Acoustic Fatigue of a Plate

By Tom Irvine

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July22, 2014

Introduction

The purpose of this paper is to show how frequency domain damage methods can be used to assess acoustic fatigue damage. This is demonstrated for a rectangular plate subjected to a uniform acoustic pressure field.

Example

Figure 1.

Figure 2.

Consider a plate with dimensions 18 x 16 x 0.063inches. The material is aluminum 6061-T6. The plate is simply-supported on all four edges. Assume 3% damping for all modes.

The plate is subjected to the Boeing 737 Aft Mach 0.78 sound pressure level from References 1 and 2. Assume that the pressure is uniformly distributed across the plate.

The sound pressure level and its corresponding power spectral density are shown in Figures 1 and 2, respectively. The data was extrapolated below 63 Hz. Some smoothing was also applied.

Calculate the stress and cumulative fatigue damage at the center of the plate with a stress concentration factor of 3. This factor could represent a hole.

Determine the time until failure at the nominal level and at 6 dB increments.

Figure 3.

The stress frequency magnitude function is shown in Figure 3 as calculated using the method in Reference 3.

The stress concentration factor is applied separately by multiply the magnitude by 3. The magnitude is then squared prior to multiplying by the force PSD in Figure 2.

The resulting stress PSD is shown in Figure 4 for the nominal applied force.

Figure 4.

Aluminum 6061-T6 has the following properties from Reference 4.

Fatigue exponent: m = 9.25

Fatigue strength coefficient: A= 9.77e+17 ksi^9.5

The damage rates are summarized in Table 1 using the averaging method from Reference 5.

Table 1. Cumulative Damage, Rectangular Plate, Center, Stress Concentration=3
Margin / Displacement / Damage Rate / Time to Failure
(dB) / (inch RMS) / (1/sec) / (sec) / (Days)
0 / 0.0126 / 1.808e-15 / 5.53e+14 / 6.40E+09
6 / 0.0252 / 1.076e-12 / 9.29e+11 / 1.08E+07
12 / 0.0504 / 6.324e-10 / 1.58e+09 / 18302
18 / 0.1008 / 3.822e-07 / 2.62e+06 / 30

Note that this analysis has neglected the membrane stresses that occur with large deflections.

The large deflection theory accounts for both membrane and bending stress. The plate will carry some of the load in direct bending and some of the load as membrane tension for large deflections. Large loads can be carried with a relatively small displacement when the plate is loaded as a membrane.

Large deflection theory will be considered in a future revision.

Also note that pressure and depressurization cycles would significantly contribute to fatigue damage if the plate were mounted on an aircraft fuselage.

References

NASA Reference Publication 1258, Vol. 2, WRDC Technical Report 90-3052, Acoustics of Flight Vehicles: Theory and Practice, 1991.

T. Irvine, Jet Aircraft Fuselage External Fluctuating Pressure Level During Cruise, Rev B, Vibrationdata, 2012.

T. Irvine, Steady-State Vibration Response of a Plate Simply-Supported on All Sides Subjected to a Uniform Pressure, Rev B, Vibrationdata, 2012.

T. Irvine, Miner’s Cumulative Damage via Rainflow Cycle Counting, Rev G, Vibrationdata, 2014.

T. Irvine, Estimating Fatigue Damage from Stress Power Spectral Density Functions, Vibrationdata, 2014.