This paper describes an original approach for computing the stationary response of linear periodic time variant MDOF systems subjected to stationary stochastic external excitation. The proposed method is derived in the frequency domain, is purely numerical, and provides the explicit power spectral density (PSD) of the response. Its implementation first requires expressing the PSD response as a function of the bilinear Fourier transform of the so-called bitemporal impulse response. Then, the spectral method is used to compute the bispectrum function. The efficiency of this spectral process is demonstrated by comparison with Monte Carlo simulations on three parametrical systems. The computational time required and the accuracy are very satisfactory.
Skip Nav Destination
e-mail: joel.perret-liaudet@ec-lyon.fr
Article navigation
January 2008
Research Papers
A Spectral Method for Describing the Response of a Parametrically Excited System Under External Random Excitation
J. Perret-Liaudet
e-mail: joel.perret-liaudet@ec-lyon.fr
J. Perret-Liaudet
LTDS
, Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, 69134 Ecully Cedex, France
Search for other works by this author on:
L. Bachelet
N. Driot
J. Perret-Liaudet
LTDS
, Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, 69134 Ecully Cedex, Francee-mail: joel.perret-liaudet@ec-lyon.fr
J. Comput. Nonlinear Dynam. Jan 2008, 3(1): 011008 (10 pages)
Published Online: November 26, 2007
Article history
Received:
January 9, 2007
Revised:
July 23, 2007
Published:
November 26, 2007
Citation
Bachelet, L., Driot, N., and Perret-Liaudet, J. (November 26, 2007). "A Spectral Method for Describing the Response of a Parametrically Excited System Under External Random Excitation." ASME. J. Comput. Nonlinear Dynam. January 2008; 3(1): 011008. https://doi.org/10.1115/1.2815333
Download citation file:
Get Email Alerts
Cited By
A numerical study for nonlinear time-space fractional reaction-diffusion model of fourth-order
J. Comput. Nonlinear Dynam
A Fast Chebyshev Collocation Method for Stability Analysis of a Robotic Machining System with Time Delay
J. Comput. Nonlinear Dynam
Characterization of Three-Mode Combination Internal Resonances in Electrostatically Actuated Flexible–Flexible Microbeams
J. Comput. Nonlinear Dynam (December 2024)
Investigation of nonlinear dynamic behaviors of vertical rotor system supported by aerostatic bearings
J. Comput. Nonlinear Dynam
Related Articles
The Maximal Lyapunov Exponent for a Three-Dimensional Stochastic System
J. Appl. Mech (September,2004)
Modeling and Simulation of Elastic Structures with Parameter Uncertainties and Relaxation of Joints
J. Vib. Acoust (January,2001)
Monte Carlo Simulation of Moment Lyapunov Exponents
J. Appl. Mech (March,2005)
Simulation of Moment Lyapunov Exponents for Linear Homogeneous Stochastic Systems
J. Appl. Mech (May,2009)
Related Proceedings Papers
Related Chapters
Random Turbulence Excitation in Single-Phase Flow
Flow-Induced Vibration Handbook for Nuclear and Process Equipment
Stability for a Class of Infinite Dimension Stochastic Systems with Delay
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)
Introduction and Background
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow