On the dynamics around targeted energy transfer for vibro-impact nonlinear energy sink

A periodically forced linear oscillator with impact attachment has been studied. An asymptotical analytical method has been developed to obtain the fixed points and to analyze the transient 1:1 resonance (two impacts per cycle) of the modulated response. The influence of parameters on dynamics has been analyzed around the slow invariant manifold (SIM). Five different response regimes have been observed from theoretical and numerical results. It is demonstrated that they are closely related to the topological structure and relative position of fixed points. The bifurcation, route to chaos and the efficiency of targeted energy transfer (TET) with the variation of different parameters (i.e., amplitude and frequency of excitation, clearance, damping, mass ratio and restitution coefficient) have been investigated and well explained around SIM. Experimental results validate the existence of different regimes and different routes to chaos by the variation of the return map of time difference between consecutive impact moments. TET phenomenon has been analyzed for a strongly modulated response, and different cases of TET have been observed and analyzed. It is clearly observed that TET depends not only on whether there exists 1:1 resonance, but also on impulse strength during the transient resonance capture.     

Improvement of the acoustic black hole effect by using energy transfer due to geometric nonlinearity

Acoustic Black Hole effect (ABH) is a passive vibration damping technique without added mass based on flexural waves properties in thin structures with variable thickness. A common implementation is a plate edge where the thickness is locally reduced with a power law profile and covered with a viscoelastic layer. The plate displacement in the small thickness region is large and easily exceeds the plate thickness. This is the origin of geometric nonlinearity which can generate couplings between linear eigenmodes of the structure and induce energy transfer between low and high frequency regimes. This phenomenon may be used to increase the efficiency of the ABH treatment in the low frequency regime where it is usually inefficient. An experimental investigation evidenced that usual ABH implementation gives rise to measurable geometric nonlinearity and typical nonlinear phenomena. In particular, strongly nonlinear regime and wave turbulence are reported. The nonlinear ABH beam is then modeled as a von Kármán plate with variable thickness. The model is solved numerically by using a modal method combined with an energy-conserving time integration scheme. The effects of both the thickness profile and the damping layer are then investigated in order to improve the damping properties of an ABH beam. It is found that a compromise between the two effects can lead to an important gain of efficiency in the low frequency range.     

Performance measures for targeted energy transfer and resonance capture cascading in nonlinear energy sinks

In vibrating mechanical systems, the targeted energy transfer mechanism (TET) of nonlinear energy sinks (NES) is employed as an alternative to linear tuned mass dampers (TMD) as passive vibrations absorbers for transient vibrations. The major advantages a NES has over a linear TMD are (1) an increased robustness to detuning and (2) the ability to dissipate multiple frequencies with only a single NES through so-called resonance capture cascading (RCC). The performance, especially the speed, of TET and RCC has rarely been a topic of research. In this research, algebraic performance measures for the speed of both TET and RCC are derived, called the pumping time and the cascading time, respectively. It shows that cascading time can be seen as a sum of single-mode pumping times, by introducing a novel modal decomposition. The strength of both measures is that they do not require numerical simulations, allowing easy optimization of the NES. The influence of different nonlinearities on the TET and RCC performance is investigated. Actual numerical simulations presented in the study validate the merit of both the pumping time and cascading time.     

Efficient targeted energy transfer of bistable nonlinear energy sink: application to optimal design

This paper addresses the tracking control problem of Euler–Lagrange systems with external disturbances in an environment containing obstacles. Based on a novel sliding manifold, a new asymptotic tracking controller is proposed to ensure the tracking errors converge to zero as time goes to infinity. Moreover, based on a modified nonsingular terminal sliding manifold, a finite-time convergent control algorithm is also developed to make sure the tracking errors converge to a small bounded area near the origin in finite time. Through introducing collision avoidance functions into the sliding manifolds, both controllers can guarantee the obstacle avoidance. Moreover, the stability of the closed-loop systems and approaches free of local minima have been rigorously analyzed. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed strategies.     

