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

A spectral characterization of nonlinear normal modes

This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to zero level sets of specific eigenfunctions of the Koopman operator. Thanks to this direct connection, a new, global parametrization of the invariant manifolds is established. Unlike the classical parametrization using a pair of state-space variables, this parametrization remains valid whenever the invariant manifold undergoes folding, which extends the computation of NNMs to regimes of greater energy. The proposed ideas are illustrated using a two-degree-of-freedom system with cubic nonlinearity.Belgian Network DYSCO (Dynamical Systems, Control, and Optimization) funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy OfficeThis is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jsv.2016.05.01

Evapotranspiration from Spider and Jade Plants Can Improve Relative Humidity in an Interior Environment

Citation: Kerschen, E., Garten, C., Williams, K., & Derby, M. (2016). Evapotranspiration from Spider and Jade Plants Can Improve Relative Humidity in an Interior Environment. HortTechnology, 26(6), 803-810. doi: 10.21273/HORTTECH03473-16Plants in the interiorscape have many documented benefits, but their potential for use in conjunction with mechanical heating, ventilation, and air conditioning (HVAC) systems to humidify dry indoor environments requires more study. In this research, evaporation and evapotranspiration rates for a root medium control, variegated spider plants (Chlorophytum comosum), and green jade plants (Crassula argentea) were measured over 24 hours at 25% and 60% relative humidity (RH) and 20 °C to generate data for calculation of the leaf surface area and number of plants necessary to influence indoor humidity levels. Evaporation and evapotranspiration rates were higher for all cases at 25% RH compared with 60% RH. At 25% RH during lighted periods, evapotranspiration rates were ?15 g·h?1 for spider plants and 8 g·h?1 for jade plants. Spider plants transpired during lighted periods due to their C3 photosynthetic pathway, whereas jade plants had greater evapotranspiration rates during dark periods—about 11 g·h?1—due to their crassulacean acid metabolism (CAM) photosynthetic pathway. A combination of plants with different photosynthetic pathways (i.e., C3 and CAM combination) could contribute to greater consistency between evapotranspiration rates from day to night for humidification of interior spaces. Using the measured data, calculations indicated that 32,300 cm2 total spider plant leaf surface area, which is 25 spider plants in 4-inch-diameter pots or fewer, larger plants, could increase the humidity of an interior bedroom from 20% RH to a more comfortable 30% RH under bright interior light conditions

Suppression Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 1: Theory

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76103/1/AIAA-24062-636.pd

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

Nonlinear MDOF system characterization and identi cation using the Hilbert-Huang transform

The Hilbert transform is one of the most successful approaches to tracking the varying nature of vibration of a large class of nonlinear systems thanks to the extraction of backbone curves from experimental data. Because signals with multiple frequency components do not admit a well-behaved Hilbert transform, it is inherently limited to the analysis of single-degree-of-freedom systems. In this study, the joint application of the complexification-averaging method and the empirical mode decomposition enables us to develop a new technique, the slow-flow model identification method. Through numerical and experimental applications, we demonstrate that the proposed method is adequate for characterizing and identifying multi-degree-offreedom nonlinear systems

Empirical Mode Decomposition in the Reduced-Order Modeling of Aeroelastic Systems

peer reviewedA relationship between IntrinsicMode Functions (IMFs), derived from the Empirical Mode Decomposition (EMD), and the slow-flow model of a nonlinear dynamical system has been exploited in the development of the Slow Flow Model Identification (SFMI) method for strongly nonlinear systems, in which the physical parameters of such systems are identified from experimental data. Both the slow flows and IMFs provide the means to expand a general multicomponent signal in terms of a series of simpler, dominant, monocomponent signals. The slow flows are obtained analytically, for example through application of the method of complexification and averaging (CxA), which transforms the equations of motion into a set of approximate equations in amplitude and phase for each modeled frequency component. In contrast, the EMD characterizes a signal through the envelope and phase of its elemental components, the IMFs. Thus, between nonlinear transitions, the equations derived using the CxA method govern the amplitude and phase of the modeled IMFs. Application of SFMI has, until now, been limited to low-dimensional systems subjected to impulsive excitation. Herein, the method is extended to identification of a planar rigid airfoi

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