STOCHASTIC AVERAGING OF STRONGLY NON-LINEAR OSCILLATORS UNDER BOUNDED NOISE EXCITATION

Abstract A stochastic averaging method for strongly non-linear oscillators under external and/or parametric excitation of bounded noise is proposed by using the so-called generalized harmonics functions. The method is then applied to study the primary resonance of Duffing oscillator with hardening spring under external excitation of bounded noise. The stochastic jump and its bifurcation of the system are observed and explained by using the stationary probability density of amplitude and phase. Subsequently, the method is applied to study the dynamical instability and parametric resonance of Duffing oscillator with hardening spring under parametric excitation of bounded noise. The primary unstable region is delineated by evaluating the Lyapunov exponent of linearized system, and the response and jump of non-linear system around the unstable region are examined by using the sample functions and stationary probability density of amplitude and phase.

[1]  Yoshiyuki Suzuki,et al.  Response and stability of strongly non-linear oscillators under wide-band random excitation , 2001 .

[2]  R. L. Stratonovich,et al.  Topics in the theory of random noise , 1967 .

[3]  Y. K. Cheung,et al.  Averaging Method Using Generalized Harmonic Functions For Strongly Non-Linear Oscillators , 1994 .

[4]  Zhenkun Huang,et al.  Effect of bounded noise on chaotic motion of duffing oscillator under parametric excitation , 2001 .

[5]  Y. Lin,et al.  Application of a new wind turbulence model in predicting motion stability of wind-excited long-span bridges , 1993 .

[6]  Mikhail F. Dimentberg,et al.  Statistical dynamics of nonlinear and time-varying systems , 1988 .

[7]  Yoshiyuki Suzuki,et al.  Stochastic averaging of strongly non-linear oscillators under combined harmonic and white-noise excitations , 2000 .

[8]  W. Q. Zhu,et al.  Stochastic Jump and Bifurcation of a Duffing Oscillator Under Narrow-Band Excitation , 1993 .

[9]  L. Socha,et al.  STATISTICAL LINEARIZATION OF THE DUFFING OSCILLATOR UNDER NON-GAUSSIAN EXTERNAL EXCITATION , 2000 .

[10]  Stochastic Stability of Viscoelastic Systems Under Bounded Noise Excitation , 1996 .

[11]  G. Cai,et al.  Random Vibration of Strongly Nonlinear Systems , 2001 .

[12]  Masanobu Shinozuka,et al.  Structural Safety and Reliability , 2000 .

[13]  Richard H. Lyon,et al.  Response of Hard‐Spring Oscillator to Narrow‐Band Excitation , 1961 .

[14]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .