A new non-Gaussian linearization method is developed for extending the analysis of Gaussian white-noise excited nonlinear oscillator to incorporate sinusoidal excitation. The non-Gaussian linearization method is developed through introducing a modulated correction factor on the linearization coefficient which is obtained by Gaussian linearization. The time average of cyclostationary response of variance and noise spectrum is analyzed through the correction factor. The validity of the present non-Gaussian approach in predicting the statistical response is supported by utilizing Monte Carlo simulations. The present non-Gaussian analysis, without imposing restrictive analytical conditions, can be obtained by solving nonlinear algebraic equations. The non-Gaussian solution effectively predicts accurate sinusoidal and noise response when the nonlinear system is subjected to both sinusoidal and white-noise excitations.
Skip Nav Destination
Article navigation
September 2017
Research-Article
Extension of Nonlinear Stochastic Solution to Include Sinusoidal Excitation—Illustrated by Duffing Oscillator
R. J. Chang
R. J. Chang
Department of Mechanical Engineering,
National Cheng Kung University,
Tainan 70101, Taiwan
e-mail: rjchang@mail.ncku.edu.tw
National Cheng Kung University,
Tainan 70101, Taiwan
e-mail: rjchang@mail.ncku.edu.tw
Search for other works by this author on:
R. J. Chang
Department of Mechanical Engineering,
National Cheng Kung University,
Tainan 70101, Taiwan
e-mail: rjchang@mail.ncku.edu.tw
National Cheng Kung University,
Tainan 70101, Taiwan
e-mail: rjchang@mail.ncku.edu.tw
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 29, 2017; final manuscript received June 1, 2017; published online July 12, 2017. Assoc. Editor: Dumitru Baleanu.
J. Comput. Nonlinear Dynam. Sep 2017, 12(5): 051030 (9 pages)
Published Online: July 12, 2017
Article history
Received:
March 29, 2017
Revised:
June 1, 2017
Citation
Chang, R. J. (July 12, 2017). "Extension of Nonlinear Stochastic Solution to Include Sinusoidal Excitation—Illustrated by Duffing Oscillator." ASME. J. Comput. Nonlinear Dynam. September 2017; 12(5): 051030. https://doi.org/10.1115/1.4037105
Download citation file:
Get Email Alerts
Cited By
Comparison of the Hysteresis Response of Super-Coiled Polymer (SCP) Actuators
J. Comput. Nonlinear Dynam
Dual Function Matrix Projective Synchronization for Fractional-Order Hyperchaotic Systems
J. Comput. Nonlinear Dynam (September 2023)
The Synchronization of a Class Fractional-Order Chaotic System by Using the Recovered State Variables and Backstepping Control
J. Comput. Nonlinear Dynam (September 2023)
Related Articles
Stochastic Averaging and Optimal Prediction
J. Vib. Acoust (December,2007)
Nonlinear Stochastic Dynamics and Control in Hamiltonian
Formulation
Appl. Mech. Rev (July,2006)
Monte Carlo Simulation of Moment Lyapunov Exponents
J. Appl. Mech (March,2005)
Linearization in Analysis of Nonlinear Stochastic Systems: Recent Results—Part I: Theory
Appl. Mech. Rev (May,2005)
Related Proceedings Papers
Related Chapters
Simulation on Vibration Radiation Noise from Rear Driving Axle of Minibus Based on Virtual Lab Acoustics
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)
Stability for a Class of Infinite Dimension Stochastic Systems with Delay
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)
Creating and Eliminating Workplace Hazards by Design
An Instructional Aid For Occupational Safety and Health in Mechanical Engineering Design