Predicting Vibratory Stresses from Aero-acoustic Loads

Open Access
Shaw, Matthew David
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
January 27, 2015
Committee Members:
  • Stephen A Hambric, Dissertation Advisor
  • Stephen A Hambric, Committee Chair
  • Robert Lee Campbell, Committee Chair
  • Philip John Morris, Committee Member
  • Stephen Clarke Conlon, Committee Member
  • Structural vibration
  • vibroacoustics
  • fatigue
  • fluid-structure interaction
Sonic fatigue has been a concern of jet aircraft engineers for many years. As engines become more powerful, structures become more lightly damped and complex, and materials become lighter, stiffer, and more complicated, the need to understand and predict structural response to aeroacoustic loads becomes more important. Despite decades of research, vibration in panels caused by random pressure loads, such as those found in a supersonic jet, is still difficult to predict. The work in this research improves on current prediction methods in several ways, in particular for the structural response due to wall pressures induced by supersonic turbulent flows. First, solutions are calculated using time-domain input pressure loads that include shock cells and their interaction with turbulent flow. The solutions include both mean (static) and oscillatory components. Second, the time series of stresses are required for many fatigue assessment counting algorithms. To do this, a method is developed to compute time-dependent solutions in the frequency domain. The method is first applied to a single-degree-of-freedom system. The equations of motion are derived and solved in both the frequency domain and the time domain. The pressure input is a random (broadband) signal representative of jet flow. The method is then applied to a simply-supported beam vibrating in flexure using a line of pressure inputs computed with computational fluid dynamics (CFD). A modal summation approach is used to compute structural response. The coupling between the pressure field and the structure, through the joint acceptance, is reviewed and discussed for its application to more complicated structures. Results from the new method and from a direct time domain method are compared for method verification. Because the match is good and the new frequency domain method is faster computationally, it is chosen for use in a more complicated structure. The vibration of a two-dimensional panel loaded by jet nozzle discharge flow is addressed. The surface pressures calculated at Pratt and Whitney using viscous and compressible CFD are analyzed and compared to surface pressure measurements made at the United Technologies Research Center (UTRC). A structural finite element model is constructed to represent a flexible panel also used in the UTRC setup. The mode shapes, resonance frequencies, modal loss factors, and surface pressures are input into the solution method. Displacement time series and power spectral densities are computed and compared to measurement and show good agreement. The concept of joint acceptance is further addressed for two-dimensional plates excited by supersonic jet flow. Static and alternating stresses in the panel are also computed, and the most highly stressed modes are identified. The surface pressures are further analyzed in the wavenumber domain for insight into the physics of sonic fatigue. Most of the energy in the wall pressure wavenumber-frequency spectrum at subsonic speeds is in turbulent structures near the convective wavenumber. In supersonic flow, however, the shock region dominates the spectrum at low frequencies, but convective behavior is still dominant at higher frequencies. When the forcing function wavenumber energy overlaps the modal wavenumbers, the acceptance of energy by the structure from the flow field is greatest. The wavenumber analysis suggests a means of designing structures to minimize overlap of excitation and structural wavenumber peaks to minimize vibration and sonic fatigue.