Numerical optimisation of a classical stochastic system for targeted energy transfer

The paper studies stochastic dynamics of a two-degree-of-freedom system, where a primary linear system is connected to a nonlinear energy sink with cubic stiffness nonlinearity and viscous damping. While the primary mass is subjected to a zero-mean Gaussian white noise excitation, the main objective of this study is to maximise the efficiency of the targeted energy transfer in the system. A surrogate optimisation algorithm is proposed for this purpose and adopted for the stochastic framework. The optimisations are conducted separately for the nonlinear stiffness coefficient alone as well as for both the nonlinear stiffness and damping coefficients together. Three different optimisation cost functions, based on either energy of the system’s components or the dissipated energy, are considered. The results demonstrate some clear trends in values of the nonlinear energy sink coefficients and show the effect of different cost functions on the optimal values of the nonlinear system’s coefficients.     

Enhanced targeted energy transfer for adaptive vibration suppression of pipes conveying fluid

Nonlinear Dynamics - In this paper, a nonlinear energy sink and a negative stiffness element are integrated for achieving enhanced, passive, and adaptive vibration suppression for a pipe conveying...     

Nonlinear targeted energy transfer: state of the art and new perspectives

Nonlinear Dynamics - Following a brief review of current progress in the field of nonlinear targeted energy transfer (TET), we discuss some general ideas and methods in this field and describe...     

Complex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments

We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible over wide frequency and energy ranges. In an effort to study the dynamics of the coupled system of oscillators, we study numerically and analytically the periodic orbits of the corresponding undamped and unforced hamiltonian system with asymptotics and reduction. We prove the existence of a family of countable infinity of periodic orbits that result from combined parametric and external resonance interactions of the masses of the NES. We numerically demonstrate that the topological structure of the periodic orbits in the frequency–energy plane of the hamiltonian system greatly influences the strength of targeted energy transfer in the damped system and, to a great extent, governs the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers. PACS numbers: 05.45.Xt, 02.30.Hq     

Energy transfer in the hybrid system dynamics (energy transfer in the axially moving double belt system)

First, as an introduction, using the author’s published references, a short survey of an analytical study of the energy transfer between two coupled subsystems, as well as between a linear and nonlinear oscillators of a hybrid system, in the free and forced vibrations of a different type of inter connections between subsystems is presented. Second, as author’s new research result, an analytical study of the energy transfer between two coupled like-string belts interconnected by light pure elastic layer in the axially moving sandwich double belt system, in the free vibrations is presented. On the basis of the obtained analytical expressions for the kinetic and potential energy of the belts and potential energy of the of light pure elastic distributed layer numerous conclusions are derived. In the pure linear elastic double belt system no transfer energy between different eigen modes of transversal vibrations of the axially moving double belt system, but in every from of the set of the infinite numbers eigen modes, there are transfer energy between belts. Each of the eigen modes of the free transversal vibrations are like two-frequency. The change of the potential energy of the booth belts is four frequency, and interaction part of the potential energy is one frequency in the each eigen mode. Changes of the kinetic energy of the both belts of the sandwich double axially moving bet system is two frequency like oscillatory regimes with two time multiplicities of the eineg frequencies of the corresponding eigen amplitude mode.     

Coexistence of strange nonchaotic attractors and a special mixed attractor caused by a new intermittency in a periodically driven vibro-impact system

Nonlinear Dynamics - We focus on the coexistence of strange nonchaotic attractors (SNAs) and a novel mixed attractor in a periodically driven three-degree-of-freedom vibro-impact system with...     

Modal interactions and energy transfers in isotropic turbulence as predicted by local energy transfer theory

Energy transfer processes in decaying, three-dimensional, isotropic turbulence are investigated using numerical results from local energy transfer (LET) theory. The study covers a wide range of evolved, microscale Reynolds numbers (5 < R_λ < 250). It is found that the energy transfer is mainly local (between scales of similar size), but there are also some signs of nonlocal transfer at higher Reynolds number. The nature of the underlying triad-wavenumber interactions, on the other hand, seems to depend on both the Reynolds number and the wavenumber range of interest. In the energy containing and dissipation ranges, both local (all three scales of the triad interaction are of comparable size) and nonlocal (one scale is much larger than the remaining two) interactions are important, with the latter becoming more dominant as the Reynolds number increases. But our nonlocal interactions tend to be less severe than those observed by Domaradzki and Rogallo. More significantly, in the inertial range of high Reynolds number flows, the LET theory predicts dominance of local and near-local interactions. While this is contrary to the result from eddy damped quasi-normal Markovian theory that the important triad interactions are mainly nonlocal, it is closer to the Kolmogorov picture of turbulence. Another interesting result is that, despite their inherent differences, the LET theory and the full simulation of Ohkitani and Kida predict inertial-range values for the energy transfer locality function in fairly good agreement, not only with each other, but also with the analytical closure theory result for infinite Reynolds number, stationary turbulence by Kraichnan. The calculated values reveal that the contributions to the net energy transfer are predominantly from near-local interactions (scale ratios ≈ 4), which is indicative of cancellation of large numbers of highly nonlocal interactions.     

