FLINOVIA 2017, State Collage, USA. Dr. Alexander Peiffer, Dr. Uwe Müller 27 th -28 th April 2017

Transcription

1 Review of efficient methods for the computation of transmission loss of plates with inhomogeneous material properties and curvature under turbulent boundary layer excitation FLINOVIA 2017, State Collage, USA Dr. Alexander Peiffer, Dr. Uwe Müller 27 th -28 th April 2017

2 Overview Introduction Theory Implementations Test case Conclusions 2

3 Introduction Motivation for TBL load consideration and the need for model reduction 3

4 Introduction Turbulent boundary layer (TBL) noise Main interior noise source in front fuselages of modern turbofan aircraft Load representation Cross correlation spectrum (computationally expensive) jet noise TBL fan noise Model reduction required Modal joint acceptance (MJA) Diagonalization? Singular value decomposition (SVD) Analytical methods / statistical energy analysis (SEA) A

5 Theory Basic outline of vibroacoustic random load response 5

6 Theory Hybrid method Hybrid method based on total stiffness matrix, see [1], [2] & [3]: (1) Random excitation defined by cross-correlation spectrum Δ (2) Displacement response: ω (3) The radiated power into the fluids is given by: a) Π, S, (4) U 6

7 Theory modal condensation Equation (1) in modal coordinates (denoted by a prime ') 1 1 (5) Modal cross spectral matrix of random response (3) is given by: ω (6) The term in parenthesis is called modal joint acceptance and are not diagonal. Transmissionloss: 10 log with assuming a DAF power irradiation and Π (7) 7

8 Theory Random modal load response Graham [1] assumes all matrices as diagonal providing a fast and simple inversion:,, (8), Is this valid for non-homogeneous mass distribution? Thus, inspection of Modal radiation stiffness: Modal joint acceptance: Radiated power, Π D S D Experience: Graham assumption is valid for homogeneous plates For non-homogeneous plates the assumption is not valid for diffuse acoustic field (DAF) but for TBL (ref. [4]). DAF response depends exclusively on because of the diffuse field reciprocity [2] 8

9 Theory Singular value decomposition The cross spectral matrix can be approximated by singular value decomposition to reduce the size of the problem. The symmetric matrix can be expressed as: (9) Columns of form an orthogonal base of unit vectors with (10) The load matrix can be approximated by deterministic load vectors sorted in order of relevance, given by the singular values.,,,, (11) 9

10 Test case Generic cases for numerical performance study 10

11 Test cases Corcos correlation model with Jolly correction ft, 0.8, 10m, m Wavenumber and space representation Not recommended for and Structural test case 1 cylindrical aluminum plate with t=4mm Lx = 0.8 m, Ly = 1.2 m damping loss 0.01 simply supported boundary conditions No 1: Homogenous shell Structural test case 2 Fuselage panel with stringer and frames Lx = 1.8 m, Ly = 1.1 m No 2: Fuselage panel 11

12 Test cases Applied reduction methods and objective Performance and precision for applied to test cases Singular value decomposition Number of required singular values in,,,, Computation time for SVD Computation time for load creation and FEM solution Hybrid method in modal space Computation time of modal radiation stiffness calculation & inversion Computation time of joint acceptance Full approach and Graham approach (only diagonal 1kHz 12

13 abs(general) Efficient methods for structural TBL response calculation Test case - SVD of TBL (Corcos Model) ~50 components required 30 min for SVD calculation + 2 hours of load case generation FEM solution not started 10 3 S ofsxy_ma0.8fl330x0= DOF:1 DOF:2 DOF:3 DOF:4 DOF:5 DOF:6 DOF:7 DOF:8 DOF:9 DOF:10 DOF:11 DOF:12 DOF:13 DOF:14 DOF:15 DOF:16 DOF:17 DOF:18 DOF:19 DOF:20 DOF:21 DOF:22 DOF:23 DOF:24 DOF: frequency 13 abs(general) 10 3 S ofsxy_ma0.8fl330x0= ~ 10 DOF:26 DOF:27 DOF:28 DOF:29 DOF:30 DOF:31 DOF:32 DOF:33 DOF:34 DOF:35 DOF:36 DOF:37 DOF:38 DOF:39 DOF:40 DOF:41 DOF:42 DOF:43 DOF:44 DOF:45 DOF:46 DOF:47 DOF:48 DOF:49 DOF: frequency

14 Test case - Singular value decomposition From the number of required components, the SVD is not efficient: 50 components minimum! Calculation time of 50 load cases: ~ 30 minutes Due to the NASTRAN way of describing dynamic surface pressure loads, the output of test cases take about 2 hours Calculation time of FEM solution not investigated From other test runs with 20 cases this way of load generation is not efficient ~1day compared to 3 minutes for modal methods Possible solutions: Low frequencies Direct load application in MATLAB Different load formulation in NASTRAN nodal forces (FORCE, DAREA) instead of PLOAD 14

15 Test case DAF and TBL transmission loss Structure 1 DAF transmission loss is slightly overestimated by the diagonal form Good agreement for TBL transmission loss Graham assumption valid for homogeneous shells computational gain ~10 DAF: TBL: 15

16 Test case DAF and TBL transmission loss Structure 2 DAF transmission loss is overestimated by the diagonal form The TBL transmission loss is slightly overestimated, but provides reliable results Graham assumption not valid for DAF but for TBL DAF: TBL: 16

17 Test case - Modal radiation stiffness Structure 1 & 2 Modal radiation stiffness: No1: No 2: Normalized Off-diagonal components Error in DAF TL 17

18 Test case - Modal joint acceptance Structure No 1 & 2 Modal joint acceptance: No1: No 2: No explanation for good TBL results? 18

19 Test case Displacement cross spectrum Only structure No 2 Displacement response: DAF: TBL: 19

20 Test case Radiated Power Only Structure No 2 Modal power matrix: DAF: Π D, TBL: 20

21 Conclusions The hybrid modal method is appropriate for vibro-acoustic random response calculations Graham assumption is applicable for homogeneous shells and TBL The diagonal version provides a large reduction in computational expense The structural response to diffuse acoustic fields requires the full modal radiation stiffness matrix for non-homogeneous (realistic) panels The randomness of TBL excitation require at least the use of 50 principle component to get singular values with one order of magnitude below the first value Currently not applicable in a separated loadcase generation, export and external solver process 21

22 Thank you for your attention! 22

23 Literature [1] W. R. Graham, BOUNDARY LAYER INDUCED NOISE IN AIRCRAFT, PART I: THE FLAT PLATE MODEL, Journal of Sound and Vibration, vol. 192, no. 1, pp , Apr I. [2] P. J. Shorter and R. S. Langley, Vibro-acoustic analysis of complex systems, Journal of Sound and Vibration, vol. 288, no. 3, pp , [3] A. Peiffer, S. Brühl, and S. Tewes, Comparison of hybrid modeling tools for interior noise prediction, in Proceedings of INTERNOISE 2009, Ottawa, Canada, [4] U. C. Mueller, Hybrid method transmission loss calculations of aircraft cabin sidewall panels: comparison of wavenumber space approach and real space coordinate approach, in Proceedings of INTERNOISE 2015, San Francisco, CA, U.S.A., 2015, vol. in15_365, pp