All structures degrade when acted upon by cyclic forces associated with earthquakes, high winds, and sea waves. Identification and prediction of degradation is thus a problem of considerable practical significance in the field of engineering mechanics. Under cyclic excitation, degradation manifests itself in the evolution of the associated hysteresis loops. Two principal tasks in connection with hysteretic evolution are addressed in this paper. First, a robust identification algorithm is devised to generate hysteretic models of a deteriorating structure from its experimental load-displacement traces. This algorithm is based upon the generalized Bouc-Wen model and the latest theory of differential evolution, streamlined through global sensitivity analysis. It can account for strength degradation, stiffness degradation, and pinching characteristics in the evolution of hysteretic traces. Second, it is shown experimentally that a hysteretic model obtained by identification can be used to predict the future performance of a degrading structure. Prediction of degradation through identification is a brute-force approach that offers a close representation of reality. There is not any method based upon the fundamental postulates of mechanics that can predict the response of a degrading structure well beyond its linear range.
The present work investigates vibro-acoustic behaviors of the fluid dynamic bearing (FDB) spindle motors for hard disk drives (HDD) through the sound spectra and the frequency response functions (FRF) of the motor structure. The quantitative evidence on the significance of the acoustic noise originated from the electromagnetic source is deduced from the sound spectra that were measured in two distinct cases of the spinning motor: in the normal operation and at the moment immediately after the power supply was disconnected. It is found that the effect of electromagnetic noise source is more dominant than the combined effect of the mechanical and aerodynamic sources. In addition, it is identified that, within the audible range of frequency, the frequency range of 13.4-20 kHz deems important to the noise problem as it is the main contributor to the acoustic noise for the FDB spindle motors. Moreover, the structural resonances that can be identified via the FRF are found to play an important role in the noise emitted by the motors. The concurrence of resonance and excitation frequencies clearly intensifies the sound spectrum, resulting in high discrete peaks, hence higher decibel level.
It is well known that an undamped linear vibratory system can be decoupled through transformation to principal coordinates. In the presence of damping, coordinate decoupling occurs only if the system is classically damped. Upon modal transformation, the system generally remains coupled by the off-diagonal elements of its modal damping matrix. A common approximation in the analysis of nonclassically damped systems is to ignore the off-diagonal elements of the modal damping matrix, which is equivalent to neglecting coupling of the principal coordinates. This procedure is termed the decoupling approximation. Intuitively, the errors of decoupling approximation should be small if the off-diagonal elements of the modal damping matrix are small. Contrary to this widely accepted belief, an example is provided to demonstrate that this criterion is not sufficient for decoupling approximation. In fact, coupling effect can even increase as the off-diagonal elements of the modal damping matrix decrease in magnitude. Discussion and explanation are provided as to why the errors increase when the modal damping matrix becomes increasingly diagonal.
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