Definition of the limits of predictability of the dynamics of vibro-acoustic systems
Abstract
This work is concerned with the variability exhibited by ensembles of vibro-acoustic systems of the Noise, Vibrations, and Harshness (NVH) properties, where the systems are produced to have same nominal characteristics. These variations pose a limit of predictability of Finite Element Methods (FEM), and in general, of deterministic prediction techniques when used at high frequencies. This limit of predictability is inherent to the systems and should not be considered a modeling defect. A quantitative definition of the limit of predictability of precise, deterministic modeling techniques of the dynamics of vibro-acoustic systems is introduced. This definition is developed for predictions of the dynamics of beams, thin plates, and acoustical enclosures and aims to characterize frequency ranges of vibration and corresponding analysis techniques that are useful and efficient. Ultimately, a frequency threshold depending on coefficients describing variabilities in the systems, the effect of damping, and averaging in frequency is derived. Frequencies below the threshold comprise the low-frequency range, where deterministic (finite element methods) predictions are appropriate. In this frequency range, the “average system” is representative of the dynamics of an ensemble of nominally identical systems. In the high-frequency range, above the threshold, predictions by statistical methods and/or energy formulations are more efficient and useful. The frequency threshold is defined by a criterion involving the modal overlap factor. The existing definition of the modal overlap factor is extended to depend on ensemble variations, damping and frequency averaging bandwidth. Approximate formulas of the modal overlap factor are derived, and they are used to obtain formulas for frequency thresholds. When connected systems are considered, a mid-frequency range is identified where neither deterministic nor statistical prediction techniques are appropriate. Frequency thresholds defined for each subsystem that makes up the connected structure are combined to predict a mid-frequency band. To illustrate and validate the results, Monte-Carlo simulations of the average response of beams, plates, and acoustic spaces are presented, together with the corresponding prediction of frequency thresholds. Simulations of the average response of a system of beams is presented to illustrate the behavior of a connected system in the mid-frequency. Also the prediction of the mid-frequency range is shown.
Degree
Ph.D.
Advisors
Bernhard, Purdue University.
Subject Area
Mechanical engineering|Mathematics
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