Reliability assessment and risk analysis of rotating machine rotors in various overload and malfunction situations present challenge to engineers and operators. In this paper a new analytical method for evaluation of rotor under large deformation is addressed. Model is presented in general form to include also composite rotors. Presented simulation procedure is based on variational work method ...

Many technical systems for the control of temperatures require a MIMO (multiple input multiple output) model for the control design. This problem arises in systems with higher geometric dimensions, more than one actuating value, strongly coupled structure, or extreme precision requirements. In this case, the assumption of equal temperatures in the complete device is not valid. If higher tempera...

We give a geometric proof of stability for spatially nonho-mogeneous equilibria in the singular perturbation problem u t = 2 u xx + f(x; u); t 2 R + ; ?1 u 1, with the Neumann boundary conditions on x 2 0; 1]. The nonlinearity is of the form f(x; u) := (1 ?u 2)(u ?c(x)) where c(x) is merely continuous with a nite number of zeros. The strength of the method is in dealing with non-transversal zer...

Experienced bow makers empirically know the influence of wood, tapering, and camber on the playing and tonal qualities of a bow. However, the way each parameter affects the bow mechanical behavior is not clearly established. An in-plane finite element model is developed to highlight the link between the adjustable design parameters and the mechanical behavior of a bow. This model takes into acc...

In this work, we study the standing wave solutions of an inhomogeneous nonlinear Schrödinger equation. The inhomogeneity considered here is a varying coefficient of the nonlinear term. In particular, the nonlinearity is chosen to be repelling (defocusing) except on a finite interval. Localized solutions on a nonzero background, e.g., dark solitons trapped by the inhomogeneity, are identified an...

Helical structures, ubiquitous in nature, have inspired design and manufacturing of helical devices with applications in nanoelecromechanical systems, morphing structures, optoelectronics, microrobotics and drug delivery devices. Meanwhile, multi-stable structures have attracted increasing attention for their applications in bio-inspired robots and deployable aerospace components. Here we show ...

A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a “small deformation” setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived. In the finite deformation setting, it is shown th...

(Watanabe [17]). But we insist, in this paper, we can attain the critical case if we assume some structure condition on the operator σ(X,D). This case is crucial in dealing with further applications to the low regularity solutions to nonlinear problems, where the structure condition corresponds to the null structure of the nonlinearity. We explain our strategy by generalizing the equation, so t...