Correlation of the Vibroacoustic Response of Structural Panels with Isight for use in Statistical Energy Analysis in Aerospace Applications

Transcription

1 Correlation of the Vibroacoustic Response of Structural Panels with Isight for use in Statistical Energy Analysis in Aerospace Applications ATA Engineering, Inc El Camino Real, Suite 200 San Diego, CA T F Prepared for: 2012 SIMULIA Community Conference Prepared by: Cory Rupp Lina Maricic Date: May 15, 2012

2 Outline Objectives and background Overview of the correlation process Example correlation problem of a sandwich panel Example correlation problem of a ribbed panel Potential use cases for Isight in vibroacoustic analysis Conclusions 2

3 Objectives and Background Vibroacoustic analysis at high frequency is often performed by statistical energy analysis (SEA) using analysis packages such as VA-One. A difficulty in performing SEA on complex aerospace structures is ensuring that the SEA subsystem (e.g. a structural panel) properly represents the actual structure. The model is often checked by comparing the response of a subsystem to that of a refined finite element (FE) mesh of the subsystem. However, modifying the SEA properties to improve the correlation between the SEA and FE responses is often cumbersome and timeconsuming, primarily involving guess-and-check work. To alleviate the difficulties in this process, we have developed a methodology and an interface between SIMULIA s Isight simulation management software and VA-One that automates the correlation process. 3

4 Methodology Setup: Isight + Matlab + VA-One 1. Use Isight to drive an optimization algorithm and make changes to design variables. 2. Use VA-One to solve vibroacoustic problems for a set of design variables and return the vibroacoustic response. Control via Matlab-based API. 3. Use Matlab as an interface between Isight and VA-One and to calculate the objective function. Data-flow Sim-flow 4

5 Objective Function Resembles a Weighted Least-Squares Approach Several objective function formulations were tested when developing the methodology for the correlation process. The formulation found to perform the best resembles a weighted least-squares approach: Weight function Simulation (SEA) response Target (FE) response ( More weight on higher frequencies) More weight on high frequencies to emphasize more accurate solution when SEA has more modes-in-band. 5

6 Example 1: Conical Sandwich Panel Conical sandwich panel properties: honeycomb Aluminum core carbon fiber composite facesheets - 50 maximum radius, 30 in height at modes calculated up to 4,600 Hz in NX Nastran - Free-free boundary condition - First bending mode is 126 Hz 6

7 FEA and SEA Models in VA-One FE subsystem of the sandwich panel created in VA-One - Modes imported into VA-One - Vibroacoustic solution to 4000 Hz in 1/42 octave bands - Panel-averaged vibroacoustic acceleration response recovered and converted to 1/3 octave bands SEA subsystem of the same sandwich panel created in VA-One as singly curved shell - Default properties used as the initial guess - Vibroacoustic solution to 4000 Hz in 1/3 octave bands Diffuse acoustic field (DAF) applied on both subsystems Four dummy SEA panels were connected to the boundaries of both FE and SEA subsystems - Response of FEM highly dependent on boundary conditions, but not the case for SEA - Dummy SEA panels ensure appropriate comparison Dummy SEA panels FE SEA 7

8 Initial Guess Model Under- Predicts Response Above 800 Hz. Panel-averaged acceleration response is under-predicted at high frequencies The low frequency SEA response can only capture the general trend because of the modal nature of the response 8

9 Isight Optimization Tools Used to Improve Correlation SEA subsystem design variables: - Material densities of core and facesheets - Thicknesses of core and facesheets - Panel radius Optimization algorithms used: - Modified method of feasible directions (MMFD) - Gradient based algorithm - Default parameters used - Downhill simplex (DS) - Simplex based exploratory algorithm - Default parameters used 9

10 Both Algorithms Performed Equally Well at Improving Correlation Both optimization algorithms improve correlation. Objective function value improved from 11.1 to: MMFD 3.95 at 89 function evaluations DS 4.18 at 64 function evaluations Low frequency response ( < 600Hz) unchanged, because of low modes-inband for SEA to conform to variation in FE response. 10

11 Comparison of Initial and Optimized SEA Panel Properties Final designs reveal relative sensitivities of design variables near the correlated design point. The panel is most sensitive to core thickness. Sandwich panel property Initial guess Opt - MMFD Opt - DS Core thickness (in) Core density (lbm/in³) Facesheet thickness (in) Facesheet density (lbm/in³) Radius of curvature (in)

12 Example 2: Cylindrical Ribbed Panel Cylindrical ribbed panel properties: - Varying thickness facesheet - Varying thickness ribs spaced 4.5 apart - 36 in height, 50 radius of curvature, 60 span - Titanium used for both facesheet and ribs 368 modes calculated up to 3700 Hz in NX Nastran - Free-free boundary condition - First bending mode is 35 Hz 12

13 Ribbed Panel FEA and SEA Models in VA-One FE subsystem of the ribbed panel created in VA- One - Modes imported into VA-One - Vibroacoustic solution to 3150 Hz in 1/42 octave bands - Panel-averaged vibroacoustic acceleration response recovered and converted to 1/3 octave bands SEA subsystem of the same ribbed panel created in VA-One - Default properties used as the initial guess - Vibroacoustic solution to 3150 Hz in 1/3 octave bands DAF applied on both FE and SEA subsystems Four dummy SEA panels were connected to the boundaries of the FE and SEA subsystems Dummy SEA panels FE SEA 13

14 Poor Correlation Between Initial Guess and FE Models Clearly poor correlation at most frequencies Reasonable modes-in-band (MIB) only above ~500 Hz Very difficult to correlate by hand because of MIB dropouts Nonlinear relationship with design variables 14

15 Isight Optimization Tools Used to Improve Correlation SEA subsystem design variables: - Material density - Facesheet thickness - Offset of the ribs from the facesheet - Spacing between ribs Optimization algorithms used: - Multi-island genetic algorithm (MIGA) - Number of islands: 5 - Pointer algorithm - Combination of several different types of algorithms - Allowable job time set to 1 hour 15

16 Both Algorithms Significantly Improved Overall Correlation Correlation is significantly improved, especially at high frequency Objective function value improved from 85.6 to: MIGA 6.83 at 501 function evaluations Pointer 3.22 at 692 function evaluations Low frequency response difficult to correlate because of few modes-inband. 16

17 Comparison of Initial and Optimized SEA Ribbed Panel Properties Final designs show very different design points even though the responses are somewhat similar. Would be difficult to explore the design space without Isight. Ribbed panel property Initial guess Opt - Pointer Opt - MIGA Panel skin density (lbm/in³) Panel skin thickness (in) Rib 1 spacing (in) Rib 1 offset (in) Rib 2 spacing (in) Rib 2 offset (in)

18 Other Potential Use Cases for Isight in Vibroacoustic Analysis Multidisciplinary design optimization where vibroacoustic analysis is an integral part of the solution - For example: have design parameters in Isight update an FE model used for static, random vibration and other analysis - Then correlate the SEA model to a new FE model definition using methodology presented here Sensitivity analysis of SEA responses due to a variety of input factors - Monte Carlo analysis due to uncertainty in the acoustic environment. - Find the sensitivity of cabin noise level or panel responses to structural inputs such as panel stiffness or mass factors. 18

19 Conclusions Isight can be effectively used to improve the correlation between SEA and FE vibroacoustic models. Since FE results are very sensitive to boundary conditions, realistic boundary conditions should be used to correlate SEA panels. The effort necessary to complete any panel correlation can be cut from up to a day of manual work to about 1.5 hours Significant reduction in the amount of engineering effort and time results in reduced costs and more accurate SEA models. 19