Transient Structural Analyses Using Frequency-Domain Computations and Fourier Transform Techniques

Open Access
Turkosz, Daniel John
Graduate Program:
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 31, 2010
Committee Members:
  • John Brian Fahnline, Thesis Advisor
  • structural acoustics
  • computational acoustics
  • frequency-domain
  • time-domain
  • fourier transform
  • transient
  • acoustics
  • finite element method
  • damping
Structural-acoustic calculations are most often performed in the frequency-domain assuming time-harmonic (i.e. steady-state) forcing functions. While frequency-domain modeling can be used for most calculations, some problems in engineering and acoustics are inherently transient. In these cases, it becomes important to model the response of the structure in the time-domain, a task that can be difficult given existing frequency-domain solution infrastructure and certain frequency-domain specific types of damping. The purpose of this thesis is to establish techniques and guidelines for frequency-domain analyses by documenting time-domain solution accuracy for frequency-domain data transformed using the Fourier Transform. These guidelines have been developed by comparing time-domain solutions that are known to be accurate with transformed frequency-domain calculations first for a simple spring mass system, and then a more complex system where the finite element method is used to compute the response. The primary guidelines involve setting frequency range and frequency resolution to values that are computationally efficient, yet still produce accurate results once transformed into the time-domain. Frequency range must be set based on the highest modal frequency of interest so its waveform is well resolved in the time-domain. Frequency resolution is tied directly to the damping of the system. The sharpest modal peak in a frequency-domain response will dictate frequency resolution, which will be set to produce accurate time-domain amplitudes. Computational savings will come mostly from limiting the modal frequency analysis range and zero-padding portions of the linear spectrum, sacrificing total sample duration in the final time-domain response and interpolating rather than directly computing certain parts of the frequency-domain response. These techniques allow for transient problems to be solved using frequency-domain results without having to create new time-domain specific analysis programs.