An extended harmonic balance method based on incremental nonlinear control parameters

Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.

doi:10.1016/j.ymssp.2016.09.008

Cited by 13 publications

(6 citation statements)

References 35 publications

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“…where Q n,i is the complex amplitude of the i th harmonic of the generalised coordinate P n (t), and I denotes the imaginary parts. To find the steady state response of the system in the frequency domain, various methods can be used including the harmonic balance method (HBM) [27,28] and complex averaging technique (CXA) [29][30][31]. In this study, the simulated response of the beam is obtained in the frequency domain using the complex averaging technique (CXA) along with the arc-length continuation method.…”

Section: Analytical Model 41 the Controlled Systemmentioning

confidence: 99%

Linear Control of a Nonlinear Equipment Mounting Link

et al. 2021

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The linear control of a nonlinear response is investigated in this paper, and a nonlinear model of the system is developed and validated. The design of the control system has been constrained based on a suggested application, wherein mass and expense are parameters to be kept to a minimum. Through these restrictions, the array of potential applications for the control system is widened. The structure is envisioned as a robot manipulator link, and the control system utilises piezoelectric elements as both sensors and actuators. A nonlinear response is induced in the structure, and the control system is employed to attenuate these vibrations which would be considered a nuisance in practical applications. The nonlinear model is developed based on Euler–Bernoulli beam theory, where unknown parameters are obtained through optimisation based on a comparison with experimentally obtained data. This updated nonlinear model is then compared with the experimental results as a method of empirical validation. This research offers both a solution to unwanted nonlinear vibrations in a system, where weight and cost are driving design factors, and a method to model the response of a flexible link under conditions which yield a nonlinear response.

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Section: Analytical Model 41 the Controlled Systemmentioning

confidence: 99%

Linear Control of a Nonlinear Equipment Mounting Link

et al. 2021

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“…Such problems have not received significant attention in the literature. In the presence of uncertainty, a semi-analytical solution such as Harmonic Balanace (HB) or Incremental Harmonic Balance (IHB) used by authors in previous papers [20,21] cannot be applied. This is because it is not feasible to perform a convergence study on the required number of truncated terms of nonlinear force for thousands of samples generated by Monte Carlo Simulation.…”

Section: A N U S C R I P Tmentioning

confidence: 99%

Minimising the effects of manufacturing uncertainties in MEMS Energy harvesters

Madinei

Khodaparast

Friswell

et al. 2018

Energy

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“…After the nonlinear panel vibration amplitudes are obtained, the modal sound radiation and radiation efficiency can be computed using the modified Rayleigh’s integral method [ 29 ]: where r is the distance between the panel corner and the observer point; ϕQ is the Q th panel mode shape; θ 1 and θ 2 are the angles between the observer vector and y-axis and between the observer vector and x -axis, respectively (see [ 29 ] for details); k h is the wave number; and C a is the speed of sound.…”

Section: Theorymentioning

confidence: 99%

Nonlinear structure-extended cavity interaction simulation using a new version of harmonic balance method

Lee¹

2018

PLoS ONE

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This study addresses the nonlinear structure-extended cavity interaction simulation using a new version of the multilevel residue harmonic balance method. This method has only been adopted once to solve a nonlinear beam problem. This is the first study to use this method to solve a nonlinear structural acoustic problem. This study has two focuses: 1) the new version of the multilevel residue harmonic balance method can generate the higher-level nonlinear solutions ignored in the previous version and 2) the effect of the extended cavity, which has not been considered in previous studies, is examined. The cavity length of a panel-cavity system is sometimes longer than the panel length. However, many studies have adopted a model in which the cavity length is equal to the panel length. The effects of excitation magnitude, cavity depth, damping and number of structural modes on sound and vibration responses are investigated for various panel cases. In the simulations, the present harmonic balance solutions agree reasonably well with those obtained from the classical harmonic balance method. There are two important findings. First, the nonlinearity of a structural acoustic system highly depends on the cavity size. If the cavity size is smaller, the nonlinearity is higher. A large cavity volume implies a low stiffness or small acoustic pressure transmitted from the source panel to the nonlinear panel. In other words, the additional volume in an extended cavity affects the nonlinearity, sound and vibration responses of a structural acoustic system. Second, if an acoustic resonance couples with a structural resonance, nonlinearity is amplified and thus the insertion loss is adversely affected.

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An extended harmonic balance method based on incremental nonlinear control parameters

Cited by 13 publications

References 35 publications

Linear Control of a Nonlinear Equipment Mounting Link

Linear Control of a Nonlinear Equipment Mounting Link

Minimising the effects of manufacturing uncertainties in MEMS Energy harvesters

Nonlinear structure-extended cavity interaction simulation using a new version of harmonic balance method

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