PSI - Issue 54

Alessandro Zanarini et al. / Procedia Structural Integrity 54 (2024) 99–106

102

4

A. Zanarini / Structural Integrity Procedia 00 (2023) 000–000

Dof [1136] VonMises Eq.Stress / N

Dof [1136] VonMises Eq.Stress / N

Step[610]=496.094 [Hz] AmpDIC=1.391e+02

Step[610]=496.094 [Hz] AmpDIC=1.432e+02

AmpESPI=1.391e+02 PhaESPI=-3.094

AmpSLDV=1.341e+02 [1/m^2] [dB]

AmpESPI=1.508e+02 PhaESPI=-2.059

AmpSLDV=1.438e+02 [1/m^2] [dB]

PhaDIC=-2.901

PhaSLDV=-2.907 [rad]

PhaDIC=-2.391

PhaSLDV=-1.987 [rad]

3.142

3.142

Pha [rad]

Pha [rad]

-3.142

-3.142

1.649e+02

1.678e+02

DIC ESPI SLDV

DIC ESPI SLDV

Amp [1/m^2] [dB]

Amp [1/m^2] [dB]

1.020e+02

1.023e+02

20.312

Frequency [Hz]

1023.438

20.312

Frequency [Hz]

1023.438

References: Geom SLDV Freq SLDV (c) ALESSANDRO ZANARINI @ TU-Wien, Austria Marie Curie FP7-PEOPLE-IEF-2011 PIEF-GA-2011-298543 Project TEFFMA - Towards Experimental Full Field Modal Analysis

Shakers: active #1[2611] mute #2[931]

References: Geom SLDV Freq SLDV (c) ALESSANDRO ZANARINI @ TU-Wien, Austria Marie Curie FP7-PEOPLE-IEF-2011 PIEF-GA-2011-298543 Project TEFFMA - Towards Experimental Full Field Modal Analysis

Shakers: mute #1[2611] active #2[931]

a b Fig. 3. Examples of von Mises equivalent stress FRF graphs from optical techniques, direct experimental impedance models in the 20-1024 Hz range, DIC-ESPI-SLDV examples: from shaker 1 in a , from shaker 2 in b .

FRF tensor components can be evaluated from Strain FRFs :

σ ω ( x , y ) ii = 2 G ε ω ( x , y ) ii +Λ ε ω ( x , y ) xx + ε ω ( x , y ) yy ; σ ω ( x , y ) i j = 2 G ε ω ( x , y ) i j ; G = E / 2(1 + ν ); Λ= E ν / ((1 + ν ) (1 − 2 ν )) .

(3)

Therefore, with the constitutive model of any specific material (anisotropic and locally linearised included), also the experiment-based Principal Stress FRF maps can be evaluated from the full-field receptance d ( x , y , j ω ).

4. Cumulative damage & fatigue life assessment by means of spectral methods

With such a broad set of detailed experiment-based Stress FRF maps , we can evaluate cumulative damage with the spectral methods for high cycles fatigue in every dof of the sensed surface, with unprecedented mapping abilities . A spectral method targets the evaluation of an equivalent range of stress cycles S eq ( x , y ), in each location ( x , y ) of the experiment-based Stress FRF maps , representative of the damage inferred by the whole spectrum of the retained dynamics on all the locations of the sensed surface. The notation ( x , y ) is used for the spatial extension to maps. Many spectral methods are based on m k = ∞ 0 f k PSD VM ( ω ) d ω , the k-th order moments of the frequency by the power spectral density (PSD) of von Mises equivalent stress PS D VM ( ω ), from which we can obtain other parameters, such as the e ff ective frequency F zerocrossing = F zc = √ m 2 / m 0 , the expected number of peaks per unit time F peaks = F p = √ m 4 / m 2 , and the irregularity factor γ = γ 2 = F zc / F p = m 2 / √ m 0 m 4 .

4.1. Dirlik semi-empirical spectral method parameters

Among the many available (see Dirlik and Benasciutti (2021); Zorman et al. (2023)), the Dirlik semi-empirical spectral method in Dirlik (1985) was here implemented, as it gives a sound prediction of the fatigue life for wide

Dof [1136] VonMises Eq.Stress PSD

Dof [1136] VonMises Eq.Stress PSD

Step[610]=496.094 [Hz] VM_PSD_DIC=2.020e+02

Step[610]=496.094 [Hz] VM_PSD_DIC=2.103e+02

VM_PSD_ESPI=2.021e+02

VM_PSD_SLDV=1.921e+02 [N^2/m^4] [dB]

VM_PSD_ESPI=2.254e+02

VM_PSD_SLDV=2.115e+02 [N^2/m^4] [dB]

WHITE NOISE excitation at step[610]=-4.000e+01 [N] [dB]

WHITE NOISE excitation at step[610]=-4.000e+01 [N] [dB]

-4.000e+01 2.538e+02

-4.000e+01 2.594e+02

DIC ESPI SLDV

DIC ESPI SLDV

Amp [N^2/m^4] [dB]

Amp [N^2/m^4] [dB]

Noise Amp [N] [dB]

Noise Amp [N] [dB]

-4.000e-02 1.200e+02

-4.000e-02 1.200e+02

20.312

Frequency [Hz]

1023.438

20.312

Frequency [Hz]

1023.438

References: Geom SLDV Freq SLDV (c) ALESSANDRO ZANARINI @ TU-Wien, Austria Marie Curie FP7-PEOPLE-IEF-2011 PIEF-GA-2011-298543 Project TEFFMA - Towards Experimental Full Field Modal Analysis

Shakers: active #1[2611] mute #2[931]

References: Geom SLDV Freq SLDV (c) ALESSANDRO ZANARINI @ TU-Wien, Austria Marie Curie FP7-PEOPLE-IEF-2011 PIEF-GA-2011-298543 Project TEFFMA - Towards Experimental Full Field Modal Analysis

Shakers: mute #1[2611] active #2[931]

a b Fig. 4. Examples of white noise von Mises equivalent stress PSD graphs from optical techniques, direct experimental impedance models in the 20-1024 Hz range, DIC-ESPI-SLDV examples: from shaker 1 in a , from shaker 2 in b .