Calculation of the Response of a Periodically Excited Beam with Frictional Contact Using Harmonic Balance Method

Weisheit, Konrad; Marburg, Steffen

doi:10.1016/j.piutam.2016.03.035

Cited by 8 publications

(4 citation statements)

References 3 publications

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“…This setup could prove that the fundamental and higher harmonics of the excitation frequency dominate the vibration response of a squeaking system configuration to a harmonic excitation [10]. Therefore, the essential prerequisite of periodicity for the usage of HBM, shown in Subsection 2.1, is met to predict the vibration response of a squeaking system.…”

Section: Validationmentioning

confidence: 99%

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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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Section: Validationmentioning

confidence: 99%

“…To prove the applicability of HBM to predict the vibration response of squeaking systems, a squeak test rig was developed [10][11][12]. As mentioned above, squeak noise originates from an in-contact tangential motion of the two squeaking components characterized by stick-slip transitions.…”

Section: Squeak Test Rigmentioning

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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“…In (16), After applying the Finite Element Method, the surface of the system is discretized. Assuming the normal velocity does not vary over the small area of each surface element, the integral in (19) x v  (17) with the number of surface elements e N and element area k A .…”

Section: Estimation Of the Radiated Sound By Calculating The Eqivalenmentioning

confidence: 99%

“…Therefore, further investigations have to be accomplished in order to account for these phenomenas in an early stage of product development and thus reducing the cost of secondary measures. Since the field of SAR noise generation is not limited to the automotive sector, it is well studied and documented in the literature (13)(14)(15)(16)(17)(18)(19) .…”

Section: Introductionmentioning

confidence: 99%

Model Reduction Technique for Analysing Friction-Induced Vibrations and Radiated Sound

Weisheit

Marburg

2018

IJAE

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A novel approach for the calculation of friction induced vibration is presented and applied to a real life example. The balance equations of continuum mechanics representing the underlying physics are simplified and then solved numerically. First, a linearised model of the example system is built to extract modal parameters such as eigenvalues and eigenvectors. A subset of eigenvectors is then used to calculate the system's response due to friction related excitation. This non-linear vibration is calculated by utilising an explicit time integration scheme. With the use of a subset of eigenvectors the degree of freedom of the system is reduced drastically, leading to considerable reduction of computational effort. The solution is compared to results from adequate experiments. Although developed in a context of noise calculation in the automotive sector, this work focuses on the calculation of friction induced vibration, rather than on noise prediction. Nevertheless, as an example the resulting noise of the vibrating system is estimated by means of the Equivalent Radiated Power (ERP).

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