scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Active control of turbulent boundary layer-induced sound transmission through the cavity-backed double panels

26 May 2018-Journal of Sound and Vibration (Academic Press)-Vol. 422, pp 161-188
TL;DR: In this article, the authors present a theoretical study of active control of turbulent boundary layer TBL induced sound transmission through the cavity-backed double panels, where a feedback control unit is located inside the acoustic cavity between the two panels.
About: This article is published in Journal of Sound and Vibration.The article was published on 2018-05-26 and is currently open access. It has received 22 citations till now. The article focuses on the topics: Sound transmission class & Sound pressure.

Summary (4 min read)

1. Introduction

  • In high speed automotive, aerospace, and railway transportation, the turbulent boundary layer (TBL) is one of the most important sources of interior noise.
  • Consequently the trim panels radiate sound into the vehicle interior.
  • Between the different models developed over the years to describe the wall pressure fluctuations due to a TBL [3], the Corcos model is among the simplest [4, 5].
  • The passive sound transmission control is ineffective in the lowfrequency range since the passive sound absorptive materials can not attenuate the large-length waves.
  • Feedback control systems can be used instead, and some promising results have been reported in the last decade [14, 20, 21, 22].

2. The model problem

  • The analytical model outlined in this section is used to predict the noise transmission through an acoustically coupled double panel system into a rectangular cavity when an active vibration isolation unit is used.
  • The problem under analysis is physically given by the interaction of an aerodynamic model, that represents the TBL pressure fluctuations on the structure, and a structural-acoustic model, that gives the noise transmission and interior sound levels.

2.1. Aerodynamic model

  • The wall pressure field, generated by a fully developed TBL with zero mean pressure gradient, can be regarded as homogeneous in space and stationary in time [3, 28].
  • It is thus possible that the results presented in the paper qualitatively differ for different convective speeds and the dimensions of the panels.
  • In the following sections the properties of the physical system used are defined in detail.
  • The longitudinal and lateral decay rates of the coherences, αx and αy respectively, are normally chosen to yield good agreement with experiments.

2.2. Structural-acoustic model

  • The model encompasses a cavitybacked homogeneous double panel driven on one side by a stationary TBL.
  • Real sensor-actuator transducers would certainly exhibit more complex highfrequency behaviour and decrease stability margins of the active control systems considered in the study.
  • In the following section, the structural-acoustic model presented describes the interaction between the vibrating structure and the turbulent flow assuming a one-way interaction, i.e. the influence of the panel vibration on the boundary layer is neglected [33].
  • In Eq. (8)-(9), v represents the distribution of source volume velocity per unit volume (including the effect of the boundary surface vibration), c0, ρ0 and σac are the sound speed in air, mean density of air and acoustic damping ratio for both cavities, respectively.

3.1. Description of the simplified model

  • The stability and performance analysis of the active control system are carried out using a simplified model.
  • Note that the first mode of each air cavity is characterised by a uniform pressure variation throughout the cavity volume and by a zero natural frequency.
  • The resulting coupled system 9 then behaves exactly as a two degree of freedom (DOF) mechanical system which, as shown in Fig. 2, is represented through mass and stiffness parameters m1,m2, k1, k2, k3, and which is characterised by two coupled mode shapes and two natural frequencies.
  • The remaining geometrical and physical properties used throughout the paper are shown in Table 1.

3.2. Stability

  • A system is stable if all roots of its characteristic equation have negative real parts.
  • Additionally, all the principal diagonal minors ∆i of the Hurwitz matrix must be positive.
  • It can be stated that in the case with β < 1 the source body, having the larger uncoupled natural frequency than the radiating body, behaves more like a fixed reference base against which the actuator can react without pronounced feedthrough effect that could otherwise compromise stability properties.
  • The frequency response function between the reaction force component and the velocity sensor is thus responsible for the stability problems in case β >.
  • This is because frequency response functions between two different points of a flexible structure do not necessarily have their phases bound within a 180 degree range, whereas the driving point FRFs do have their phase limited within a 180 degrees range.

3.3. Performance

  • The performance of the active control system is analysed by using two different load conditions.
  • Firstly, a white noise forcing is assumed on m1, Fig. 2, where the mass m1 represents the source panel and is thus referred to as the source body.
  • Then, the mean squared velocity of the mass m2 is found by calculating the integral over all frequencies of the squared magnitude of the transfer mobility, Eq. (28), of the system in Fig.
  • Note that the mean squared displacement of the mass m2 is proportional to the mean squared pressure in the cavity c2 according to the two mode assumption, see Eq. (29).
  • The frequency- and space-averaged velocity PSD of the radiating panel is used.

