... at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running...

.... The proposed approach is also compared with the linear regression method. 23 04 2011 12 08 2011 05 10 2011 05 10 2011 Newton method nonlinear differential equations nonlinear dynamical systems optimisation parameter estimation regression analysis deterministic...

... 2011 22 07 2011 22 07 2011 Galerkin method Legendre polynomials nonlinear differential equations wave equations Legendre multiwavelet DGRLW equation Ritz method Galerkin method The damped generalized regularized long-wave (DGRLW) equation is a partial differential...

... catastrophic failures. 20 10 2009 02 07 2010 16 12 2010 16 12 2010 approximation theory closed loop systems discrete systems feedback linear systems nonlinear control systems nonlinear differential equations partial differential equations piezoelectric actuators plates...

... rapid convergency to the optimal solution of optimization problem than the integer order ones. 25 11 2009 15 03 2010 20 10 2010 20 10 2010 nonlinear differential equations nonlinear dynamical systems nonlinear programming penalty function dynamical system fractional...

... trajectory, and then carry out the approximation of the Lyapunov exponents using techniques for linear problems. 27 05 2009 20 04 2010 27 09 2010 27 09 2010 approximation theory Jacobian matrices Lyapunov methods nonlinear differential equations vectors Lyapunov...

... in the form of uniformly convergent series is obtained. The same orbit is also obtained numerically by a technique enunciated by Magnitskii and Sidorov, reproducing the necessary important features. 21 10 2008 03 06 2009 18 11 2009 18 11 2009 chaos nonlinear differential equations...

...-order approximation of homotopy Padé technique leads to accurate solutions with a maximum relative error less than 0.068 percent for all the considered cases. 20 09 2008 12 05 2009 18 11 2009 18 11 2009 beams (structures) nonlinear differential equations vibrations...

... with an unbalanced motor of excitation with limited power supply. The control of motion and the attenuation of the Sommerfeld effect of the considered nonideal system are analyzed in this paper. The mathematical model of the system is represented by coupled nonlinear differential equations. The identification...

... function gear dynamics path integration nonsmooth dynamics chaos gears noise nonlinear differential equations probability stochastic processes 23 08 2007 28 08 2008 20 05 2009 2009 American Society of Mechanical Engineers ...

... physical systems for the study of their nonlinear dynamics ( 6 7 ). multiple time scales method normal form theory Duffing equation internal resonance spring-mass-pendulum system nonlinear differential equations nonlinear dynamical systems perturbation theory 26 11 2007 23...

... ( x 1 − x 2 ) 2 + d ( x 1 − x 2 ) 3 18 03 2007 03 07 2007 07 12 2007 nonlinear differential equations parameter estimation time-varying systems NLTV systems parameter estimation Chebyshev spectral collocation Nonlinear...

.... 7 . 22 02 2007 20 06 2007 12 11 2007 chaos differential equations Lyapunov methods nonlinear dynamical systems periodicity ratio Lyapunov exponent irregular motions nonlinear dynamics nonlinear differential equations chaos periodic behavior quasiperiodic...

.... This confirms how the response in Fig. 11 is quasiperiodic. PSDs of q s -response histories corresponding to Figs. 8d ( a ), 8e ( b ), 9 ( c ), and 11 ( d ) 15 09 2006 28 03 2007 bifurcation chaos elastodynamics nonlinear differential equations oscillations...

... nonlinear differential equations Historically the analysis community has acknowledged the role of joints in structural dynamics ambivalently. We ascribe the nonlinearities of our structures to the presence of joints, but we go ahead and use linear models. Though using linear models, we acknowledge...

.... 0295-5075 10.1209/epl/i2005-10017-3 , 70 , pp. 425 – 431 . 17 07 2006 04 10 2006 nonlinear dynamical systems nonlinear differential equations oscillators perturbation theory modified Lindstedt–Poincaré method strong nonlinearity mixed-parity Nonlinear...

... to which a neuron is optimally tuned to respond, and are illustrated using phase reductions of neural models valid near typical bifurcations to periodic firing, as well as the Hodgkin-Huxley equations. neural nets variational techniques bifurcation nonlinear differential equations oscillations...

... in the model. N-body problems linearisation techniques nonlinear differential equations differential algebraic equations state-space methods 08 11 2005 25 02 2006 2006 American Society of Mechanical Engineers ...