Mechanische trillingen LES 8 MODALE ANALYSE Patrick Guillaume
- Slides: 45
Mechanische trillingen LES 8 – MODALE ANALYSE Patrick Guillaume E-mail: patrick. guillaume@vub. ac. be Tel. : 02/6293566 Faculty of Engineering Department of Mechanical Engineering ACOUSTICS & VIBRATION RESEARCH GROUP Pleinlaan 2 • B-1050 Brussel • Belgium avrg@vub. ac. be • http: //avrg. vub. ac. be 1 11/30/2020 MECHANISCHE TRILLINGEN, LES 8, 2005
Signal vs. System Analysis Signal Analysis / Fourier Analysis – Only the responses (due to the unknown operating forces) are measured System Analysis / Modal Analysis – The system is stimulated with known forces (in laboratory conditions) – Applied forces and resulting responses are measured 2 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Basic Equations for a 2 -DOF System Forces acting on mass 1 f 2(t) – m 2 f 1(t) x 2(t) c 2 k 2 m 1 k 1 – x 1(t) c 1 – – 3 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Basic Equations for a 2 -DOF System Time domain Frequency domain (Laplace) Matrix notations Dynamic stiffness matrix Transfer function matrix 4 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
FRF of 2 -DOF System f 2(t) m 2 f 1(t) x 2(t) c 2 k 2 m 1 k 1 x 1(t) c 1 0° -180° -360° 5 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Multiple Degree of Freedom (MDOF) Dynamic stiffness matrix Transfer function matrix 6 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
FRF and IRF of MDOF Systems POLES: FREQUENCY RESPONSE FUNCTION (GLOBAL PARAMETERS) IMPULSE RESPONSE FUNCTION 7 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Modal Decomposition IRF FRF 8 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Eigenvalues and Eigenvectors No Damping 9 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Modal Mass and Stiffness No Damping – Modal mass and stiffness are not unique ! 10 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Modal Coordinates 11 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Modal Model 12 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Scaling of the Mode Shapes 13 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Modal Model – Modal Parameters Modal participation factors 14 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Modal Model – Modal Parameters 15 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Modal Model – Modal Parameters 16 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Mode Shape Vector Mode shape is a deflectionpattern associated with a modal frequency – or pole Relative displacements Mode shapes are continuous functions of position Sampled mode shapes = mode shape vector “Spatial resolution” and “Spatial aliasing” 17 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Normal and Complex Modes Normal modes (or real modes) – All points are moving in phase or out of phase – Node points Complex modes – Mode shape vectors are complex – Node points are not well defined anymore Warning: Poor measurements 18 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Cantilever Beam 19 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
FRF in respectievelijk knooppunt 1 en 2 Mode 1 2 3 20 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Real-Imaginary Plot – Peak Picking (normal modes) 21 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Simple Structure – Mode Shapes 22 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Peak Picking 23 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Shaker Testing - Fixed FRF Measurements 24 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Impact Testing - Roving FRF Measurements 25 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Roving or Fixed FRF Measurements 26 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Noise in the Output Measurement Force measurement – Electrical noise Response measurement – Electrical noise – Machines, footsteps, wind, sound, … will result in mechanical noise (process noise) Least-Squares Estimation – Minimize the effect of output noise 27 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Noise in the Output Measurement – Multivariable 28 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Noise in the Input Measurement At its natural frequencies the structure becomes very compliant Least-Squares Estimation – Minimize the effect of input noise 29 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
The Coherence Function Degree of linearity Smaller than 1 when … – Noise in the measurements – Nonlinearities 30 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Noise in the Input and Output Measurements Choice of optimal FRF estimator – H 1 – Under estimation – H 2 – Over estimation – H 3, Hv, Hiv, … 31 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Implementing the Excitation Attached exciters – – Electrodynamic exciter Hydraulic exciter Eccentric rotating masses More exotic devices such as rockets, … Non-attached exciters – Hammers, impactors – Acoustic excitation 32 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Force Measurements Piezo-electric force transducer – – Small size and mass Linearity Wide dynamic range Wide frequency band Exciter attachment – “Stringer” – High axial stiffness – Low transverse and rotational stiffness – Mechanical “fuse” – Protection against destructive overload 33 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Random Excitation Random sequence with Gaussian distribution – Random amplitudes and phases Averaging is needed – Converge to flat amplitude spectrum – Remark: Force is not flat in general due to interaction with the structure Signal processing errors (leakage errors) Effect of nonlinearities is reduced by averaging 34 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Random Noise 35 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Uniform Window 36 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Hanning Window 37 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Burst Random 38 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Burst Random with Uniform Window 39 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Exponential Window 40 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Periodic Random / Pseudo-Random Excitation Periodic random – No leakage errors (periodic signal) in steady-state conditions – Averaging is required Pseudo random – Constant amplitudes and random phases – No leakage errors (periodic signal) in steady-state conditions – Averaging is not required 41 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Impact Excitation Force transducer and tip Advantages – Easy to use – No interaction with structure – Force is flat in useful frequency range – Relatively inexpensive 42 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Impact Excitation Disadvantages – Large crest factor – Nonlinearities – Limited control of amplitude spectrum 43 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Force Window Force window (or transient window) – Remove noise Effect of “Double Hits” 44 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
Response Window Lightly damped structure – Leakage errors Heavily damped structure – Remove noise 45 MECHANISCHE TRILLINGEN, LES 8, 2005 Acoustics & Vibration Research Group Vrije Universiteit Brussel
- Mechanische trillingen
- Mechanische trillingen
- Trillingen meten
- Apollinaire les sapins
- Piezomechanische antriebstechnik
- Schlagwurf mit schleife
- Werfen nach dem hebelprinzip
- Mechanische beanspruchung verpackung
- Manuelle rechenmaschine
- Modale
- Modalsätze mit dadurch dass und indem
- Klasse indeling
- Qnqqq
- Modale hulpwerkwoord
- Stingel en blaar diagram
- Frequenza assoluta e relativa
- Subordinata concessiva
- Subordinata condizionale esplicita
- Konzessive nebensätze
- Alcune frasi
- Kontinue data
- Joueurs de skat otto dix
- Les outils de l analyse spatiale
- Otto dix assaut sous les gaz analyse
- Guillaume laberge
- Deug stpi
- Guillaume de machaut aussprache
- Rumfordov experiment
- Guillaume jacono
- Guillaume villemaud
- Ben taskar
- Guillaume labb
- Guillaume aubard
- Unconscious
- Xbrl rendering tool
- Spm ucl
- Guillaume painsar
- Docteur recher
- Guillaume flandin
- Casnav
- Panel satisfaction carrefour
- Guillaume de machault
- Guillaume brat
- Guillaume gaouyer
- Guillaume budé
- Guillaume saës