Frequency Range Selection for Random Vibration

What Is It?

Frequency range selection for random vibration analysis involves choosing the lower and upper frequency limits for the modal extraction and the random response solution. The range must cover the PSD input specification, capture the structural modes that contribute to the response, and be computationally practical. Selecting the wrong range can miss significant response or waste computation on irrelevant frequencies.

Why It Matters

The frequency range determines what is included in the analysis. A range that is too narrow misses modes and response — non-conservative. A range that is too wide wastes computation on frequencies that contribute little. The right range balances accuracy and efficiency. Understanding the factors that determine the appropriate range is essential for setting up and reviewing random vibration analyses.

PSD Specification Range

The PSD specification defines the minimum frequency range — the analysis must cover at least the PSD frequency range. If the PSD is defined from 20 to 2000 Hz, the analysis must cover 20 to 2000 Hz. Excitation outside this range is zero — there is nothing to analyse. The PSD range is the starting point for frequency range selection.

• PSD specification defines the minimum frequency range
• Analysis must cover at least the PSD frequency range
• No excitation outside the PSD range — nothing to analyse
• PSD range is the starting point for frequency range selection

Structural Modes

Structural modes within and slightly beyond the PSD range contribute to the response. Modes within the PSD range are directly excited. Modes just above the PSD range may contribute through the tails of their transfer functions. The modal extraction range should extend beyond the PSD upper frequency to capture these modes. A common rule is to extract modes up to 1.2-1.5 times the PSD upper frequency.

Modal extraction range:

f_min,extract  ≤  f_min,PSD  (typically 0 or f_min,PSD)
f_max,extract  ≥  1.2 × f_max,PSD  to  1.5 × f_max,PSD

This ensures modes just above the PSD range
are captured for their tail contributions
and for effective mass convergence.

Solver Range

The random response solution range — the range over which the response PSD is computed — should match the PSD input range. Computing the response outside the PSD range adds nothing because the input is zero. The solver output frequency points should span the PSD range with sufficient resolution to capture resonant peaks.

Upper-Frequency Coverage

Adequate upper-frequency coverage is critical. If the upper frequency is too low, high-frequency modes that contribute to the response — particularly stress at stress concentrations and high-frequency acceleration — are omitted. The effective mass at the upper frequency should be checked. If it is still increasing significantly, the upper frequency should be extended.

Check effective mass at the upper extraction frequency. If it is still increasing, extend the range. Omitted high-frequency modes can significantly affect stress at stress concentrations and high-frequency acceleration.

Omitted Modes

Modes above the extraction range are omitted — their contribution to the response is lost. For low-frequency response quantities (displacement, low-frequency acceleration), this is usually acceptable because high-frequency modes contribute little. For high-frequency response quantities (stress at concentrations, high-frequency acceleration), omitted modes can be significant. Residual mass correction can approximate the contribution of omitted modes for some response quantities.

Computational Cost

The frequency range affects computational cost in two ways. First, a wider modal extraction range requires more modes to be extracted, which increases modal analysis time. Second, a wider response range requires more frequency response evaluations, which increases random response solution time. The cost must be balanced against the need for accuracy. For large models, the cost of extending the range can be significant.

• Wider modal extraction range → more modes → more modal analysis time
• Wider response range → more frequency evaluations → more solution time
• Balance cost against accuracy — extend range only where needed
• For large models, frequency range has significant cost implications

Practical Guidelines

The following guidelines provide a practical starting point for frequency range selection. They should be verified for each specific case using the effective mass criterion and convergence checks.

• Modal extraction: from 0 (or PSD minimum) to 1.2-1.5 × PSD maximum frequency
• Random response: match the PSD input frequency range
• Check cumulative effective mass at extraction upper frequency — target >90%
• Check for local modes at critical locations within the PSD range
• Run convergence check — if response changes significantly with more modes, extend the range

Key Takeaways

• Frequency range must cover the PSD specification range at minimum
• Modal extraction should extend to 1.2-1.5 × PSD upper frequency for adequate mass coverage
• Omitted high-frequency modes can affect stress at concentrations and high-frequency acceleration
• Balance computational cost against accuracy — extend range only where needed
• Verify range adequacy with effective mass criterion and convergence checks

Engineering judgement — what can change the conclusion

For Frequency Range Selection for Random Vibration, the harmonised review should concentrate on the statistical and frequency-domain assumptions that connect the specified environment to structural RMS and peak response. The engineering value comes from identifying the assumptions that can move the governing margin or failure mode, then testing those assumptions deliberately rather than adding complexity indiscriminately. Where simplified and high-fidelity methods coexist, the simpler method should be used as an independent trend or magnitude check so that agreement is based on physics rather than shared modelling assumptions.