Vibration statistics of the Duffing oscillator

Michalakis C. Constantinou

doi:10.1016/0261-7277(85)90041-5

Vibration statistics of the Duffing oscillator

Michalakis C. Constantinou

Department of Civil, Structural & Environmental Engineering

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

The stationary response of the Duffing oscillator excited by white noise is considered. Based on the associated Fokker-Planck equation, the joint moments, of all orders, of the displacement and velocity are obtained in closed-form, in terms of parabolic cylinder functions. An asymptotic expansion, valid for large values of a dimensionless parameter, is also presented. It is shown that all moments of the Duffing oscillator are bounded by the corresponding moments of the linear oscillator.

Original language	English
Pages (from-to)	221-223
Number of pages	3
Journal	International journal of soil dynamics and earthquake engineering
Volume	4
Issue number	4
DOIs	https://doi.org/10.1016/0261-7277(85)90041-5
State	Published - Oct 1985

Keywords

nonlinear
statistics
vibration

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10.1016/0261-7277(85)90041-5

Cite this

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title = "Vibration statistics of the Duffing oscillator",

abstract = "The stationary response of the Duffing oscillator excited by white noise is considered. Based on the associated Fokker-Planck equation, the joint moments, of all orders, of the displacement and velocity are obtained in closed-form, in terms of parabolic cylinder functions. An asymptotic expansion, valid for large values of a dimensionless parameter, is also presented. It is shown that all moments of the Duffing oscillator are bounded by the corresponding moments of the linear oscillator.",

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year = "1985",

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doi = "10.1016/0261-7277(85)90041-5",

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AU - Constantinou, Michalakis C.

PY - 1985/10

Y1 - 1985/10

N2 - The stationary response of the Duffing oscillator excited by white noise is considered. Based on the associated Fokker-Planck equation, the joint moments, of all orders, of the displacement and velocity are obtained in closed-form, in terms of parabolic cylinder functions. An asymptotic expansion, valid for large values of a dimensionless parameter, is also presented. It is shown that all moments of the Duffing oscillator are bounded by the corresponding moments of the linear oscillator.

AB - The stationary response of the Duffing oscillator excited by white noise is considered. Based on the associated Fokker-Planck equation, the joint moments, of all orders, of the displacement and velocity are obtained in closed-form, in terms of parabolic cylinder functions. An asymptotic expansion, valid for large values of a dimensionless parameter, is also presented. It is shown that all moments of the Duffing oscillator are bounded by the corresponding moments of the linear oscillator.

KW - nonlinear

KW - statistics

KW - vibration

UR - https://www.scopus.com/pages/publications/0022144754

U2 - 10.1016/0261-7277(85)90041-5

DO - 10.1016/0261-7277(85)90041-5

M3 - Article

AN - SCOPUS:0022144754

SN - 0261-7277

VL - 4

SP - 221

EP - 223

JO - International journal of soil dynamics and earthquake engineering

JF - International journal of soil dynamics and earthquake engineering

IS - 4

ER -

Vibration statistics of the Duffing oscillator

Abstract

Keywords

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