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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.

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Figures (20)
Citations
More filters
Journal ArticleDOI
TL;DR: In this article , an active metamaterial cell that does not obey the reciprocity principle is considered, which attenuates vibration transmission through it in one direction and increases it in the opposite direction.

3 citations

Journal ArticleDOI
TL;DR: In this article , the wall-pressure and velocity statistics in the turbulent boundary layer (TBL) on a cambered controlled-diffusion aerofoil at $8^{\circ }$ incidence, a Mach number of 0.25 and a chord-based Reynolds number was analyzed at four locations on the suction side with zero and adverse pressure gradients (ZPG and APG), characterised by increasing Reynolds numbers based on momentum thickness, ${Re}_{\theta }=319, 390, 877 and $1036$.
Abstract: Abstract Wall-pressure and velocity statistics in the turbulent boundary layer (TBL) on a cambered controlled-diffusion aerofoil at $8^{\circ }$ incidence, a Mach number of 0.25 and a chord-based Reynolds number ${Re}_c=1.5\times 10^{5}$ are analysed at four locations on the suction side with zero and adverse pressure gradients (ZPG and APG), characterised by increasing Reynolds numbers based on momentum thickness, ${Re}_{\theta }=319$, 390, 877 and $1036$. The strong APG yields a highly non-equilibrium TBL at the trailing edge that significantly affects the turbulent flow statistics. Different normalisations of the full wall-pressure statistics involved in trailing-edge noise are analysed for the first time in such strong APG with convex curvature, and compared with available experimental and numerical data. Good overall agreement is found in the ZPG region, and most results obtained in previous APG TBL can be extended to the present highly non-equilibrium case. The presence of strong APG augments the intensity of wall-pressure fluctuations noticeably at low frequencies, shortens the streamwise and broadens the spanwise coherence of wall-pressure fluctuations in both time and space, and significantly reduces the convection velocity. The wall-pressure power spectral density are found to scale with the displacement thickness, the Zaragola–Smits velocity and the root-mean-squared pressure, the latter possibly being replaced by the local maximum Reynolds shear stress. The other two key parameters to trailing-edge noise modelling, the spanwise coherence length and the convection velocity, rather scale with displacement thickness and friction velocity, respectively.

2 citations

Dissertation
17 May 2019
TL;DR: In this article, the authors present a model of an unutrasnjosti vozila based on the ACTRAN model, and razvijen je model koji ukljucuje slobodno oslonjenu deformabilnu pravokutnu plocu, kojom se modelira vatronepropusni zid između prostora motora.
Abstract: Proizvođaci automobila postaju sve svjesniji da razina buke u unutrasnjosti vozila uvelike utjece na odluku kupca o kupnji. To se osobito odnosi na osobna vozila visoke klase. Stoga, poboljsanje vibroakusticke kvalitete osobnih vozila postaje važan i neizbježan predmet razvoja i istraživanja u automobilskoj industriji. Za inženjere koji se bave bukom i vibracijama vrlo je važno moci tocno predvidjeti zvuk u unutrasnjosti vozila u ranoj fazi konstruiranja. Na taj nacin izbjegavaju se znatno veci troskovi u kasnijim fazama razvoja novih modela vozila. U ovom radu, razvijena je metoda za proracun buke u unutrasnjosti osobnog vozila u programskom paketu ACTRAN. Programski paket se temelji na metodi konacnih elemenata (MKE). Ovaj programski paket jedan je od zastupljenijih numerickih alata za vibroakusticke analize u suvremenoj europskoj automobilskoj industriji. U prvom dijelu rada, razvijen je model koji ukljucuje slobodno oslonjenu deformabilnu pravokutnu plocu, kojom se modelira vatronepropusni zid između prostora motora s unutrasnjim izgaranjem i putnickog prostora, potpuno spregnutu s pravokutnom akustickom supljinom kojom se modelira putnicki prostor automobila. Preostalih 5 zidova akusticke supljine pretpostavljeni su krutima. Dimenzije modela izabrane su tako da približno odgovaraju dimenzijama stvarnog vozila. Pocevsi s diferencijalnim jednadžbama gibanja posebno za plocu i akusticku supljinu, metodom modalne dekompozicije izvedena je matricna jednadžba za potpuno spregnuti vibro-akusticki model. Također, izrađen je i analogni numericki model pomocu programskog paketa ACTRAN. Uspoređujuci karakteristicne rezultate dobivene analitickom i numerickom metodom, određene su prikladne velicine konacnih elementa i maksimalna frekvencija kod koje se razina buke u unutrasnjosti vozila dade odrediti s dovoljnom tocnoscu. U drugom dijelu rada razvijena je numericka metoda za proracun zvuka u unutrasnjosti stvarnog vozila koristeci ACTRAN. Proucavaju se tri najvažnija izvora buke kod vozila: buka koju proizvodi motor s unutrasnjim izgaranjem, buka koja nastaje kotrljanjem kotaca po podlozi te buka koju proizvodi ispusni sustav. Geometrija primjera vozila odgovara geometriji jedne luksuzne limuzine. Razvijena metoda temelji se na pristupu koji se sastoji od tri koraka, a primijenjena je u frekvencijskom rasponu od 100 Hz do 1600 Hz. U prvom koraku kreira se numericki simulacijski model koji opisuje radijaciju zvuka iz izvora smjestenih izvan vozila. Navedeni model služi za racunanje raspodjele zvucnog tlaka na krutoj ovojnici karoserije vozila. Zvucno polje nastaje uslijed zvuka narinutog iz akustickih izvora karakteristicne volumne brzine (engl. "volume velocity source"). Izvori zvuka smjesteni su na cetiri karakteristicna mjesta: kod lijevog stražnjeg kotaca, kod lijevog prednjeg kotaca, u prostoru motora te kod ispusnog lonca. U drugom koraku, polje kompleksnog akustickog tlaka izracunato po povrsini krute ovojnice vozila projicira se na pojedine dijelove karoserije. U trecem koraku, izracunato polje akustickog tlaka se koristi kao uzbuda za deformabilne dijelove karoserije (tzv. konfiguracija "body-in-blue"). Na kraju, izracunate su funkcije frekvencijskog odziva između akustickog tlaka u sest karakteristicnih tocaka unutrasnjosti vozila i volumne brzine izvora sa cetiri navedene lokacije. Također, izracunata je, prikazana i diskutirana raspodjela akustickog tlaka u cijelom putnickom prostoru.

