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Marek Lampart and Jaroslav Zapoměl

Abstract

This paper concentrates on the vibrations attenuation of a rotor driven by a DC motor and its frame flexibly coupled with a baseplate by linear cylindrical helical springs and damped by an element that can work either in inertia or impact regime. The system oscillation is governed by three mutually coupled second-order ordinary differential equations. The nonlinear behaviour occurs if the impact regime is adjusted. The damping element operating in inertia mode reduces efficiently the oscillations amplitude only in a narrow frequency interval. In contrast, the damping device working in impact regime attenuates vibrations of the rotor frame in a wider range of the excitation frequencies and it can be easily extended if the clearances between the rotor casing and the damping element are controlled. The development of a computational procedure for investigation of vibration of a flexibly supported rotor and for its attenuation by the inertia and impact dampers; learning more on efficiency of the individual damping regimes; finding possibilities of extension of the frequency intervals of applicability of the damping device; and obtaining more information on the character of the vibration induced by impacts are the main contributions of this research work.

Open access

M. Fernández-Martínez

Abstract

Along the years, the foundations of Fractal Geometry have received contributions starting from mathematicians like Cantor, Peano, Hilbert, Hausdorff, Carathéodory, Sierpiński, and Besicovitch, to quote some of them. They were some of the pioneers exploring objects having self-similar patterns or showing anomalous properties with respect to standard analytic attributes. Among the new tools developed to deal with this kind of objects, fractal dimension has become one of the most applied since it constitutes a single quantity which throws useful information concerning fractal patterns on sets. Several years later, fractal structures were introduced from Asymmetric Topology to characterize self-similar symbolic spaces. Our aim in this survey is to collect several results involving distinct definitions of fractal dimension we proved jointly with Prof.M.A. Sánchez-Granero in the context of fractal structures.

Open access

Li Bing and You Ning

Abstract

In this paper we focus on integrated Reconnaissance/Strike LAV, in order to reveal the evolution regularity when group LAVs combats cooperatively. The evolution of cooperative behavior of group LAVs, which is described with finite state machine, can be regarded as a conversion process of a LAV in different task states, using the rate equation for probability analysis. Then based on the missions of integration of reconnaissance, attack, and damage effectiveness evaluation, we build the model of finite state machine based on behavior state transition. Solved with Runge-Kutta method. We can analyze how the key technology quota of LAV impact on the operational effectiveness of Group LAVs.the fractional order control approach.

Open access

Jose Luis Roca González, Juan Antonio Vera López and Manuel Fernández Martínez

Abstract

The bird strike damage on aircrafts is a widely studied matter [1] with a high economic impact on stakeholders finances. Some authors estimate it in about USD1.2 Billion for nowadays commercial worldwide activity [2], and more than USD937 million in direct and other monetary losses per year just for the United States, as an example of civil aviation industry [3]. The present techniques to face this problem have been previously analyzed in order to decrease the wild life hazards at the airport facilities [4] however nowadays there is a new point of view to prevent this risk at airports that requires an interesting approach in relationship with industrial process improvement examples, such approach lies on preserving the natural life at the airport facilities by developing raptor micro-habitats than change into exclusion areas when the risk of being hunted is recognized by the existing wildlife.

Therefore, the main goal of this paper is to share several experiences developed at the Spanish dual airport (military & civilian) of San Javier (Spain), as a case of study in where the mathematics and nonlinear sciences provides the foundations of the ontological knowledge for falconry performance as a Wildlife Control Technique for airport facilities.

Open access

F. Crespo, G. Díaz-Toca, S. Ferrer and M. Lara

Abstract

This paper is devoted to studying Hamiltonian oscillators in 1:1:1:1 resonance with symmetries, which include several models of perturbed Keplerian systems. Normal forms are computed in Poisson and symplectic formalisms, by mean of invariants and Lie-transforms respectively. The first procedure relies on the quadratic invariants associated to the symmetries, and is carried out using Gröner bases. In the symplectic approach, hinging on the maximally superintegrable character of the isotropic oscillator, the normal form is computed a la Delaunay, using a generalization of those variables for 4-DOF systems. Due to the symmetries of the system, isolated as well as circles of stationary points and invariant tori should be expected. These solutions manifest themselves rather differently in both approaches, due to the constraints among the invariants versus the singularities associated to the Delaunay chart.

Taking the generalized van der Waals family as a benchmark, the explicit expression of the Delaunay normalized Hamiltonian up to the second order is presented, showing that it may be extended to higher orders in a straightforward way. The search for the relative equilibria is used for comparison of their main features of both treatments. The pros and cons are given in detail for some values of the parameter and the integrals.

Open access

N.S. Awadalla, M.A. Hanna, M.N. Ismail, I.A. Hassan and M.A. Elkhamisy

Abstract

We analyzed the first set of complete CCD light curves of the W UMa type eclipsing binary IK Boo in the BVRI bands by using the PHOEBE code and deduced its first photometric parameters with, mass ratio q = 0.648 and orbital inclination i = 63o. We have applied a spotted model due to the light curves asymmetry. The system shows a distinct O’Connell effect. The best solution fit to the light curves suggested the influence of star spot(s) on both components. Such presence of star spot(s) is common among the RS CVn and W UMa chromospheric active late type stars.

We also present an analysis of mid–eclipse time measurements of IK Boo. The analysis indicates a period decrease rate dP/dt = −1.68 × 10−7d/yr, which can be interpreted in terms of mass transfer of rate 3.1 × 10−7M/yr, from the more massive to the less massive component.

Open access

Francisco Balibrea

Abstract

Most of problems in Topological Dynamics in the theory of general autonomous discrete dynamical systems have been addressed in the non-autonomous setting. In this paper we will review some of them, giving references and stating open questions.

Open access

José Valero

Abstract

In this paper we prove that the global attractor generated by strong solutions of a reaction-diffusion equation without uniqueness of the Cauchy problem is bounded in suitable Lr-spaces. In order to obtain this result we prove first that the concepts of weak and mild solutions are equivalent under an appropriate assumption.

Also, when the nonlinear term of the equation satisfies a supercritical growth condition the existence of a weak attractor is established.

Open access

M. Maldonado, J. Prada and M. J. Senosiain

Abstract

We make a survey of results published by the authors about the backward and forward unilateral weighted shift operators in Kóthe spaces, the so-called generalized derivation and integration operators, extending well-known results for spaces of analytic functions.

Open access

Harishchandra S. Ramane and Raju B. Jummannaver

Abstract

The forgotten topological index of a graph G is defined as the sum of the cube of the degrees of its vertices. In the recent paper [6], [W. Gao et al. (2016), Forgotten topological index of chemical structure in drugs, Saudi Pharmaceutical Journal, 24, 258-264], the forgotten topological index of some chemical structures has been obtained. In this note, we correct their result regarding triangular benzenoid. Also, we have given the expression for the forgotten topological index of graphene structure which is more compact than the one was obtained in the paper above.