Resonant and coupled response of hysteretic two-degree-of-freedom systems using harmonic balance method

Masiani, Renato; Capecchi, Danilo; Vestroni, Fabrizio

doi:10.1016/s0020-7462(02)00023-9

Cited by 41 publications

(32 citation statements)

References 32 publications

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“…Such nonlinear systems range from models such as the simple the Duffing oscillator [14] to more complex models such as cracked rotors [15]. More applications of the harmonic balance method can be found in the study of the nonlinear response of airfoils [16]- [17], non-linear conservative systems [18], hysteretic two-degree-of-freedom systems [19], the third order (jerk) differential equations [20] and the Jeffcott rotor [21]. By using the HBM, some interesting phenomena unique to nonlinear systems have been observed, among which the most well-known is jump phenomenon where the response amplitude of a nonlinear oscillator changes suddenly at some critical value of the frequency of the excitation [13].…”

Section: Introductionmentioning

confidence: 99%

Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis

Peng

Lang

Billings

et al. 2008

Journal of Sound and Vibration

112

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By using the Duffing oscillator as a case study, this paper shows that the harmonic components in the nonlinear system response to a sinusoidal input calculated using the Nonlinear Output Frequency Response Functions (NOFRFs) are one of the solutions obtained using the Harmonic Balance Method (HBM). A comparison of the performances of the two methods shows that the HBM can capture the well-known jump phenomenon, but is restricted by computational limits for some strongly nonlinear systems and can fail to provide accurate predictions for some harmonic components.Although the NOFRFs cannot capture the jump phenomenon, the method has few computational restrictions. For the nonlinear damping systems, the NOFRFs can give better predictions for all the harmonic components in the system response than the HBM even when the damping system is strongly nonlinear.

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Section: Introductionmentioning

confidence: 99%

Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis

Peng

Lang

Billings

et al. 2008

Journal of Sound and Vibration

112

View full text Add to dashboard Cite

show abstract

“…Yoon and Yoon [9] employed the HBM to investigate the dynamic characteristics of a single-degree-of-freedom (DOF) torsional system accompanied by a multi-stage clutch damper model. Other studies have examined various vibration problems using the HBM [10][11][12][13][14][15][16][17][18][19][20][21][22]. For instance, nonlinear problems using a Duffing oscillator or cubic stiffness have been settled by utilizing the nonlinear output frequency response functions (NOFRFs) and incremental harmonic balance (IHB) method [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…Also, chaotic behaviors of physical systems have been examined [12,13]. Additionally, the response of a system with a hysteretic restoring force has been studied by applying two degree of freedom chain systems with sinusoidal inputs [14]. Incremental or multi-component HBMs have been employed as well to investigate the nonlinear system responses [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Vibro-Impact Energy Analysis of a Geared System with Piecewise-Type Nonlinearities Using Various Parameter Values

Yoon

Kim

2015

Energies

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Torsional systems with gear pairs such as the gearbox of wind turbines or vehicle driveline systems inherently show impact phenomena due to clearance-type nonlinearities when the system experiences sinusoidal excitation. This research investigates the vibro-impact energy of unloaded gears in geared systems using the harmonic balance method (HBM) in both the frequency and time domains. To achieve accurate simulations, nonlinear models with piecewise and clearance-type nonlinearities and drag torques are defined and implemented in the HBM. Next, the nonlinear frequency responses are examined by focusing on the resonance areas where the impact phenomena occur, along with variations in key parameters such as clutch stiffness, drag torque, and inertias of the flywheel and the unloaded gear. Finally, the effects of the parameters on the vibro-impacts at a specific excitation frequency are explained using bifurcation diagrams. The results are correlated with prior research by defining the gear rattle criteria with key parameters. This article suggests a method to simulate the impact phenomena in torsional systems using the HBM and successfully assesses vibro-impact energy using bifurcation diagrams.

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“…This phenomenon is associated with the NVH performance (vibration and noise) of the target system and is highly nonlinear behavior, and difficult to analyze. In order to investigate nonlinear dynamic responses in a simple mechanical system, many studies have been conducted using the harmonic balance method (HBM) [4][5][6][7][8][9][10][11][12]. For example, Peng et al [4] suggested nonlinear output frequency response functions using the Duffing oscillator to simulate strong nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

“…Genesio and Tesi [7] presented two practical methods to predict the existence and the location of chaotic motions. Masiani et al [8] examined the system responses under a hysteretic restoring force by employing two degree-of-freedom (DOF) chain systems given sinusoidal input. Raghothama and Narayanan [9] used the incremental harmonic balance method to obtain the periodic motions of a 3DOF nonlinear model of a geared rotor system subjected to parametric excitation under sinusoidal excitation.…”

Section: Introductionmentioning

confidence: 99%

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Yoon

Kim

2015

Energies

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Dynamic behaviors in practical driveline systems for wind turbines or vehicles are inherently affected by multiple nonlinearities such as piecewise-type torsional springs. However, various excitation conditions with different levels of magnitudes also show strong relationships to the dynamic behaviors when system responses are examined in both frequency and time domains. This study investigated the nonlinear responses of torsional systems under various excitations by using the harmonic balance method and numerical analysis. In order to understand the effect of piecewise-type nonlinearities on vibrational energy with different excitations, the nonlinear responses were investigated with various comparisons. First, two different jumping phenomena with frequency up-and down-sweeping conditions were determined under severe excitation levels. Second, practical system analysis using the phase plane and Poincaré map was conducted in various ways. When the system responses were composed of quasi-periodic components, Poincaré map analysis clearly revealed the nonlinear dynamic characteristics and thus it is suggested to investigate complicated nonlinear dynamic responses in practical driveline systems.

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Resonant and coupled response of hysteretic two-degree-of-freedom systems using harmonic balance method

Cited by 41 publications

References 32 publications

Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis

Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis

Vibro-Impact Energy Analysis of a Geared System with Piecewise-Type Nonlinearities Using Various Parameter Values

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

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