Issue 78

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

RMS Equivalence Random background and harmonic components are independent processes.

Lalanne’s method

White Noise Approximation Same as Lalanne’s; The local approximation of a PSD to white noise.

Rice’s PDF

Irvine’s method Two signals that cause the same damage to an SDOF system, for a given Q value, are also equally damaging towards every system with the same Q value. Random PSD; Sinusoidal amplitudes and frequencies; SN curve’s slope m and intercept C ; SDOF system’s quality factor Q ; Sine to NB conversion band f  . Fast implementation; Allows the direct use of spectral method. Depends on m ; Depends on the choice of f  ; Different f  values give different equivalent PSDs. Requires the Q value of an SDOF system. Low.

Underlying assumptions

Random component is NB; Incommensurable frequencies; Harmonic frequencies are within the random band. Low when the number of sinusoids equals 1. High otherwise.

Two signals with the same FDS, for a given Q value, are also equally damaging towards every system with the same Q value.

Computational Complexity

Extremely low.

Low.

Extremely Low.

Required Input Parameters

Random PSD; Sinusoidal amplitudes and frequencies;

Random PSD; Sinusoidal amplitudes and frequencies; SN curve’s slope m and intercept C ; SoR FDS; Quality factor Q used for the FDS evaluation. Extremely fast implementation; Allows the direct use of spectral method. Depends on m ; Need to evaluate the SoR FDS; Requires the Q value of the set of SDOF systems used for the FDS evaluation.

Random PSD; Sinusoidal amplitudes and frequencies.

Random PSD; Sinusoidal amplitudes and frequencies; Sine to NB random conversion band f  .

SN curve’s slope m and intercept C ; SoR Fatigue Damage Spectrum.

Main Advantages Potentially high statistical fidelity; Provides a stress cycle pdf; High accuracy within underlying hypothesis.

Fast implementation; Allows the direct use of spectral method.

Does not require system dynamics; Does not depend on m nor Q ; Fast implementation; Allows the direct use of spectral method. Depends on the choice of ; f  Different f  values give different equivalent PSDs.

Principal Limitations

Restricted domain of validity; Too conservative if

Depends on m ; Need to evaluate the SoR FDS. Requires the Q value of the set of SDOF systems used for the FDS evaluation. Design for safety; WB random background; k values close to unity; Multiple sinusoids.

outside of the assumptions;

Long computational times for more than one sinusoid.

Recommended Applications k values close to unity; Other methods are preferred for realistic MIL-SDT like profiles. Table 1: Summary table for direct comparison of the SoR fatigue assessment approaches (based of the selected values of Q and m ). Every environment that falls under the underlying assumptions. Load profiles with a single harmonic. Design and optimisation; Any random bandwidth; Any number of sinusoids. Design and optimisation; Any random bandwidth; Any number of sinusoids.

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