... not been exhibited in existing investigations on nonlinear vibrations of gear transmission systems. Nonlinear phenomena and resonances of the gear transmission system are revealed by considering different numbers of degrees-of-freedom of the system. The bifurcations containing saddle-node, period-doubling...

... nonlinear vibration Stick-slip motion has serious and undesirable consequences, such as vibration and noise, high energy loss, surface damage, and component failure in a wide range of the mechanical system, especially for the brake system [ 1 ]. This type of dysfunction was mainly investigated using...

... changes Fig. 4 Nonlinear vibration response of the sensor for various parameters: ( a ) ε changes, ( b ) l changes, ( c ) h changes, and ( d ) v changes Table 1 System parameters l (mm) b (mm) h ( μ m) v ( μ m) ε 0 (c 2 N −1 m −2 ) E (GPa) U...

... received May 25, 2015; published online June 30, 2015. Assoc. Editor: Carmen M. Lilley. 11 03 2013 25 05 2015 30 06 2015 In this paper, nonlinear vibration of a single-walled carbon nanotube (SWCNT) with simply supported ends is investigated based on von Karman's geometric...

...Jian Jiang; Zhao-Qing Wang; Jian-Hua Wang; Bing-Tao Tang In this article, a powerful computational methodology, named as barycentric rational interpolation iteration collocation method (BRICM), for obtaining the numerical solutions of nonlinear vibration problems is presented. The nonlinear...

... results in order to confirm the validity of the theoretical analysis. intrinsic localized mode nonlinear vibration pendulum array harmonic oscillation frequency response curve bifurcation set Hopf bifurcation amplitude modulated motion chaotic vibration When systems with identical...

.... Furthermore, time histories are shown for the case of N = 10, and many patterns of ILMs may appear depending on the initial conditions. intrinsic localized mode nonlinear vibration harmonic oscillation frequency response curve basin of attraction bifurcation set Hopf bifurcation amplitude...

... . [12] Stoker , J. J. , 1950 , Nonlinear Vibrations , John Wily & Sons , New York . [13] Awrejcewicz , J. , and Krysko , V. A. , 2006 , Introduction to Asymptotic Methods , Chapman and Hall, CRC Press , Boca Raton, NY . [14] Doedel , E. J. , Champneys , A. R...

...Takashi Ikeda Nonlinear vibrations of an elastic structure with two partially filled liquid tanks subjected to horizontal harmonic excitation are investigated. The natural frequencies of the structure and sloshing satisfy the tuning condition 1:1:1 when tuned liquid dampers are used. The equations...

... ,” ASME J. Comput. Nonlinear Dyn. 1555-1423 , 5 ( 2 ), p. 021012 . 10.1115/1.4000790 Stoker , J. J. , 1950 , Nonlinear Vibrations , Wiley , New York . Wolf , A. , Swift , J. B. , Swinney , H. L. , and Vastano , J. A. , 1985 , “ Determining Lyapunov Exponents...

... ( a − b ) 2 + 2 k m ) 1 / 2 20 09 2008 12 05 2009 18 11 2009 18 11 2009 beams (structures) nonlinear differential equations vibrations nonlinear vibration two degrees of freedom analytical solution homotopy analysis method homotopy...

..., the natural frequencies and associated mode shapes. These are the natural characteristics of continuous elastic vibrating structures and are present in the forced response of the structure. However, the same is not true for the nonlinear vibrations of such elastic systems, as the rates of oscillations (i.e...