..., and a total power) are calculated, investigated, and shown for different regimes, regular and chaotic ones for parametric resonance interactions. non-ideal power sources parametric resonance chaos In this section, we analyze the movement of the fluid surface. A detailed Lagrangian description can...

... bifurcation chaos elastic hysteresis electromagnetic actuators electromechanical actuators Lyapunov methods nonlinear dynamical systems robot dynamics torque motors vibrations In manufacturing industries, electromotor is an essential component for the automation of processes. Recently, many...

... oscillations, bifurcations, and chaos of thin plates. Finite- and infinite-dimensional analyses for flow-induced oscillations and bifurcations of thin plates were studied ( 1 2 ), then the problem was simplified ( 3 ) to a two-degree-of-freedom nonlinear system and the theory of normal forms and center...

... shifted symmetric trajectory at ϵ = 10 , ϵ B = − 2.5 , and ϵ A = 2.8 Yet another interesting result from Low et al. is the evidence of chaos within a narrow spread of displacement and velocity coupling strengths. Figure 3 shows the time series of one such region...

... cables (mechanical) chaos suspensions vibrations shallow suspended cable multiple internal resonances the method of multiple scales frequency-response curves out-of-plane vibration Cable structures are important in many engineering applications such as voltage transmission lines...

... spectra, and the Poincaré maps are used to carry out the analyses of bifurcation and chaotic motion. Period doubling, quasiperiod loop breaking, and mechanism of intermittency are observed as the routes to chaos. 26 11 2007 16 04 2009 21 10 2009 Wen , B. C. , Wu , X. H...

... if x is smooth. Therefore, if the dynamics of x is chaotic, then also is y , while the same parameters are used. In Eq. 3 , the right hand side provides a very simple form of the nonlinear feedback excitation needed for inducing chaos, which depends only on the velocity y...

...) numerical Lyapunov exponent are obtained, and it is found that chaos can appear suddenly, through period doubling, period adding, or torus breakdown. The extreme sensitivity of the electromechanical system to both initial conditions and tiny variations of the coupling coefficients is also outlined...

... with the following weight function 21 w ( η ) = h − 2 ( δ η ) sin ( π η ) 05 11 2003 14 07 2005 vibrations structural acoustics rotors turbomachinery bifurcation variational techniques chaos Poincare mapping boundary layers aeroacoustics Fluid...

... chaotic vibration, due to the 1 to ( − 1 ) type internal resonance at the major critical speed and twice the major critical speed are investigated. The following are clarified theoretically and experimentally: (a) the Hopf bifurcation and consecutive period doubling bifurcations possible route to chaos...

... in the periodically forced, piecewise linear system are obtained and the initial grazing manifolds are predicted analytically. The initial grazing manifolds are invariant. The fragmentation mechanism of the strange attractor is briefly discussed. The grazing in chaos for such a piecewise linear system is observed...

... of polynomial chaos is demonstrated by considering a simple model of bladed disk assembly with one mode of vibration for each blade, Fig. 1 . Statistics of an individual blade’s amplitude and the maximum amplitude on a rotor from polynomial chaoses are compared to those from Monte Carlo simulations...

... 05 2005 electric machines nonlinear dynamical systems chaos vibrations rotors mechanical stability machine bearings state-space methods Poincare mapping fast Fourier transforms Lyapunov methods condition monitoring Elwell R. C. , and Findlay J. A. , 1969...

... drastically different modal response from that due to the steady-state thermal field. Chaos is found being induced by the transient in-plane thermal field, or by both transient in-plane and transverse thermal fields. Unique bifurcation behavior is observed with different thermal frequencies. Different loading...

... of the measured signal. The developed control scheme allows chaos suppression despite uncertainties in the model as well as unmeasured disturbances. The Chua and Φ 6 -Duffing are used to illustrate the performance of the proposed controller. The robust asymptotic controller is designed by means of the following...

.... 01 Sept 2000 01 Sept 2002 01 04 2003 relaxation oscillators oscillations chaos synchronisation limit cycles Limit cycle oscillators arise in many biological, mechanical and electrical systems such as large groups of crickets that synchronously chirp 1 , cell division...

... motions instead of symmetrical period-1 motion is observed. A numerical investigation for symmetrical, period-1 motion to chaos is completed. The numerical and analytical results of periodic motions are in very good agreement. The methodology presented in this paper is applicable to other discontinuous...

... and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS . Manuscript received May 2001; revised March 2002. Associate Editor: G. Flowers. 01 May 2001 01 March 2002 12 06 2002 resonance magnetic bearings machine bearings rotors chaos nonlinear dynamical systems...

... cycles at s = 3.0 (case 2) 13 Variation c r with embedding dimension at s = 3.0 (case 2) ( a ) and variation of correlation dimension with embedding dimension ( b ) The bifurcation and chaos of the unbalanced response of a rigid...

.... 2001. Associate Editor: S. C. Sinha. 01 Nov 1999 01 Sept 2001 chaos vibrations bifurcation mechanical stability resonance The first recorded work on the chaotic vibrations of a buckled beam was by Tseng and Dugundji 1 where the harmonic balance method was used to solve...