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Christian Lalanne’s concept of Fatigue Damage Spectrum (FDS) is extended to describe a triaxial vibration excitation. At the same time, complicated non-stationary vibration is simplified to a stationary Gaussian random vibration, maintaining its fatigue effect on a linear time-invariant structure. This simplification facilitates efficient fatigue analysis in frequency domain or multiaxial vibration testing. The resulting fatigue-equivalent stationary random vibration PSD matrix is derived from many uniaxial FDS calculations along different projections in space, not only three orthogonal directions. A fatigue-equivalent PSD is calculated for each projection and the desired \(3\times 3\) PSD matrix is solved from an over-determined system of equations from all projections. Validation shows good agreement in fatigue damage, when comparing the frequency domain fatigue calculation from the \(3\times 3\) PSD matrix with time domain calculation from the original triaxial non-stationary vibration.

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Simplifying Any Vibration Excitation as a PSD Matrix Maintaining Its Fatigue Damage Effect

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  • 发表日期：

    2026年

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  • Albin Bäckstrand,
  • Martin Olofsson

摘要

Christian Lalanne’s concept of Fatigue Damage Spectrum (FDS) is extended to describe a triaxial vibration excitation. At the same time, complicated non-stationary vibration is simplified to a stationary Gaussian random vibration, maintaining its fatigue effect on a linear time-invariant structure. This simplification facilitates efficient fatigue analysis in frequency domain or multiaxial vibration testing. The resulting fatigue-equivalent stationary random vibration PSD matrix is derived from many uniaxial FDS calculations along different projections in space, not only three orthogonal directions. A fatigue-equivalent PSD is calculated for each projection and the desired \(3\times 3\) PSD matrix is solved from an over-determined system of equations from all projections. Validation shows good agreement in fatigue damage, when comparing the frequency domain fatigue calculation from the \(3\times 3\) PSD matrix with time domain calculation from the original triaxial non-stationary vibration.