Identification of Structural Parameters Based on Acoustic Measurements
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1 Identification of Structural Parameters Based on Acoustic Measurements Prof. Dr.-Ing. (habil.) Thomas Kletschkowski supported by Daniel Sadra, B.Eng. HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 1
2 Identification of Structural Parameters Based on Acoustic Measurements Prof. Dr.-Ing. (habil.) Thomas Kletschkowski supported by Daniel Sadra, B.Eng. HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 2
3 Motivation HAW Department of Automotive and Aeronautical Engineering (1.200 students, 45 professors/lecturers, 6 degree programs) HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 3
4 Motivation HAW Department of Automotive and Aeronautical Engineering (1.200 students, 45 professors/lecturers, 6 degree programs) Mɺɺ x + Dxɺ + K x = f HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 4
5 Motivation Characterization of Vibrating structures: Natural frequencies Mode shapes Modal damping HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 5
6 Motivation Characterization of vibrating structures: Natural frequencies Mode shapes Modal damping Problem: Attachment of sensors changes structural response Inductive sensors valid for metallic structure Optical methods are a proper choice in ground-tests Weber (2010) HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 6
7 Motivation Characterization of Vibrating structures: Natural frequencies Mode shapes Modal damping Problem: Attachment of sensors changes structural response Inductive sensors valid for metallic structure Optical methods are a proper choice in ground-tests Solution: Contact-free sensing of acoustic quantities Weber (2010) HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 7
8 Overview Motivation Why acoustic measurements? Description of a simple test rig Outline of parameter identification approach Discussion of experimental results Way forward in 2013 HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 8
9 Simplified Test Rig Set up Inspiration Johansson (2000) HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 9
10 Simplified Test Rig Set up Inspiration Johansson (2000) Test-Rig 159g 290g 158g 150g 900mm Sadra (2012) HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 10
11 Parameter Identification Approach - Idea HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 11
12 Parameter Identification Approach - Idea 1.) Initial Measurement (k, m unknown) mx ɺɺ t ( ) + kx( t) = 0 ω = 2 0 k m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 12
13 Parameter Identification Approach - Idea 1.) Initial Measurement (k, m unknown) mx ɺɺ t ( ) + kx( t) = 0 ω = 2 0 k m 2.) Measurement with additional mass ( m known) [ m + m] ɺɺ x( t) + kx( t) = 0 ω = 2 0 k m + m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 13
![) Measurement with additional mass ( m known) [ m + m] ɺɺ x( t) + kx( t) =](/docs-images/44/23170993/images/page_13.jpg "0 ω = 2 0 k m + m HAW Hamburg / Adaptronics and Structural Dynamics, Prof.")
14 Parameter Identification Approach - Idea 1.) Initial Measurement (k, m unknown) mx ɺɺ t ( ) + kx( t) = 0 ω = 2 0 k m 2.) Measurement with additional mass ( m known) [ m + m] ɺɺ x( t) + kx( t) = 0 3.) Calculation of mass 2 ω0 m = m 2 2 ω ω 0 0 ω = 2 0 k m + m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 14
![) Measurement with additional mass ( m known) [ m + m] ɺɺ x( t) + kx( t) = 0 3.](/docs-images/44/23170993/images/page_14.jpg ") Calculation of mass 2 ω0 m = m 2 2 ω ω 0 0 ω = 2 0 k m + m HAW Hamburg / Adaptronics")
15 Parameter Identification Approach - Idea 1.) Initial Measurement (k, m unknown) mx ɺɺ t ( ) + kx( t) = 0 ω = 2 0 k m 2.) Measurement with additional mass ( m known) [ m + m] ɺɺ x( t) + kx( t) = 0 3.) Calculation of mass 2 ω0 m = m 2 2 ω ω ) Calculation of stiffness k = ω m 2 0 ω = 2 0 k m + m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 15
![) Measurement with additional mass ( m known) [ m + m] ɺɺ x( t) + kx( t) = 0 3.](/docs-images/44/23170993/images/page_15.jpg ") Calculation of mass 2 ω0 m = m 2 2 ω ω 0 0 4.")
16 Parameter Identification for Lumped Model HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 16
17 Parameter Identification for Lumped Model Scaling of additional mass HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 17
18 Parameter Identification for Lumped Model Scaling of additional mass Calculation of modal mass HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 18
19 Parameter Identification for Lumped Model Scaling of additional mass Calculation of modal mass Calculation of modal stiffness HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 19
20 Parameter Identification for Lumped Model Scaling of additional mass Calculation of modal mass Calculation of modal stiffness Calculation of structural parameters HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 20
21 Simulation of Identification Procedure HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 21
22 Simulation of Identification Procedure Finite Element Model of Test Structure 3x lumped mass 4x Euler-Beam with mass-effect Simply supported beam L/2 L/4 HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 22
23 Simulation of Identification Procedure Finite Element Model of Test Structure 3x lumped mass 4x Euler-Beam with mass-effect L/2 L/4 simply supported beam ( t) ( t) with ( t) x ( t)... x ( t)... x ( t) T Mx ɺɺ + Kx = 0 x = 1 i 8 HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 23
24 Simulation of Identification Procedure Finite Element Model of Test Structure 3x lumped mass 4x Euler-Beam with mass-effect L/2 L/4 simply supported beam ( t) ( t) with ( t) x ( t)... x ( t)... x ( t) T Mx ɺɺ + Kx = 0 x = 1 i 8 ( ) 2 Solution of Eigenvalue Problem K ω M x = 0 yields 0 ˆ Natural frequencies Mode shapes (at discrete mass points) 2.4Hz [1.0, 1.42, 1.0] 11.0Hz [1.0, 0.00, -1.0] 21.2Hz [1.0, -0.85, 1.0] HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 24
25 Simulation of Identification Procedure Finite Element Model of Test Structure 3x lumped mass 4x Euler-Beam with mass-effect L/2 L/4 simply supported beam ( t) ( t) with ( t) x ( t)... x ( t)... x ( t) T Mx ɺɺ + Kx = 0 x = 1 i 8 ( ) 2 Solution of Eigenvalue Problem K ω M x = 0 yields 0 ˆ Natural frequencies Mode shapes (at discrete mass points) 2.4Hz 2.1Hz [1.0, 1.42, 1.0] [1.0, 1.42, 1.0] 11.0Hz 9.8Hz [1.0, 0.00, -1.0] [1.0, 0.00, -1.0] 21.2Hz 18.8Hz [1.0, -0.85, 1.0] [1.0, -0.81, 1.0] HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 25
26 Simulation of Identification Procedure Finite Element Model of Test Structure L/2 L/4 3x lumped mass 4x Euler-Beam with mass-effect simply supported beam +50g +100g +50g ( t) ( t) with ( t) x ( t)... x ( t)... x ( t) T Mx ɺɺ + Kx = 0 x = 1 i 8 ( ) 2 Solution of Eigenvalue Problem K ω M x = 0 yields 0 ˆ Natural frequencies Mode shapes (at discrete mass points) 2.4Hz 2.1Hz [1.0, 1.42, 1.0] [1.0, 1.42, 1.0] 11.0Hz 9.8Hz [1.0, 0.00, -1.0] [1.0, 0.00, -1.0] 21.2Hz 18.8Hz [1.0, -0.85, 1.0] [1.0, -0.81, 1.0] HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 26
27 Discussion of Experimental Results (1) HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 27
28 Discussion of Experimental Results (1) 1. Initial identification of natural frequencies and mode shapes Finite Element Model Accelerometer Microflown pu-probe 2.4 Hz [1.0, 1.4, 1.0] 3.6 Hz [1.0, 1.9, 1.1] 3.7 Hz [1.0, 1.4, 1.0] 11.0 Hz [1.0, 0.0, -1.0] 11.1 Hz [1.0, 0.0, -1.0] 11.6 Hz [1.0, 0.1, -1.1] 21.2 Hz [1.0, -0.9, 1.0] 23.1 Hz [1.0, -0.8, 1.1] 23.2 Hz [1.0, -1.0, 1.3] HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 28
29 Discussion of Experimental Results (1) 1. Initial identification of natural frequencies and mode shapes Finite Element Model Accelerometer Microflown pu-probe 2.4 Hz [1.0, 1.4, 1.0] 3.6 Hz [1.0, 1.9, 1.1] 3.7 Hz [1.0, 1.4, 1.0] 11.0 Hz [1.0, 0.0, -1.0] 11.1 Hz [1.0, 0.0, -1.0] 11.6 Hz [1.0, 0.1, -1.1] 21.2 Hz [1.0, -0.9, 1.0] 23.1 Hz [1.0, -0.8, 1.1] 23.2 Hz [1.0, -1.0, 1.3] HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 29
30 Discussion of Experimental Results (1) 1. Initial identification of natural frequencies and mode shapes Finite Element Model Accelerometer Microflown pu-probe 2.4 Hz [1.0, 1.4, 1.0] 3.6 Hz [1.0, 1.9, 1.1] 3.7 Hz [1.0, 1.4, 1.0] 11.0 Hz [1.0, 0.0, -1.0] 11.1 Hz [1.0, 0.0, -1.0] 11.6 Hz [1.0, 0.1, -1.1] 21.2 Hz [1.0, -0.9, 1.0] 23.1 Hz [1.0, -0.8, 1.1] 23.2 Hz [1.0, -1.0, 1.3] HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 30
31 Discussion of Experimental Results (1) 1. Initial identification of natural frequencies and mode shapes Finite Element Model Accelerometer Microflown pu-probe 2.4 Hz [1.0, 1.4, 1.0] 3.6 Hz [1.0, 1.9, 1.1] 3.7 Hz [1.0, 1.4, 1.0] 11.0 Hz [1.0, 0.0, -1.0] 11.1 Hz [1.0, 0.0, -1.0] 11.6 Hz [1.0, 0.1, -1.1] 21.2 Hz [1.0, -0.9, 1.0] 23.1 Hz [1.0, -0.8, 1.1] 23.2 Hz [1.0, -1.0, 1.3] 2. Identification of natural frequencies with additional masses Finite Element Model Accelerometer Microflown pu-probe 2.1 Hz 3.1 Hz 3.2 Hz 9.8 Hz 10.1 Hz 10.5 Hz 18.8 Hz 20.6 Hz 20.8 Hz HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 31
