320 research outputs found
Multi-scaled analysis of the damped dynamics of an elastic rod with an essentially nonlinear end attachment
We study multi-frequency transitions in the transient dynamics of a viscously damped dispersive finite rod with an essentially nonlinear end attachment. The attachment consists of a small mass connected to the rod by means of an essentially nonlinear stiffness in parallel to a viscous damper. First, the periodic orbits of the underlying hamiltonian system with no damping are computed, and depicted in a frequency–energy plot (FEP). This representation enables one to clearly distinguish between the different types of periodic motions, forming back bone curves and subharmonic tongues. Then the damped dynamics of the system is computed; the rod and attachment responses are initially analyzed by the numerical Morlet wavelet transform (WT), and then by the empirical mode decomposition (EMD) or Hilbert–Huang transform (HTT), whereby, the time series are decomposed in terms of intrinsic mode functions (IMFs) at different characteristic time scales (or, equivalently, frequency scales). Comparisons of the evolutions of the instantaneous frequencies of the IMFs to the WT spectra of the time series enables one to identify the dominant IMFs of the signals, as well as, the time scales at which the dominant dynamics evolve at different time windows of the responses; hence, it is possible to reconstruct complex transient responses as superposition of the dominant IMFs involving different time scales of the dynamical response.
Moreover, by superimposing the WT spectra and the instantaneous frequencies of the IMFs to the FEPs of the underlying hamiltonian system, one is able to clearly identify the multi-scaled transitions that occur in the transient damped dynamics, and to interpret them as ‘jumps’ between different branches of periodic orbits of the underlying hamiltonian system. As a result, this work develops a physics-based, multi-scaled framework and provides the necessary computational tools for multi-scaled analysis of complex multi-frequency transitions of essentially nonlinear dynamical systems
The slow-flow method of identification in nonlinear structural dynamics
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-flowmodel identification method, which is demonstrated using numerical examples
Assessing the Dissipative Capacity of Particle Impact Dampers Based on their Nonlinear Bandwidth Characteristics
The dissipative capacity as quantified by the nonlinear bandwidth measure of
impulsively loaded primary structures (PSs) coupled to particle impact dampers
(PIDs) is assessed. The considered PIDs are designed by initially placing
different numbers of spherical, linearly viscoelastic granules at different 2D
initial topologies and clearances. The strongly nonlinear and highly
discontinuous dynamics of the PIDs are simulated via the discrete element
method taking Hertzian interactions, slipping friction and granular rotations
into account. The general definition of nonlinear bandwidth is used to evaluate
the energy dissipation capacity of the integrated PS-PID systems. Moreover, the
effect of the dynamics of the PIDs on the time-bandwidth product of these
systems is studied, as a measure of their capacity to store or dissipate
vibration energy. It is found that the initial topologies of the granules in
the PID drastically affect the time-bandwidth product, which, depending on
shock intensity, may break the classical limit of unity which holds for linear
time-invariant dissipative resonators. The optimal PS-PID systems composed of
multiple granules produce large nonlinear bandwidths, indicating strong
dissipative capacity of broadband input energy by the PIDs. Additionally, in
the optimal configurations, the time-bandwidth product, i.e., the measure of
the frequency bandwidth of the input shock that is stored in the PS-PID system,
in tandem with the amount of time it takes for the system to dissipate (1/e) of
the initial energy, can be tuned either above or below unity by varying the
applied shock intensity. The implications of these findings on the dissipative
capacity of the system considered are discussed, showing that it can be
predictively assessed so that PIDs can act as highly effective nonlinear energy
sinks capable of rapid and efficient suppression of vibration induced by
shocks
PASSIVE SUPPRESSION OF AEROELASTIC INSTABILITIES OF IN-FLOW WINGS BY TARGETED ENERGY TRANSFERS TO LIGHTWEIGHT ESSENTIALLY NONLINEAR ATTACHMENTS
Theoretical and experimental suppression of aeroelastic instabilities by means of broadband passive targeted energy transfers has been recently studied. A single-degree-offreedom (SDOF) nonlinear energy sink (NES) was coupled to a 2-DOF rigid wing modeled in the low-speed, subsonic regime with quasi-steady aerodynamic theory. The nonlinear attachment was designed and optimized to suppress the critical nonlinear modal energy exchanges between the flow and the (pitch and heave) wing modes, thus suppressing the (transient) triggering mechanism of aeroelastic instability. We performed bifurcation analysis to find regions of robust passive aeroelastic suppression in parameter space. Then, we employed multi-degreeof-freedom nonlinear energy sinks (MDOF NESs) to improve robustness of the aeroelastic instability suppression. Bifurcation analysis by a numerical continuation technique demonstrated that controlling the occurrence of a limit point cycle (LPC or saddle-node) bifurcation point above a Hopf bifurcation point is crucial to enhancing suppression robustness. MDOF NESs not only can enhance robustness of suppression against even strong gust-like disturbances, but they require lower NES mass compared to SDOF NES designs. The validity of the theoretical findings was proven by a series of wind tunnel experiments
Aspects of Type 0 String Theory
A construction of compact tachyon-free orientifolds of the non-supersymmetric
Type 0B string theory is presented. Moreover, we study effective
non-supersymmetric gauge theories arising on self-dual D3-branes in Type 0B
orbifolds and orientifolds.Comment: 9 pages, LATEX; submitted to Proceedings of Strings '9
Understanding Fields Using Strings: A Review for Particle Physicists
In addition to being a prime candidate for a fundamental unified theory of
all interactions in nature, string theory provides a natural setting to
understand gauge field theories. This is linked to the concept of "D-branes":
extended, solitonic excitations of string theory which can be studied using
techniques of string theory and which support gauge fields localized along
their world-volumes. It follows that the techniques of string theory can be
very useful even for those particle physicists who are not specifically
interested in unification and/or quantum gravity. In this talk I attempt to
review how strings help us to understand fields. The discussion is restricted
to 3+1 spacetime dimensions.Comment: LaTeX, 22 pages, 4 eps figures (included); v2: Name of conference
corrected, no other change
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An overview of reliability assessment and control for design of civil engineering structures
Random variations, whether they occur in the input signal or the system parameters, are phenomena that occur in nearly all engineering systems of interest. As a result, nondeterministic modeling techniques must somehow account for these variations to ensure validity of the solution. As might be expected, this is a difficult proposition and the focus of many current research efforts. Controlling seismically excited structures is one pertinent application of nondeterministic analysis and is the subject of the work presented herein. This overview paper is organized into two sections. First, techniques to assess system reliability, in a context familiar to civil engineers, are discussed. Second, and as a consequence of the first, active control methods that ensure good performance in this random environment are presented. It is the hope of the authors that these discussions will ignite further interest in the area of reliability assessment and design of controlled civil engineering structures
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