Measurement techniques of the sensitivity functions to characterize the vibroacoustic response of panels under random excitations

Transcription

1 Measurement techniques of the sensitivity functions to characterize the vibroacoustic response of panels under random ecitations C.MARCHETTO (1-2), L. MAXIT (1), O. ROBIN (2), A. BERRY (2) (1) Laboratoire Vibrations Acoustique (LVA), Lyon FRANCE (2) Groupe d Acoustique de l Université de Sherbrooke (GAUS), Sherbrooke CANADA

2 1 Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields

3 1 Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields DAF TBL

4 1 Reverberant room, synthesized pressure field Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields DAF TBL

5 1 Reverberant room, synthesized pressure field Wind tunnel, in situ, synthesized pressure field Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields DAF TBL

6 1 Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields Reverberant room, synthesized pressure field Wind tunnel, in situ, synthesized pressure field Eperimental VA response by direct measurement DAF TBL

7 1 Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields Reverberant room, synthesized pressure field Wind tunnel, in situ, synthesized pressure field Eperimental VA response by direct measurement Issues of repeatability and very costly DAF TBL

8 1 Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields Reverberant room, synthesized pressure field Wind tunnel, in situ, synthesized pressure field Eperimental VA response by direct measurement Not fully representative of a DAF Issues of repeatability and very costly DAF TBL

9 1 Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields Reverberant room, synthesized pressure field Wind tunnel, in situ, synthesized pressure field Eperimental VA response by direct measurement Not fully representative of a DAF Issues of repeatability and very costly DAF TBL Wall-pressure spectrum

10 1 Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields Reverberant room, synthesized pressure field Wind tunnel, in situ, synthesized pressure field Eperimental VA response by direct measurement Not fully representative of a DAF Issues of repeatability and very costly DAF TBL Wall-pressure spectrum Analytical/semi-empirical model, measurements, etc. any data representing the considered ecitation

11 1 Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields Reverberant room, synthesized pressure field Wind tunnel, in situ, synthesized pressure field Eperimental VA response by direct measurement Not fully representative of a DAF Issues of repeatability and very costly DAF TBL Wall-pressure spectrum Sensitivity functions eperimentally determined using a reciprocity principle Analytical/semi-empirical model, measurements, etc. any data representing the considered ecitation

12 1 Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields Reverberant room, synthesized pressure field Wind tunnel, in situ, synthesized pressure field Eperimental VA response by direct measurement Not fully representative of a DAF Issues of repeatability and very costly DAF TBL Wall-pressure spectrum Sensitivity functions eperimentally determined using a reciprocity principle Eperimental VA response through post-processing Analytical/semi-empirical model, measurements, etc. any data representing the considered ecitation

13 1 Contet of the study Aim: vibroacoustic (VA) response of a plane panel to random pressure fields Reverberant room, synthesized pressure field Wind tunnel, in situ, synthesized pressure field Eperimental VA response by direct measurement Not fully representative of a DAF Issues of repeatability and very costly DAF TBL Wall-pressure spectrum Sensitivity functions eperimentally determined using a reciprocity principle Eperimental VA response through post-processing Analytical/semi-empirical model, measurements, etc. any data representing the considered ecitation C. Marchetto, L. Mait, O. Robin, A. Berry, Vibroacoustic response of panels under diffuse acoustic field ecitation from sensitivity functions and reciprocity principles, J. Acoust. Soc. Am., (submitted in 2017).

14 1 Today s presentation Wind tunnel, in situ, synthesized pressure field Eperimental VA response by direct measurement TBL Wall-pressure spectrum Sensitivity functions eperimentally determined using a reciprocity principle Eperimental VA response through post-processing Analytical/semi-empirical model, measurements, etc. any data representing the considered ecitation

15 2 System and coordinates Mathematical formulation of the problem Plane panel y TBL = (, y)

16 2 System and coordinates Mathematical formulation of the problem Plane panel y TBL = (, y) Assumptions for mathematical development: system is linear (elastic material and low strains),

17 2 System and coordinates Mathematical formulation of the problem Plane panel y TBL = (, y) Assumptions for mathematical development: system is linear (elastic material and low strains), ecitation is spatially homogeneous and stationary in time,

18 2 System and coordinates Mathematical formulation of the problem Plane panel y TBL = (, y) Assumptions for mathematical development: system is linear (elastic material and low strains), ecitation is spatially homogeneous and stationary in time, random process is considered ergodic.

19 2 System and coordinates Mathematical formulation of the problem Plane panel y TBL = (, y) k = (k, k y ) Vibration response of the panel + S vv, ω = 1 4π 2 H v, k, ω 2 S pb p b k, ω dk

20 2 System and coordinates Mathematical formulation of the problem Plane panel y TBL = (, y) k = (k, k y ) Vibration response of the panel S vv, ω = 1 characterizes the ecitation + 4π 2 H v, k, ω 2 S pb p b k, ω dk

21 2 System and coordinates Mathematical formulation of the problem Plane panel y TBL = (, y) k = (k, k y ) Vibration response of the panel S vv, ω = 1 characterizes the ecitation + 4π 2 H v, k, ω 2 S pb p b k, ω dk «sensitivity functions» : H v, k, ω = H v/fn,, ω e jk d S

22 System and coordinates Mathematical formulation of the problem Plane panel y TBL = (, y) k = (k, k y ) Vibration response of the panel S vv, ω = 1 characterizes the ecitation + 4π 2 H v, k, ω 2 S pb p b k, ω dk «sensitivity functions» : H v, k, ω = H v/fn,, ω e jk d S panel s response at point when ecited at point by a normal force F n 2

23 3 Definition of the sensitivity functions: reciprocity principle Sensitivity functions H v, k, ω = H v/fn,, ω e jk d S

24 3 Definition of the sensitivity functions: reciprocity principle Sensitivity functions Direct interpretation Velocity response at point when the panel is ecited at points by a wall-pressure plane wave of wavenumber k. H v, k, ω = H v/fn,, ω e jk d S z v() k H v (, k) = v()

25 3 Definition of the sensitivity functions: reciprocity principle Sensitivity functions H v, k, ω = H v/fn,, ω e jk d S Direct interpretation Velocity response at point when the panel is ecited at points by a wall-pressure plane wave of wavenumber k. Reciprocal interpretation H v/fn,, ω = H v/fn,, ω z v() k H v (, k) = v()

26 3 Definition of the sensitivity functions: reciprocity principle Sensitivity functions H v, k, ω = H v/fn,, ω e jk d S Direct interpretation Velocity response at point when the panel is ecited at points by a wall-pressure plane wave of wavenumber k. Reciprocal interpretation H v/fn,, ω = H v/fn,, ω H v, k, ω = H v/fn,, ω e jk d S z v() k H v (, k) = v()

27 3 Definition of the sensitivity functions: reciprocity principle Sensitivity functions H v, k, ω = H v/fn,, ω e jk d S Direct interpretation Velocity response at point when the panel is ecited at points by a wall-pressure plane wave of wavenumber k. Reciprocal interpretation H v/fn,, ω = H v/fn,, ω H v, k, ω = TF H v/fn,, ω z v() k H v (, k) = v()

28 3 Definition of the sensitivity functions: reciprocity principle Sensitivity functions H v, k, ω = H v/fn,, ω e jk d S Direct interpretation Velocity response at point when the panel is ecited at points by a wall-pressure plane wave of wavenumber k. z v() k H v (, k) = v() Reciprocal interpretation H v/fn,, ω = H v/fn,, ω H v, k, ω = TF H v/fn,, ω z F n () v H v (, k) = DFT(v )

29 Overview Wind tunnel Eperimental vibration response by direct measurement TBL Wall-pressure spectrum Sensitivity functions eperimentally determined using a reciprocity principle Eperimental vibration response through post-processing Analytical/semi-empirical model, measurements, etc. any data representing the considered ecitation

30 4 Models in the literature How to describe the ecitation? Semi-empirical models: Corcos, Mellen Analytical models: Chase Adjustable through eponential decay parameters (α, α y )

31 4 Models in the literature How to describe the ecitation? Semi-empirical models: Corcos, Mellen Analytical models: Chase Adjustable through eponential decay parameters (α, α y ) Currently, no model is fully satisfactory to predict the wall-pressure fluctuations induced by a TBL.

32 4 Models in the literature How to describe the ecitation? Semi-empirical models: Corcos, Mellen Analytical models: Chase Adjustable through eponential decay parameters (α, α y ) Currently, no model is fully satisfactory to predict the wall-pressure fluctuations induced by a TBL. Measurement of the wall-pressure fluctuations in an anechoic wind tunnel Flush mounted microphone array (spiral shape)

33 4 Models in the literature How to describe the ecitation? Semi-empirical models: Corcos, Mellen Analytical models: Chase Adjustable through eponential decay parameters (α, α y ) Currently, no model is fully satisfactory to predict the wall-pressure fluctuations induced by a TBL. Measurement of the wall-pressure fluctuations in an anechoic wind tunnel Flush mounted microphone array (spiral shape) Radial resolution of 2 mm Rotation of 2 degrees

34 4 Models in the literature How to describe the ecitation? Semi-empirical models: Corcos, Mellen Analytical models: Chase Adjustable through eponential decay parameters (α, α y ) Currently, no model is fully satisfactory to predict the wall-pressure fluctuations induced by a TBL. Measurement of the wall-pressure fluctuations in an anechoic wind tunnel Flush mounted microphone array (spiral shape) Radial resolution of 2 mm Rotation of 2 degrees kth ma 1570 m 1

35 Overview Wind tunnel Eperimental vibration response by direct measurement TBL Wall-pressure spectrum Sensitivity functions eperimentally determined using a reciprocity principle Eperimental vibration response through post-processing Analytical/semi-empirical model, measurements, etc. any data representing the considered ecitation

36 5 Considered test case Numerical and eperimental validation Simply supported aluminum plate y M L = 480 mm l = 420 mm e = 3.19 mm coordinates of point M: = 420 ; y = 300 mm

37 5 Considered test case Numerical and eperimental validation Simply supported aluminum plate y M L = 480 mm l = 420 mm e = 3.19 mm coordinates of point M: Ecitation = 420 ; y = 300 mm TBL reproduced in the anechoic wind tunnel: U = 40 m/s in direction.

38 5 Considered test case Numerical and eperimental validation Simply supported aluminum plate y M L = 480 mm l = 420 mm e = 3.19 mm coordinates of point M: Ecitation = 420 ; y = 300 mm TBL reproduced in the anechoic wind tunnel: U = 40 m/s in direction. Frequency range: 170,2000 Hz

39 5 Considered test case Numerical and eperimental validation Simply supported aluminum plate y M L = 480 mm l = 420 mm e = 3.19 mm coordinates of point M: Ecitation = 420 ; y = 300 mm TBL reproduced in the anechoic wind tunnel: U = 40 m/s in direction. Frequency range: 170,2000 Hz Response of the plate S vv M, ω = + 1 4π 2 H v M, k, ω 2 S meas pb p b k, ω dk

40 5 Considered test case Numerical and eperimental validation Simply supported aluminum plate y M L = 480 mm l = 420 mm e = 3.19 mm coordinates of point M: Ecitation = 420 ; y = 300 mm TBL reproduced in the anechoic wind tunnel: U = 40 m/s in direction. Frequency range: 170,2000 Hz Response of the plate S vv M, ω = k ma k y ma 1 4π 2 H v M, k, ω 2 S meas pb p b k, ω k k k y =kmin =kmin y

41 5 Considered test case Numerical and eperimental validation Simply supported aluminum plate y M L = 480 mm l = 420 mm e = 3.19 mm coordinates of point M: Ecitation = 420 ; y = 300 mm TBL reproduced in the anechoic wind tunnel: U = 40 m/s in direction. Frequency range: 170,2000 Hz Response of the plate S vv M, ω = k ma Ω k? k y ma 1 4π 2 H v M, k, ω 2 S meas pb p b k, ω k k k y =kmin =kmin y

42 5 Considered test case Numerical and eperimental validation Simply supported aluminum plate y M L = 480 mm l = 420 mm e = 3.19 mm coordinates of point M: Ecitation = 420 ; y = 300 mm TBL reproduced in the anechoic wind tunnel: U = 40 m/s in direction. Frequency range: 170,2000 Hz Response of the plate S vv M, ω = k ma Ω k? k y ma structure filters out the ecitation 1 4π 2 H v M, k, ω 2 S meas pb p b k, ω k k k y =kmin =kmin y

43 6 Numerical and eperimental validation Defining the wavenumber domain Estimation of S pb p b (k, ω) on the largest domain possible (limited by computational power).

44 6 Numerical and eperimental validation Defining the wavenumber domain Estimation of S pb p b (k, ω) on the largest domain possible (limited by computational power). Filtering effect of the plate defined by: 10 log 10 (H v S pb p b ) ma 10 log 10 H v S pb p b 10 db.

45 6 Numerical and eperimental validation Defining the wavenumber domain Estimation of S pb p b (k, ω) on the largest domain possible (limited by computational power). Filtering effect of the plate defined by: 10 log 10 (H v S pb p b ) ma 10 log 10 H v S pb p b 10 db. k ma

46 6 Numerical and eperimental validation Defining the wavenumber domain Estimation of S pb p b (k, ω) on the largest domain possible (limited by computational power). Filtering effect of the plate defined by: 10 log 10 (H v S pb p b ) ma 10 log 10 H v S pb p b 10 db. k ma on the whole frequency range k ma

47 Overview Wind tunnel Eperimental vibration response by direct measurement TBL Wall-pressure spectrum Sensitivity functions eperimentally determined using a reciprocity principle Eperimental vibration response through post-processing Analytical/semi-empirical model, measurements, etc. any data representing the considered ecitation

48 7 Numerical and eperimental validation Measurement of the sensitivity functions Simply supported plate shaker M y M: = 420 ; y = 300 mm

49 7 Numerical and eperimental validation Measurement of the sensitivity functions Simply supported plate shaker M y N y = 27 scanning laser vibrometer M: = 420 ; y = 300 mm

50 7 Numerical and eperimental validation Measurement of the sensitivity functions Simply supported plate shaker M y N y = 27 scanning laser vibrometer M: = 420 ; y = 300 mm H v/fn N N y, M, ω

