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Unusual one-way edge state in acoustic gyroscopic continuum

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Science China(Physics,Mechanics & Astronomy) 2019年第1期62卷 76-82页

作者： XiaoMing Zhou YuChen Zhao Key Laboratory of Dynamics and Control of Flight Vehicle Ministry of Education and School of Aerospace Engineering Beijing Institute of Technology

Unusual one-way edge states have been observed in composite structures composed of periodic lattices loaded with gyroscopes.Here, we provide a continuum-mechanics understanding to the one-way edge state by formulating surface state equations of acoustic gyroscopic mediums with Hermite mass density tensor. We discover that the unidirectional edge effect arises from nontrivial off-diagonal components of Hermite densities, which causes the symmetric breaking of surface wave propagation towards forward and backward directions. Theoretical predictions on the velocity and decay length of surface waves coincide excellently with numerical simulations. The unidirectional edge state in a two-interface gyroscopic medium is also analyzed.Due to the rotational symmetry in geometry, the unidirectional edge state on one interface is able to prevent itself from the coupling to surface waves on the other interface regardless of the slab thickness. With these anomalous effects, surface waves residing on gyroscopic mediums can flow around the edge defects without back-scatterings, or can be split into two beams of equal energy magnitudes. Our findings may make a bridge that would help to reach the design of non-reciprocal composite materials via an effective medium approach.

关键词： gyroscopic medium one-way edge state quantum Hall effect

Construction of a new Lyapunov function for a dissipative gyroscopic system using the residual energy function

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Frontiers of Information Technology & Electronic Engineering 2020年第4期21卷 629-634页

作者： Cem CiVELEK Ozge CiHANBEGENDi Faculty of Engineering Department of Electrical and Electronics EngineeringEge UniversityBornova-izmir 35100Turkey Faculty of Engineering Department of Electrical and Electronics EngineeringDokuz Eylul UniversityBuca-izmir 35160Turkey

In a dissipative gyroscopic system with four degrees of freedom and tensorial variables in contravariant(right upper index)and covariant(right lower index)forms,a Lagrangian-dissipative model,i.e.,{L,D}-model,is obtained using second-order linear differential equations.The generalized elements are determined using the{L,D}-model of the system.When the prerequisite of a Legendre transform is fulfilled,the Hamiltonian is found.The Lyapunov function is obtained as a residual energy function(REF).The REF consists of the sum of Hamiltonian and losses or dissipative energies(which are negative),and can be used for stability by Lyapunov’s second method.Stability conditions are mathematically proven.

关键词： Lyapunov function Residual energy function Stability of dissipative gyroscopic system

Minimum Curve Radii for High-Speed Trains, Including the gyroscopic Moments of the Wheels

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World Journal of Engineering and Technology 2017年第1期5卷 113-124页

作者： Ronald L. Huston Emeritus of Mechanics Mechanical and Materials Engineering University of Cincinnati Cincinnati OH USA

This paper studies the title problem including an analysis of the gyroscopic effects of the wheels of a rail-car travelling at high-speed around a level, horizontal curve. The analysis is based upon the fundamental principles of dynamics. The result is a design formula for the minimum curve radius needed to prevent derailment. Aside from the rail car geometric and physical properties, the minimum curve radius depends upon the square the train speed. An illustrative example shows that the wheel gyroscopic effect is destabilizing and additive to the centrifugal force derailment tendency. From a track design perspective, however, the gyroscopic effect is relatively small compared with the centrifugal force effect.

关键词： High-Speed Train Rail Track Design Wheel gyroscopic Moments

Coupled Bending-Bending-Axial-Torsional Vibrations of Rotating Blades

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Acta Mechanica Solida Sinica 2019年第3期32卷 326-338页

作者： Feng Liang Zhen Li Xiao-Dong Yang Wei Zhang Tian-Zhi Yang College of Mechanical Engineering Yangzhou University Yangzhou 225127 China Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering College of Mechanical Engineering and Applied Electronics Beijing University of Technology Beijing 100124 China Department of Engineering Mechanics Shenyang Aerospace University Shenyang 110136 China

