Periodic Response of a Duffing Oscillator Under Combined Harmonic and Random Excitations

Zhu, Hongtao; Guo, Siu-Siu

doi:10.1115/1.4029993

Cited by 25 publications

(7 citation statements)

References 22 publications

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“…There has been much effort made to obtain exact and approximate steady-state solutions of the PDF [2][3][4][5][6]. Many methods have been developed for steady-state solutions of the PDF including detailed balance [6][7][8], exponential polynomial closure (EPC) [9,10], stochastic averaging and equivalent linearization [11,12], random walk [13,14], path integral [15][16][17][18], finite element method [19,20] , finite difference method [21,22] and generalized cell mapping [23]. A highly efficient method for constructing analytical solutions of the steady-state FPK equation for nonlinear stochastic dynamic systems is reported in [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Random vibration analysis with radial basis function neural networks

Wang

Hong

Sun

2021

Int. J. Dynam. Control

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Random vibrations occur in many engineering systems including buildings subject to earthquake excitation, vehicles traveling on a rough road and off-shore platform in random waves. Analysis of random vibrations for linear systems has been well studied. For nonlinear systems, particularly for multi-degree-of-freedom systems, however, there are still many challenges including analyzing the probability distribution of transient responses of the system. Monte Carlo simulation was considered the only viable method for this task. In this paper, We propose a method to construct semi-analytical transient solutions of the probability distribution of transient responses of nonlinear systems by using the radial basis function neural networks. The activation functions consist of normalized Gaussian probability density functions. Two examples are presented to show the effectiveness of the proposed solution method. The transient probability distributions and response moments of these examples are presented, which have not been reported in the literature before.

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Section: Introductionmentioning

confidence: 99%

Random vibration analysis with radial basis function neural networks

Wang

Hong

Sun

2021

Int. J. Dynam. Control

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“…To improve energy harvesting efficiency, Zhang et al [21] carried out theoretical and numerical studies on an electromechanically coupled VEH under colored noise and periodic excitation. By utilizing the implicit harmonic balance method and the Gaussian closure method, Zhu et al [22] discussed the periodic response of a Duffing oscillator under harmonic and random combined excitation. Shi et al [23] studied an asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.…”

Section: Introductionmentioning

confidence: 99%

Dynamic responses of an energy harvesting system based on piezoelectric and electromagnetic mechanisms under colored noise

et al. 2023

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Because of the increasing demand for electrical energy, vibration energy harvesters (VEHs) that convert vibratory energy into electrical energy are a promising technology. In order to improve the efficiency of harvesting energy from environmental vibration, the hybrid vibration energy harvester (VEH) is investigated. Unlike previous studies, this article analyzes the stochastic responses of the hybrid piezoelectric and electromagnetic energy harvesting system (EHS) with viscoelastic material under narrow-band (colored) noise. Firstly, a mass-spring-damping system model coupled with piezoelectric and electromagnetic circuits under fundamental acceleration excitation is established and analytical solutions to the dimensionless equations are derived. Then, the formula of the amplitude-frequency responses in the deterministic case and the first-order and second-order steady-state moments (FSSM) of the amplitude in the stochastic case are obtained by the multi-scales method. And the amplitude-frequency analytical solutions are in good agreement with the numerical solutions obtained by the Monte Carlo method. Furthermore, the stochastic bifurcation diagram is plotted for the first-order steady-state moment of the amplitude with respect to the detuning frequency and viscoelastic parameter. Eventually, the influence of system parameters on mean-square electric voltage, mean-square electric current and mean output power is discussed. Results show that the electromechanical coupling coefficients, random excitation and viscoelastic parameter have a positive effect on the output power of the system.

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“…For example, in Refs. 9,10,12,26,35 the methods are presented specifically for the Duffing oscillator, while Anh et al 13 and Manohar and Iyengar 14 are specific to the van der Pol oscillator. This means that the proposed methods cannot be easily applied to alternative nonlinearities, particularly for nonlinearities that are not polynomial, like contact or friction nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

“…The first group consists of methods based on combining nonlinear deterministic and stochastic dynamic analysis techniques to derive coupled equations which are then solved for the response quantities of interest. For example HBM has been used alongside Gaussian closure, 8,9 stochastic averaging, 10 and equivalent linearization. 11 Spanos et al 11 use HBM to derive a set of equations for the deterministic response component as functions of the random response statistical moments.…”

Section: Introductionmentioning

confidence: 99%

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

Hickey,

Butlin,

Langley

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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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.

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Periodic Response of a Duffing Oscillator Under Combined Harmonic and Random Excitations

Cited by 25 publications

References 22 publications

Random vibration analysis with radial basis function neural networks

Random vibration analysis with radial basis function neural networks

Dynamic responses of an energy harvesting system based on piezoelectric and electromagnetic mechanisms under colored noise

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

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