51 7 Numerical and eperimental validation Measurement of the sensitivity functions Simply supported plate shaker M y N y = 27 scanning laser vibrometer M: = 420 ; y = 300 mm H v/fn N N y, M, ω TF H v/fn N N y, M, ω

52 7 Numerical and eperimental validation Measurement of the sensitivity functions Simply supported plate shaker M y N y = 27 scanning laser vibrometer M: = 420 ; y = 300 mm H v/fn N N y, M, ω TF H v/fn N N y, M, ω = H v M, k, ω

53 8 Numerical and eperimental validation Comparison of sensitivity functions on the reduced wavenumber domain H v th (M, k, ω) H v ep (M, k, ω) using the reciprocity principle

54 Overview Wind tunnel Eperimental vibration response by direct measurement TBL Wall-pressure spectrum Sensitivity functions eperimentally determined using a reciprocity principle Eperimental vibration response through post-processing Analytical/semi-empirical model, measurements, etc. any data representing the considered ecitation

55 9 Numerical and eperimental validation Theory versus eperimental reciprocity approach S vv M, ω = 1 4π 2 H v th M, k, ω 2 S meas pb p b k, ω k k k largest domain S vv M, ω = 1 4π 2 H v meas M, k, ω 2 S meas pb p b k, ω k k k reduced domain

56 Overview Wind tunnel Eperimental vibration response by direct measurement? TBL Wall-pressure spectrum Sensitivity functions eperimentally determined using a reciprocity principle Eperimental vibration response through post-processing Analytical/semi-empirical model, measurements, etc. any data representing the considered ecitation

57 10 Confrontation to measurement in an anechoic wind tunnel 8 4 plywood panel ¾ of thickness

58 10 Confrontation to measurement in an anechoic wind tunnel Simply supported plate flush mounted 8 4 plywood panel ¾ of thickness

59 10 Confrontation to measurement in an anechoic wind tunnel Sandpaper strip Simply supported plate flush mounted 8 4 plywood panel ¾ of thickness

60 10 Confrontation to measurement in an anechoic wind tunnel Sandpaper strip Simply supported plate flush mounted 8 4 plywood panel ¾ of thickness Accelerometer

61 10 Confrontation to measurement in an anechoic wind tunnel z position of the plate U [m/s] U = 0,99 U

62 10 Confrontation to measurement in an anechoic wind tunnel z

63 10 Confrontation to measurement in an anechoic wind tunnel z

64 10 Confrontation to measurement in an anechoic wind tunnel z

65 10 Confrontation to measurement in an anechoic wind tunnel z

66 10 Confrontation to measurement in an anechoic wind tunnel z

67 11 Confrontation to measurement in an anechoic wind tunnel Wind tunnel measurements versus eperimental reciprocity approach S vv meas M, ω S vv M, ω = 1 4π 2 H v meas M, k, ω 2 S meas pb p b k, ω k k k reduced domain

68 12 Conclusion and future work Conclusion: sensitivity functions can be eperimentally determined based on the reciprocity principle,

69 12 Conclusion and future work Conclusion: sensitivity functions can be eperimentally determined based on the reciprocity principle, plate vibration response under TBL is well predicted using the proposed methodology,

70 12 Conclusion and future work Conclusion: sensitivity functions can be eperimentally determined based on the reciprocity principle, plate vibration response under TBL is well predicted using the proposed methodology, the proposed methodology could be used (at least in a development phase) as a substitute to wind tunnel testing to estimate the response of a panel to a TBL.

71 12 Conclusion and future work Conclusion: sensitivity functions can be eperimentally determined based on the reciprocity principle, plate vibration response under TBL is well predicted using the proposed methodology, the proposed methodology could be used (at least in a development phase) as a substitute to wind tunnel testing to estimate the response of a panel to a TBL. Future work: tests under several flow speeds and at several points on the plate,

72 12 Conclusion and future work Conclusion: sensitivity functions can be eperimentally determined based on the reciprocity principle, plate vibration response under TBL is well predicted using the proposed methodology, the proposed methodology could be used (at least in a development phase) as a substitute to wind tunnel testing to estimate the response of a panel to a TBL. Future work: tests under several flow speeds and at several points on the plate, test of panels with unknown properties,

73 12 Conclusion and future work Conclusion: sensitivity functions can be eperimentally determined based on the reciprocity principle, plate vibration response under TBL is well predicted using the proposed methodology, the proposed methodology could be used (at least in a development phase) as a substitute to wind tunnel testing to estimate the response of a panel to a TBL. Future work: tests under several flow speeds and at several points on the plate, test of panels with unknown properties, compare TL or other VA indicators values between DAF and TBL ecitations.

74 Thank you for your attention!

75 Thank you for your attention!

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