In this paper, the coupled bending-bending-axial-torsional free vibrations of rotating blades are investigated based on the Euler-Bernoulli beam model. The coupled partial differential equations governing flapwisc, edgewise, axial and torsional motions are derived by the Hamilton's principle, wherein three types of velocity-dependent terms, namely static centrifugal terms, dynamic centrifugal terms and gyroscopic coupling terms, are focused. The ordinary di& ferential equations are acquired by the Galerkin truncation, and the natural frequencies in all directions and complex mode shapes of the rotating blades are analyzed in detail. It is revealed that the three types of velocity-dependent terms have different effects on the natural frequencies. The natural frequencies are noticeably dependent on the rotating speed and preset angle, except for the axial vibration, which is almost immune to the preset angle. The complex modal motions are displayed by a series of positions of the central line and free-end cross section for different time instants, showing the coupled vibrations among different directions.

关键词： Rotating blades Coupled vibrations gyroscopic coupling Complex modes Preset angle

A review of chatter vibration research in milling

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Chinese Journal of Aeronautics 2019年第2期32卷 215-242页

作者： Caixu YUE Haining GAO Xianli LIU Steven Y.LIANG Lihui WANG Harbin University of Science and Technology Georgia Institute of Technology KTH Royal Institute of Technology

Chatter is a self-excited vibration of parts in machining systems. It is widely present across a range of cutting processes, and has an impact upon both efficiency and quality in production processing. A great deal of research has been dedicated to the development of technologies that are able to predict and detect chatter. The purpose of these technologies is to facilitate the avoidance of chatter during cutting processes, which leads to better surface precision, higher productivity,and longer tool life. This paper summarizes the current state of the art in research regarding the problems of how to arrive at stable chatter prediction, chatter identification, and chatter control/-suppression, with a focus on milling processes. Particular focus is placed on the theoretical relationship between cutting chatter and process damping, tool runout, and gyroscopic effect, as well as the importance of this for chatter prediction. The paper concludes with some reflections regarding possible directions for future research in this field.

关键词： Chatter gyroscopic effects Milling Process damping Tool runout

Magnetic field effects on the nonlinear vibration of a rotor

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Applied Mathematics and Mechanics(English Edition) 2020年第2期41卷 289-312页

作者： M.EFTEKHARI A.DASHTI-RAHMATABADI A.MAZIDI Department of Mechanical Engineering Yazd UniversityYazd 89195-741Iran

The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated,resulting in the production of a load on the rotor since the air-gap distribution between the rotor and the stator is not uniform. This electromagnetic load is a nonlinear function of the distance between the geometric centers of the rotor and the stator. The nonlinear equation of motion is obtained by the inclusion of the nonlinearity in the inertia, the curvature, and the electromagnetic load. After discretization of the governing partial differential equations by the Galerkin method, the multiple-scale perturbation method is used to derive the approximate solutions to the equations. In the numerical results, the effects of the electromagnetic parameter load, the damping coefficient, the amplitude of the initial displacement, the mass moment of inertia, and the rotation speed on the linear and nonlinear backward and forward frequencies are investigated. The results show that the magnetic field has significant effects on the nonlinear frequency of oscillation.

关键词： nonlinear vibration in-extensional rotor nonlinear curvature gyroscopic effect magnetic field

A review of dual-spin projectile stability

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Defence Technology（防务技术） 2020年第1期16卷 1-9页

作者： James Norris Amer Hameed John Economou Simon Parker Centre for Defence Engineering Cranfield UniversityDefence Academy of the United KingdomShrivenhamSN68LA United Kingdom BAE Systems United Kingdom

This paper gives a succinct review of dual-spinprojectile stability and some technologies relating to them.It describes how the traditional stability factors from linear projectile theory are modified to better describe a controlled dual-spin projectile.Finally,it reviews works which have investigated how different aspects of a controlled dual-spin design can affect flight stability,primarily airframe structure and canard properties.A conclusion is given,highlighting important guidelines from the enclosed discussions.

关键词： Guided projectiles Dual-spin gyroscopic Dynamic Stability Canards