Issue 78

F. Veschi et alii, Fracture and Structural Integrity, 78 (2026) 44-73; DOI: 10.3221/IGF-ESIS.78.04

[30] Angeli, A., Cornelis, B., Troncossi, M. (2018). Synthesis of Sine-on-Random vibration profiles for accelerated life tests based on Fatigue Damage Spectrum equivalence, Mechanical Systems and Signal Processing., 103(2). DOI: https://doi.org/10.1016/j.ymssp.2017.10.022. [31] Lalanne, C. (2009). Mechanical Vibration and Shock Analysis. Random Vibration, 3.

N OMENCLATURE

Sinusoidal Amplitude

a

Sinusoidal Stress Amplitude

S a

Amplitude of the Sinusoidal Response of an SDOF System according to Irvine’s Method

resp a

Intercept Parameter of an SN Curve Frequency Resolution of a PSD

C df

Palmgren-Miner’s Linear Cumulative Damage

D

Damage Evaluated on the SDOF System Sinusoidal Response according to Irvine’s Method

sine D start D  E

Damage Evaluated on the SDOF System Response to

start NB G

Expected Value Operator

Frequency

f

Natural Frequency

0 f

Random PSD Central Frequency

r f

Main Rotor Frequency Sinusoidal Frequency Hypergeometric Function Fatigue Damage Spectrum

rot f ଵ ଵ FDS 0 FDS S f

FDS derived from

0 G

Target Sine on Random FDS for Lalanne’s Method

target FDS

  

Fourier Transform Function

First Guess PSD for Lalanne’s Method

0 G

Final Equivalent NB PSD Level according to Irvine’s Method for Sine to Random conversion Initial Equivalent NB PSD Level according to Irvine’s Method for Sine to Random conversion

NB G

start NB G

Random Component PSD according to the RMS Equivalence Method Random Gaussian PSD Equivalent to a Sine on Random Signal

r G

SoR G

Single-Sided Power Spectral Density

xx G

Single-Sided PSD of a Stationary Gaussian Random Acceleration Signal

G

¨ ¨ xx

Convolution Integral Integration Variable

h

Frequency Response Function between Input Acceleration and Output Relative Displacement

H

¨ / Z x

Modified Bessel Function of Order Zero

0 I 0 J k K m

Bessel Function of Order Zero

Frequency Ratio

Proportionality Factor Between Relative Response Displacements and Stresses

Slope Parameter of an SN Curve Spectral Moment of n -th Order

n m

Number of Blades

b n i n

Number of Cycles at amplitude

, p i Z

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