32 Discussion of Experimental Results (2) Structural parameters calculated for simplified test rig Finite Element Model Accelerometer Microflown pu-probe m ij kg k ij 3 10 N m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 32
33 Discussion of Experimental Results (2) Structural parameters calculated for simplified test rig Finite Element Model Accelerometer Microflown pu-probe m ij kg k ij 3 10 N m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 33
34 Discussion of Experimental Results (2) Structural parameters calculated for simplified test rig Finite Element Model Accelerometer Microflown pu-probe m ij kg k ij 3 10 N m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 34
35 Discussion of Experimental Results (2) Structural parameters calculated for simplified test rig Finite Element Model Accelerometer Microflown pu-probe m ij kg k ij 3 10 N m Stiffness-matrix according to Bernoulli-theory + N/m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 35
36 Discussion of Experimental Results (2) Structural parameters calculated for simplified test rig Finite Element Model Accelerometer Microflown pu-probe m ij kg k ij 3 10 N m Stiffness-matrix according to Bernoulli-theory + N/m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 36
37 Discussion of Experimental Results (2) Structural parameters calculated for simplified test rig Finite Element Model Accelerometer Microflown pu-probe m ij kg k ij 3 10 N m % Stiffness-matrix according to Bernoulli-theory + N/m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 37
38 Parameter Identification Improvements (1) HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 38
39 Parameter Identification Improvements (1) Calculation of generalized masses HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 39
40 Parameter Identification Improvements (1) Calculation of generalized masses Least Square Problem A11... A13 mgen1 m gen2 m1 Aij m gen3 m 2 = 0 m 3 0 A61... A63 0 HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 40
41 Parameter Identification Improvements (1) Calculation of generalized masses Least Square Problem A11... A13 mgen1 m gen2 m1 Aij m gen3 m 2 = 0 m 3 0 A61... A63 0 Improved modal stiffness k = ω m 2 gen, i 0 i gen, i HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 41
42 Parameter Identification Improvements (1) Calculation of generalized masses Least Square Problem A11... A13 mgen1 m gen2 m1 Aij m gen3 m 2 = 0 m 3 0 A61... A63 0 Improved modal stiffness k = ω m 2 gen, i 0 i gen, i Improved parameters HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 42
43 Parameter Identification Improvements (2) Structural parameters calculated for simplified test rig Finite Element Model Accelerometer improved Microflown improved m ij kg k ij 3 10 N m % Stiffness-matrix according to Bernoulli-theory + N/m HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 43
44 Parameter Identification Summary HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 44
45 Parameter Identification Summary Simplified test rig HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 45
46 Parameter Identification Summary Simplified test rig Parameter Identification (known from structural dynamics) verified with FE-Model of test rig HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 46
47 Parameter Identification Summary Simplified test rig Parameter Identification (known from structural dynamics) verified with FE-Model of test rig Experimental parameter identification performed with A) structural sensors B) Microflown pu-probe HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 47
48 Parameter Identification Summary Simplified test rig Parameter Identification (known from structural dynamics) verified with FE-Model of test rig Experimental parameter identification performed with A) structural sensors B) Microflown pu-probe Results are in fair agreement HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 48
49 Way Forward in 2013 Master-Thesis (03/ /2013): Contact-free Vibration Measurements with Particle Velocity Probes Self-noise of sensor(s) Dynamic range (m/s²) relative to other sensors Level of background noise relative to the signal from a vibrating Proper working distance What is the (very) near field? => To be Continued at DAGA 2014 HAW Hamburg / Adaptronics and Structural Dynamics, Prof. Dr.-Ing. (habil.) Kletschkowski 49
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