Vibroacoustic Scaling Tool

Calculate vibration response using Barrett, Franken, and dynamic pressure scaling methods.

Franken Calculator
Empirical method for cylindrical skin vibration response
Results:
f_c × d:5000 Hz·ft
Y-value (from curve):-128.0 dB
Assumed Bandwidth:115.8 Hz
G_rms:3.9811 g
PSD:1.369e-1 g²/Hz
Ring Frequency (Aluminum):
f_r = 5264 / d = 526 Hz
Franken Curve
Jupiter/Titan empirical data for cylindrical structures
1005001k5k10k50kf_c × d (Hz·ft)-161-152-143-134-12520log₁₀(G_rms) + 20log₁₀(W) - SPL (dB)
  • Upper Limit
  • Lower Limit
  • Your Point
Worked Example: Franken Method

Problem:

An aluminum cylinder has a diameter of 40 inches (3.333 ft) and skin thickness of 0.25 inches. The acoustic environment has an SPL of 120 dB at 100 Hz (1/3 octave band). Estimate the vibration response.

Given:

  • d = 3.333 ft (40 in)
  • W = 3.6 psf (0.25 in aluminum skin)
  • SPL = 120 dB
  • f_c = 100 Hz

Reference: Irvine, T., "Vibration Response of a Cylindrical Skin to Acoustic Pressure via the Franken Method," vibrationdata.com, 2008.

Solution:

Step 1: Calculate X-axis value

f_c × d = 100 × 3.333 = 333.3 Hz·ft

Step 2: Read Y-value from Franken curve (upper limit)

F = -142 dB (at f_c×d = 333.3 Hz·ft)

Step 3: Solve for G_rms

F = 20log₁₀(G_rms) + 20log₁₀(W) - SPL
-142 = 20log₁₀(G_rms) + 20log₁₀(3.6) - 120
-142 = 20log₁₀(G_rms) + 11.1 - 120
20log₁₀(G_rms) = -142 - 11.1 + 120 = -33.1
G_rms = 10^(-33.1/20) = 0.022 g

Step 4: Convert to PSD (optional)

Assume G_rms is constant over the bandwidth:
1/3 octave bandwidth at f_c=100 Hz:
BW = 100 × 0.2316 ≈ 23 Hz
PSD = G_rms² / BW = (0.022)² / 23
PSD = 2.1×10⁻⁵ g²/Hz
Note: This assumes the PSD is constant over the assumed bandwidth. For different bandwidths, use the calculator above with the "Custom (Hz)" option.
Multi-Band Franken Calculator
Calculate total GRMS from full SPL spectrum using RSS summation
CSV Import Format

Import your SPL spectrum data using the "Import CSV" button. Expected format:

  • Column 1: Frequency (Hz)
  • Column 2: SPL (dB re 20 µPa)

Supports comma, tab, or space delimited files. Header row is optional.

Frequency,SPL
20,130
25,132
31.5,134
...
Total GRMS (RSS)
9.5384 g
Freq (Hz)SPL (dB)f×d (Hz·ft)Y (dB)BW (Hz)G_rms (g)PSD (g²/Hz)
200-150.04.60.10002.16e-3
250-146.55.80.18846.13e-3
315-142.97.30.36011.78e-2
400-140.29.30.61694.11e-2
500-138.011.61.00008.64e-2
630-136.314.61.52531.59e-1
800-134.618.52.08702.35e-1
1000-133.023.22.81843.43e-1
1250-132.028.93.14983.43e-1
1600-131.037.13.17482.72e-1
2000-130.046.33.16232.16e-1
2500-128.957.93.19911.77e-1
3150-128.073.03.16231.37e-1
4000-128.092.62.81848.57e-2
5000-128.0115.82.51195.45e-2
6300-128.7145.92.06852.93e-2
8000-129.7185.31.63141.44e-2
10000-131.0231.61.25896.84e-3
12500-132.3289.50.96743.23e-3
16000-133.7370.60.73181.45e-3
20000-135.0463.20.56236.83e-4
PSD Spectrum (Vibration Test Criteria)
Log-log plot of acceleration PSD vs frequency
1020501002005001k2k5k10kFrequency (Hz)1e-34e-31e-24e-21e-13e-1PSD (g²/Hz)
  • PSD Spectrum
Total GRMS (RSS)
9.5384 g
G_total = √(Σ G_rms,i²)
Frequency Range
20 - 2000 Hz
21 frequency bands