3.3.1. Point force excitation

  • The mean squared velocity of the radiating body is plotted as function of the passive and active damping ratio in Fig.
  • This is however only due to a) the limitations of the reduced order model and its inability to capture the high-frequency behaviour of the double panel structure, and b) the fact that idealised sensor and actuator transducers are assumed.
  • The passive damping ratio is again set to the optimal value that lies on the white dash-dotted line in Fig.
  • In addition, the roll-off at higher dimensionless frequencies, above approximately 2.1, is compromised as shown in Fig. 5-a.
  • In conclusion, the inconsistent impact of the passive damping ratio at various frequency ranges is the reason why the frequency averaged kinetic energy of the radiating panel plotted in Fig. 6-a has a minimum which corresponds to the optimal passive damping coefficient ηopt.

3.3.2. Turbulent boundary layer excitation

  • The performance of the control system in reducing the TBL−induced sound transmission is studied by using the simplified, reduced order model.
  • As with the point force excitation, the radiating panel kinetic energy decreases monotonically with ξ when β < 1 Fig. 7-(b) and Fig. 8-(b).
  • By comparing the situation with the TBL excitation to the scenario with the white noise force excitation discussed in the previous subsection, it can be stated that the stochastic TBL pressure distribution results in a steeper high frequency roll-off of the velocity PSD, shown in Fig.
  • This requires careful tuning of the passive and active damping ratios to the optimum combination.

4. Results with the full order model

  • The stability and performance of the active control system are again discussed in terms of the mean squared vibration velocity of the radiating panel and the mean squared acoustic pressure in the cavity c2.
  • The number of modes used enables accurate calculation of the mean squared pressure and velocity up to 1000 Hz.
  • Two load conditions are analysed: 1) white noise point force excitation; and 2) TBL excitation.
  • The large number of modes precludes the use of the Routh-Hurwitz criterion to assess the stability of the active system such that the Nyquist criterion is used instead.

4.1. Stability

  • The sensor-actuator OL − FRF can be used to analyse the stability of the closed loop control system by using the Nyquist criterion.
  • In Fig. 11 - 12, the corresponding Bode and Nyquist plots are shown.
  • Thus the system with β < 1 is unconditionally stable under the assumption of ideal sensor-actuator frequency response.
  • Regarding the high-frequency behaviour, it is still interesting that the phase of the OL − FRF is bound between ±90 degrees, given the fact that the sensor and the actuator are not dual and collocated.
  • Therefore the relative importance of the non-collocated FRF decreases as the frequency increases.

4.2. Performance

  • In the following subsection, the performance of the control system assuming a full order model is analysed for both load conditions: point force and TBL.
  • The frequency-averaged vibration velocity of the radiating panel and the sound pressure in the acoustic enclosure c2 are used as the metrics for the quality of the sound transmission control.

4.2.1. Point force excitation

  • In the case of a point force excitation on the radiating panel, the mean squared velocity at the centre of the radiating panel and the mean squared acoustic pressure near the corner of 24 the cavity c2 are calculated using the procedure described in Section 2.2.
  • The squared magnitude of either frequency response function is integrated numerically over the frequency range 0 − 1000 Hz.
  • The amplitude of the velocity at the centre of the radiating panel per unit excitation force on the source panel is shown in Fig. 14-b, and the amplitude of the sound pressure per unit excitation force at the pressure monitoring point in the cavity c2 is shown in Fig. 15-b.
  • Again, the results with the active approach are contrasted to the results using a fully passive approach.

4.2.2. Turbulent boundary layer excitation

  • For the full order model assuming the TBL excitation on the source panel, the performance of the control system is analysed in terms of: a) the velocity PSD at the centre of the radiating panel, pr, and b) the pressure PSD near the corner of the cavity c2, see Fig.
  • The pressure PSD near the corner of c2 is plotted versus frequency in Fig. 17-b with β < 1 and Fig. 19-b with β > 1 for three cases: without control, with passive control using cp only, and finally with active control using both cp and g.
  • By comparing the right-hand side plot of Fig. 16 to the right hand side plot of Fig. 17, it can be concluded that large contributions to the interior sound pressure are due to the two lowest double panel modes.
  • Additional mode shapes obtained using the full order model are shown and discussed.

5. Conclusions

  • The active control of TBL noise transmission through a cavity-backed double panel is investigated.
  • Stability and performance of the velocity feedback active control system are carried out for a reduced order model and an increased order model.
  • The theoretical analysis indicates that the first fundamental mode and the mass-air-mass mode of the coupled system are the strongest radiators of sound into the back cavity.
  • Closed form expressions for these stability limits are given in terms of the minimal/maximal active damping ratio.
  • The fundamental resonance frequency of the source panel is larger than the fundamental resonance frequency of the radiating panel, which results in unconditionally stable control systems such that very large feedback gains can be used.