1 citations


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

  • ...Although the summation of rigid wall acoustic modes does not converge to the correct boundary normal velocity, it does converge correctly to the surface pressure, which is all that is needed for a correct formulation of the coupled equations [16],[17]....

    [...]

Dissertation
30 Jan 2020
Abstract: The subject of this research is the improvement of the dynamic behaviour of structures using passive and active approaches to vibration control by using inerters. Inerter is a relatively new element in the theory of mechanical networks. It is a mechanical device that generates force proportional to the relative acceleration between its terminals. The use of inerters is still relatively unexplored and offers many new possibilities of reducing unwanted vibration effects, which is of particular importance in the resonant working conditions of the structure. In the first part of the thesis, passive linear dynamic systems are considered. In the second part, the passive systems are enhanced by the active control. Stability analysis of the active systems is performed. In addition to the parameters that ensure stable operation of the system, the optimization of vibration behaviour of active structures is carried out. The main optimization criterion used is the minimization of the specific kinetic energy of system vibration in a broad frequency band. Throughout the work, analytical and numerical methods are combined, depending on the complexity of the considered system. The achieved results are compared through discussion on the usefulness of the active control and inerter implementation, depending on the system considered. The motivation for the work are synergistic effects regarding the utilization of inerters in parallel with active control systems. The result of the research is a development of new methods for passive and active vibration control. Furthermore, it is shown that employing the inerter in isolation systems can yield with substantial improvements in fatigue life of isolator coupling components, i.e. springs. Novel cylindrical helical spring stress and displacement correction factors are proposed.

1 citations


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

  • ...Hence, the idea behind the sky-hook damper is that the ideal DVF isolator would enforce the payload to maintain a stable posture as if it was suspended by a fixed imaginary hook in the sky [38], unaffected by the disturbance....

    [...]

  • ...This is evident in numerous inerter-related suspension performance benefits reported by various researchers [2],[21]-[23],[38],[54],[58]-[60],[64],[85]-[95]....

    [...]

15 Sep 2022
TL;DR: In this paper , an original numerical framework is developed in order to estimate the free field sound radiation from baffled structural panels subjected to turbulent boundary layer (TBL) flow-induced excitation.
Abstract: An original numerical framework is developed in the present research work in order to estimate the free field sound radiation from baffled structural panels subjected to turbulent boundary layer (TBL) flow-induced excitation. A semi-analytical method is used to estimate the TBL wall pressure spectrum which is decomposed using Cholesky’s technique to obtain random wall pressure in the frequency domain. Structural panels are modeled using the finite element technique and a coupled finite element-boundary element modeling technique is developed to estimate the sound power level radiating into the free field. Results are obtained for laminated composite structural panels with various fiber orientations and significant findings are discussed. The developed technique has the potential to be further extended for complex structures in terms of geometry, material properties, and boundary conditions. The complete numerical toolbox, developed in an in-house MATLAB environment, enables the prediction of turbulent-structure acoustic coupled behavior at an early design stage.
References
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Abstract: A type of force generator which can respond to general feedback signals from a vibrating system in order to control the vibration but which does not require the power supply of a servomechanism is described. Computer simulation studies show that performance comparable to that of fully active vibration control systems can be achieved with the semi-active type of device. Physical embodiments of the concept are discussed and compared to hardware used in active and passive vibration control systems.

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TL;DR: In this paper, the authors introduce the idea of joint probability distributions and average for linear systems and their response to random vibrational signals. But they do not discuss the relationship between these distributions and the average.
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Abstract: An algorithm is presented to adapt the coefficients of an array of FIR filters, whose outputs are linearly coupled to another array of error detection points, so that the sum of all the mean square error signals is minimized. The algorithm uses the instantaneous gradient of the total error, and for a single filter and error reduces to the "filtered x LMS" algorithm. The application of this algorithm to active sound and vibration control is discussed, by which suitably driven secondary sources are used to reduce the levels of acoustic or vibrational fields by minimizing the sum of the squares of a number of error sensor signals. A practical implementation of the algorithm is presented for the active control of sound at a single frequency. The algorithm converges on a timescale comparable to the response time of the system to be controlled, and is found to be very robust. If the pure tone reference signal is synchronously sampled, it is found that the behavior of the adaptive system can be completely described by a matrix of linear, time invariant, transfer functions. This is used to explain the behavior observed in simulations of a simplified single input, single output adaptive system, which retains many of the properties of the multichannel algorithm.

820 citations


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

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