KEYWORDS: Acoustics, Mechanics, Structural dynamics, Systems modeling, Wave propagation, 3D metrology, 3D modeling, Mechanical engineering, Commercial off the shelf technology, Resistance, 3D acquisition, Solids, Aerospace engineering
The problem of free vibration of a linear uniform axial bar, fixed at one end and connected to ground at the other end through a linear viscous damper has been carefully studied by several researchers. It’s known that, for a fixed set of bar parameters and the special case of the damping coefficient λ equal to EA / c (c being the speed of sound in the continuum), no eigenvalues exist. Thus, energy imparted to the bar via harmonic motion of the fixed support will propagate through the bar and be fully dissipated in the damper, in effect making the bar appear to be semi-infinite. I will show some recent results by the present authors in which this phenomenon has been exploited in several other nondispersive media, the taut string and the circular acoustic duct, incorporating viscoelastic supports or absorbers to produce responses to harmonic motion at one or both boundaries that exhibit complete separation of traveling and standing waves, in effect localizing the vibration over a portion of the domain.
The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary
signals in terms of elemental components through what has been called the empirical mode decomposition. The HHT
has been utilized extensively despite the absence of a serious analytical foundation, as it provides a concise basis for the
analysis of strongly nonlinear systems. In this paper, we attempt to provide the missing link, showing the relationship
between the EMD and the slow-flow equations of the system. The slow-flow model is established by performing a
partition between slow and fast dynamics using the complexification-averaging technique, and a dynamical system
described by slowly-varying amplitudes and phases is obtained. These variables can also be extracted directly from the
experimental measurements using the Hilbert transform coupled with the EMD. The comparison between the
experimental and analytical results forms the basis of a nonlinear system identification method, termed the slow-flow
model identification method, which is demonstrated using numerical examples.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.