Quantitative prediction of rattle noise: An experimentally validated approach using the harmonic balance method

The dynamic characteristics of the fractional Duffing system with nonlinear time delay term are studied according to the average method and the harmonic balance method. First, the steady‐state solutions of the fractional Duffing system with a nonlinear time delay term are obtained by applying the average method and the harmonic balance method. The analytical expressions of the amplitude–frequency characteristic curves under the average method and the harmonic balance method are also established. Second, the stability criterion of the system is obtained according to the indirect method of studying the motion stability problem, and the concept of the stability condition parameter is proposed in this process. Third, the transient solution of the fractional Duffing system with a nonlinear time delay term is obtained utilizing the average method, and the approximate analytical solution of the fractional Duffing system with nonlinear time delay term is obtained. Finally, the amplitude–frequency characteristic curves of the different fractional differential terms, coefficients of different fractional differential terms, magnitude of different time delay quantities, and feedback strength of different delay are analyzed by numerical simulation. Furthermore, the amplitude–frequency characteristic curves obtained by the average method and the harmonic balance method under different order of fractional differential term are compared and analyzed by numerical simulation. The time sequence and phase diagrams of the system under different order of fractional differential term and different time delay quantities are analyzed by numerical simulation. In addition, the correctness of the analytical analysis is verified by comparing the analytical results with the numerical simulation results under the average method and the harmonic balance method, respectively, by numerical simulation.

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“…According to the harmonic balance principle [27–34], we can obtain

- m Λ ω^{2} + k Λ + \frac{3}{4} β {normalΛ}^{3} \cos ωτ + K Λ ω^{α} \cos \frac{italicαπ}{2} = f \cos γ,

c Λ ω - \frac{3}{4} β {normalΛ}^{3} \sin ωτ + K Λ ω^{α} \sin \frac{italicαπ}{2} = f \sin γ .

…”

Section: Steady‐state Solutionmentioning

confidence: 99%

Dynamics analysis for a class of fractional Duffing systems with nonlinear time delay terms

Yang

Jiao

2023

Math Methods in App Sciences

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“…The vibration response of the rattle test rig is measured using 3D laser Doppler vibrometers. The evaluation of the experimental measurements of the vibration response of the rattling test rig demonstrated that the vibration response of a rattling system configuration is dominated by the base and higher harmonics of the excitation frequency [14]. Hence, the fundamental prerequisite of periodicity, as described in Subsection 2.1, for using the HBM to predict the vibration response of a rattling system, is met.…”

Section: Rattle Test Rigmentioning

confidence: 99%

“…To research the applicability of HBM to predict the vibration response of rattling system configurations, a rattle test rig was developed [14, 15]. The rattle test rig consists of two support frames.…”

Section: Validationmentioning

confidence: 99%

Squeak and rattle noise prediction in vehicle acoustics

Rauter,

Utzig,

Weisheit

et al. 2023

Proc Appl Math and Mech

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Squeak and rattle belong to unintended noise audible by occupants of a vehicle. This noise negatively affects the perceived built quality, leading to nonbuying decisions, high warranty costs, and poor brand reputation. Therefore, vehicle manufacturers seek to prevent the emergence of such noise, preferably in the early development phase and during production at the latest. This causes substantial monetary and temporal expenditure, which must be minimized. Rattle is defined as repeated impact. The underlying physical phenomenon is impulsive short‐duration contact normal to the surface. Squeak, in contrast, originates from an in‐contact motion in the tangential direction and is a friction‐induced stick‐slip phenomenon. State‐of‐the‐art numerical squeak and rattle prediction is based on linear analysis resulting in an empirical noise risk index. However, quantification of noise and assessment of audibility is not possible. The reason is the nonlinearity of the contact forces. Hence, the actual system response is not calculable with a linear approach. Mathematically, the nature of both excitation events is nonlinear due to frictional contact and nonsmooth due to short impulsive behavior in time. This makes linear simplification and a solution process in the time domain challenging. Both events appear periodically, leading to an oscillation characterized by fundamental and higher harmonics. Due to this periodic character, squeak and rattle phenomena fulfill the prerequisite for applying the harmonic balance method (HBM) to solve the governing nonlinear equation of motion. The more harmonics considered, the more precise the modeling and the dynamic response prediction. In addition, the alternating frequency/time domain method (AFT) allows for switching between the frequency and the time domain during the iterative solution process. Thus, the nonlinear contact forces can be evaluated in the time domain. The equation‐solving process results in the calculation of surface velocities. This gives way to determining a proxy for the emitted sound power of the oscillatory system. The simulation method based on combining HBM and AFT was validated on test rigs for squeak and rattle noise. The industrial applicability of this simulation approach was demonstrated numerically and experimentally on an actual vehicle part showing promising results. Thereby, important steps in nonlinear structural dynamics and vehicle acoustics were made toward a calm, smooth, and enjoyable ride for vehicle occupants.

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