procedures, and a reduction in the required number of duodenal intubation...

The nonlinear effects exhibited by structures under the action of wind loads have gradually stepped into vision wind-resistant researchers. By summarizing prominent wind-induced problems four types wind-sensitive structures, namely tall buildings, high-rise flexible bridges, and transmission lines, occurrence mechanism their is revealed, providing cutting-edge research progress in theoretical s...

In this paper, the dynamic response of resonating nano-beams is investigated using a strain gradient elasticity theory. A nonlinear model is obtained based on the Galerkin decomposition method to find the dynamic response of the investigated beam around its statically deflected position. The mid-plane stretching, axial residual stress and nonlinear interaction due to the electrostatic force on ...

The renormalization group method of Chen, Goldenfeld, and Oono offers a comprehensive approach to formally computing asymptotic expansions of the solutions to singular perturbation problems and multi-scale problems. In particular, the RG method applies to a broad array of problems customarily treated with disparate methods, such as the method of multiple scales, boundary layer theory, matched a...

It is shown that the logical bases of the static perturbation method, which is currently used in static bifurcation analysis, can also be applied to dynamic bifurcations. A two-time version of the Lindstedt–Poincaré Method and the Multiple Scale Method are employed to analyze a bifurcation problem of codimension two. It is found that the Multiple Scale Method furnishes, in a straightforward way...

The Poincaré–Lindstedt method in perturbation theory is used to compute periodic solutions in perturbed differential equations through a nearby periodic orbit of the unperturbed problem. The adaptation of this technique to systems of differential equations of first order could produce meaningful advances in the qualitative analysis of many dynamical systems. In this paper, we present a new symb...

We investigate the differentiability of minimal average energy associated to the functionals S ε(u) = ∫ Rd 1 2 |∇u|2 + εV(x, u) dx, using numerical and perturbative methods. We use the Sobolev gradient descent method as a numerical tool to compute solutions of the Euler-Lagrange equations with some periodicity conditions; this is the cell problem in homogenization. We use these solutions to det...

We present a method to obtain arbitrarily accurate solutions for conservative classical oscillators. The method that we propose here works both for small and large nonlinearities and provides simple analytical approximations. A comparison with the standard Lindstedt-Poincaré method is presented, from which the advantages of our method are clear.