Did you find this useful? Give us your feedback

Figures (20)
Citations
More filters
Journal ArticleDOI
TL;DR: In this article, the authors collected all of the existent papers in the field of acoustic transmission across multilayered plate constructions and proposed a comprehensive source consisting of approximately 410 papers.
Abstract: This study collects all of the existent papers in the field of acoustic transmission across multilayered plate constructions. Herewith, a comprehensive source is proposed wherein approximately 410 ...

39 citations

Journal ArticleDOI
TL;DR: In this article, a three-dimensional analytical model for control of sound transmission through an acoustically baffled simply supported hybrid smart double sandwich panel partition of rectangular plan is developed for sound transmission.
Abstract: A three-dimensional analytical model is developed for control of sound transmission through an acoustically baffled simply supported hybrid smart double sandwich panel partition of rectangular plan...

21 citations


Cites background from "Active control of turbulent boundar..."

  • ...[44] presented a fully coupled analytical structural-acoustic model to study active control of turbulent boundary layer (TBL)-induced sound transmission through a cavity-backed flexible double panel....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the effects of active feedback control on elastic wave metamaterials were studied and the effective mass density and sound radiation by a point force excitation was investigated.
Abstract: To show the effects of active feedback control on elastic wave metamaterials, this research is focused on effective mass density and sound radiation by a point force excitation. The expressions of ...

17 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of the active feedback control system on the effective mass density and sound transmission in elastic wave metamaterials was investigated using the principle of virtual work.

15 citations

Journal ArticleDOI
TL;DR: In this article, an analytical analysis and optimization of vibration-induced fatigue in a generalized, linear two-degree-of-freedom inerter-based vibration isolation system is presented.
Abstract: This paper presents an analytical analysis and optimization of vibration-induced fatigue in a generalized, linear two-degree-of-freedom inerter-based vibration isolation system. The system consists of a source body and a receiving body, coupled through an isolator. The isolator consists of a spring, a damper, and an inerter. A broadband frequency force excitation of the source body is assumed throughout the investigation. Optimized system, in which the kinetic energy of the receiving body is minimized, is compared with sub-optimal systems by contrasting the fatigue life of a receiving body helical spring with several alternative isolator setup cases. The optimization is based on minimizing specific kinetic energy, but it also increases the number of cycles to fatigue failure of the considered helical spring. A significant portion of this improvement is due to the inclusion of an optimally tuned inerter in the isolator. Various helical spring deflection and stress correction factors from referent literature are discussed. Most convenient spring stress and deflection correction factors are adopted and employed in conjunction with pure shear governed proportional stress in the context of high-cycle fatigue.

9 citations

References
More filters
Journal ArticleDOI
TL;DR: In this paper, the authors investigated the application of the blended velocity feedback on subcritical 2DoF systems using an auto-tuning controller, and proposed an algorithm to gradually change the relative and absolute feedback gains until the active isolation performance reaches its best by applying an optimal combination of the two gains.
Abstract: It has been previously shown that skyhook damping can be used to actively reduce vibration transmission between masses in supercritical 2 degree of freedom (dof) systems. The method is based on measuring the absolute velocity of the clean body, multiplying it by a negative gain, and feeding the result back to a force actuator reacting between the clean and the dirty body. This approach results in a broadband vibration isolation. For subcritical 2 dof systems this is normally not possible due to control stability problems. These stability problems can be mitigated by including an appropriate amount of relative damping between the clean and the dirty body in addition to the absolute damping. This approach has been referred to as blended velocity feedback. In this paper the application of the blended velocity feedback on subcritical 2 dof systems is investigated using an auto-tuning controller. An algorithm to gradually change the relative and absolute feedback gains until the active isolation performance reaches its best by applying an optimal combination of the two gains is applied. There is only one such optimal combination which minimises the kinetic energy of the clean body, and consequently the performance surface has a global minimum. Furthermore there are no local minima so a trial and error algorithm could be applied. Although in the frequency domain finding the minimum of the performance surface is straightforward, in the time domain the determining the clean body mean squared velocity can take a considerable time per step of the algorithm, such that the convergence of the trial and error algorithm can be relatively slow. It is hypothesized that more sophisticated algorithms may speed-up the convergence but this would be at cost of using a model-based approach.

4 citations


"Active control of turbulent boundar..." refers background in this paper

  • ...In this context, some very effective feedback control methods have been proposed for vibration isolation [23, 24, 25]....

    [...]

  • ...have been typically considered in the situations where the mechanical systems at hand can be accurately represented through their lumped parameter approximation [23, 24, 25]....

    [...]

12 Jun 2009

4 citations


"Active control of turbulent boundar..." refers methods in this paper

  • ...Aerodynamic model The wall pressure field, generated by a fully developed TBL with zero mean pressure gradient, can be regarded as homogeneous in space and stationary in time [3, 28]....

    [...]