Research project: Acoustic fatigue prediction for advanced aerospace structures

The research aims to improve and extend the existing simplified prediction methodology, so that the effects of vibroacoustic coupling, curvature, nonlinearity and elevated temperature can be incorporated for a general, efficient and accurate structural response prediction.

The project is funded by the BISE-FEE Joint Laboratory (BISE is the Beijing Institute of Structure & Environmental Engineering). Full scale numerical simulations were made using the IRIDIS HPC Facility at the university.

There are four aspects of content relating to the methodology for vibroacoustic response prediction that are investigated in the research project.

1. The vibroacoustic response of stiffened thin plates to incident sound.

An efficient modal model was developed for the vibroacoustic response prediction. A relationship between the Joint Acceptance Function and modal radiation efficiency was derived as a function of existing formulated vibroacoustic quantities and in-vacuo modal parameters. The model was applied to stiffened plates with arbitrary boundary conditions subjected to either plane wave or diffuse field excitations, shown in Figure 1.

Figure 1 (a) A flat stiffened plate subjected to incident sound wave. (b) The basic model extended for diffuse field excitation and comparison of the results with numerical (Finite Element and Boundary Element) simulations (displacement response at 94 dB excitation in the fundamental mode)

The main conclusions in this study are

• The stiffeners can enhance vibroacoustic coupling leading to a significant reduction of the dominant resonance level.
• The acoustic excitation type affects more the high frequency range, while modal cross terms affect more the low frequency range.
• The proposed approach was verified by comparison with a coupled FE-BE model and good overall agreement was achieved with a significant reduction in the computational cost.

2. The vibroacoustic linear analytical response of stiffened cylinders.

A solution for the scattering as well as the full coupling with incident and re-radiated sound fields was given for the analysis of stiffened cylinders, shown in Figure 2. An experimental investigation into the vibroacoustic response of a scaled stiffened fuselage was made, shown in Figure 3.

Figure 2 A thin walled, stiffened cylinder subjected to acoustic plane wave excitation, subsequently extended to diffuse field excitation

Figure 3 An experimental investigation into the vibroacoustic response of stiffened cylinder. (a) Acoustic test in anechoic chamber in ISVR. (b) Layout of the acoustic response test system used in this measurement.

The main conclusions of this study are

• A good agreement with FE for the two excitation models, i.e. doubling pressure and scattering pressure, was achieved.
• The effects of radiation damping and fluid loading were highlighted in the fully coupled FE-BE model.
• Overall, good agreement was achieved for the pressure prediction in measurement, but less satisfactory agreement for the vibration response was achieved in the non-resonance region over the frequency range 200 – 600Hz.

3. The nonlinear reduced order model (NLROM) for the vibroacoustic response of stiffened, curved and elevated temperature structure.

A numerical investigation of NLROM was performed, with application on the response of stiffened plates and cylinders under thermal-acoustic and mechanical excitation. An overview of the steps involved are shown in Figure 4.

Figure 4 A flowchart and implementation of a Nonlinear Reduced Order Model (NLROM) solution.

The main conclusions in the NLROM study are

• Linearly excited modes up to twice the frequency excitation bandwidth is recommended. Hot-mode NLROM predictions are more accurate than cold-mode NLROM, but the former has a lower capacity to converge in the static characterisation stage.
• The stiffness proportional damping model is recommended. A trade-off can be made in the selection of the level of stiffness proportional damping and the sampling rate in terms of the accuracy and efficiency when producing the comparison of NLROM and FEM simulations.
• The feature of structures possessing deep stiffeners and high curvature causes the appearance of nonlinearity to be less detectable in the response range.

4. Fatigue life calculation: the effects of vibroacoustic coupling, nonlinearity and elevated temperature.

The project compared some existing fatigue life estimation methods and investigated the effects of different assumptions on the fatigue life estimation. The main conclusions of this study are

• Dirlik’s method gives best agreement to Rainflow counting method for multi-modal response compared to other spectral methods.
• The effect of vibroacoustic coupling is higher than that of nonlinearity for the stiffened plate.
• Compared to vibroacoustic coupling, the effect of nonlinearity increases as the excitation level increases, but it decreases as the temperature increases.