PSI - Issue 77

First page Table of contents Previous page 15 Next page Last page

Alessandro Zanarini et al. / Procedia Structural Integrity 77 (2026) 71–78 A. Zanarini / Structural Integrity Procedia 00 (2025) 1–8

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

Pha [rad]

-3.142

1.649e+02

1.678e+02

DIC ESPI SLDV

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]

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

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]

-4.000e+01 2.538e+02

-4.000e+01 2.594e+02

DIC ESPI SLDV

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

Noise Amp [N] [dB]

-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]

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

3.2. Dynamic Stress FRFs With the introduction of a constitutive model (linear isotropic here, for the aluminium sample in Fig.1 b , with the following material parameters: E elastic modulus, ν Poisson ratio, G shear modulus, Λ Lame´ constant), the Stress FRF tensor components can be evaluated from Strain FRFs in Eqs.1-2: 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 airborne retrieved structural force on all the locations of the sensed surface. The notation ( x , y ) is used for the spatial extension tomaps. 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 other parameters can be obtained, 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. The role of von Mises equivalent stress FRFs from optical techniques The PSD of von Mises equivalent stress is crucial and evaluated from the von Mises equivalent stress FRFs and respective excitations, here rendered in the maps at a single frequency in Fig.2 and in single dof graphs of Fig.3, from both shakers (here white noise excitation). Instead, the retrieved (in Part A) airborne structural force of Fig.5 has quite 4

Made with FlippingBook flipbook maker