A time and ensemble equivalent linearization method for nonlinear systems under combined harmonic and random excitation

An Equivalent Linearization technique, termed an Equivalent Linearization Time and Ensemble Expectation (EL-TEE) approach, is used to develop an alternative method for estimating the response of a nonlinear oscillator to a combination of deterministic harmonic and random white noise excitation. The...

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Bibliographic Details
Published in:Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science Journal of mechanical engineering science, 2024-05, Vol.238 (9), p.3724-3745
Main Authors: Hickey, John, Butlin, Tore, Langley, Robin, Onozato, Naoki
Format: Article
Language:English
Subjects:
Computational efficiency
Computing costs
Degrees of freedom
Duffing oscillators
Equivalence
Harmonic excitation
Linearization
Nonlinear equations
Nonlinear systems
Nonlinearity
Polynomials
Random excitation
Time integration
White noise
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Summary:An Equivalent Linearization technique, termed an Equivalent Linearization Time and Ensemble Expectation (EL-TEE) approach, is used to develop an alternative method for estimating the response of a nonlinear oscillator to a combination of deterministic harmonic and random white noise excitation. The approach is based on applying equivalent linearization and averaging over the time period of one harmonic excitation cycle. This gives a set of coupled nonlinear equations that can be solved for the response averaged over time and across the ensemble. The primary advantages of the proposed method are its computational speed, ability to return physically meaningful linearization matrices and that it can be applied to a wide variety of nonlinearities. The method is applied to three example test systems: the well-known single degree of freedom Duffing oscillator; a single degree of freedom system with a displacement constraint imposing a discontinuous nonlinearity; and a multi degree of freedom oscillator with a localized polynomial nonlinearity that has also been examined experimentally. It is shown that the response predicted matches well with Monte Carlo results from direct time integration at a fraction of the computational cost, and the method is capable of reproducing key results observed experimentally.
ISSN:0954-4062
2041-2983
DOI:10.1177/09544062231203844