Heat transfer on A/C humidifier operating by solar energy

A solar humidifier unit used for humidification of an air conditioning system is presented. A Runge–Kutta procedure of fifth order has been used to solve the governing equations. Solar energy data as well as ambient temperature data for one hot summer day were used in calculation the inside temperature of the humidifier as well as other parameters to determine the effective use of the solar humidifier. The results obtained are promising to corporate it with an A/C system. The amount of vapor produced reaches a maximum value at the time when the ambient temperature reaches also a maximum value and the relative humidity reaches a minimum values. Received on 8 October 1998     

Thermoplastic damage of a stretched plane caused by a moving energy source

A thermoplastic stress and strain calculation is made to analyze the energy distribution around an energy source traveling in a prestretched panel. The technique of finite element is applied such that the motion of the energy source is discretized into a finite number of time increments. Remeshing of the grid pattern is carried out for every time increment.The energy source may represent a welding torch or laser beam with a high local intensity that causes the material to deform beyond its elastic limit and experience permanent damage by evaporation. This reduces the local stiffness and can lead to global instability. The failure analysis is based on the application of the strain energy density theory which is into the incremental theory of thermoplasticity. The specific example involves examining the experimental data of a 7075-T651 aluminum panel subjected to tensile loading. The energy source is assumed to have a finite radius and travels along the line of symmetry being normal to the direction of applied tension. The possible failure location is predicted for each time increment by analyzing the fluctuation of the local strain energy density field. A critical point corresponding to incipient fracture is found. The panel has a width of 45.72 cm and length of 55.88 cm. The prediction is consistent with the experimental observation.     

Ductile tearing energy of sheet metals determined by the multiple tensile testing (MTT) method

Tearing energy of aluminium, copper and brass sheets, having different mechanical characteristics, has been studied by the multiple tensile testing (MTT) method. In this method, different test pieces of various gage lengths were employed. The total energy required to tear the specimens was assumed to be composed of two components; one associated with uniform plastic deformation, which occurs in the work-hardening range of the material, and the other with post-uniform deformation and tearing which leads to the failure of the specimens. Tearing energy was calculated by plotting the total energy divided by the specimen cross-sectional area against the gage length of the specimens. In this plot, a straight line is obtained, the intercept of which gives the value of tearing energy. The results have been analyzed on the basis of the mechanical characteristics of the materials.     

A parametric analysis of moisture migration in an unsaturated porous slab caused by convective heat and mass transfer

An analysis is performed which describes the approach to a quasisteady state of heat and moisture migration in an unsaturated porous slab where one surface is impermeable to heat and mass transfer whereas convective heat and mass transfer occur at the other surface. The initial temperature and moisture content are uniform. The surface atx=0 is suddenly exposed to a gas stream at different temperature and with relative humidity. The conservation equations describing the heat and moisture migration are developed and then simplified with the assumption that the properties can be considered to be constant. The difference between the initial and the wet bulb temperature is used to make the equations dimensionless. In this way, the dimensionless temperature profiles are a function of only one parameter - a modified Biot number, and the dimensionless moisture profiles are functions of four parameters. The numerical results are presented in the form of temperature and moisture profiles as well as temperature and moisture gradients at the surface as a function of those parameters. The heat and moisture transfer at the surface as well as the time for the approach to the quasisteady state can be obtained from these results.

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Eine parametrische Analyse der Feuchtigkeitswanderung in einer nichtsaturierten porösen Wand erzeugt durch konvektiven Wärme- und Stoffübergang

Zusammenfassung Eine analytische Untersuchung beschreibt den Übergang vom Anfangszum quasistationären Endzustand (im ersten Trocknungsabschnitt) der Wärme- und Stoffwanderung in einer ungesättigten porösen Wand, deren eine Oberfläche für Wärme und Stoff undurchlässig ist, während an der anderen Oberfläche konvektiver Wärme- und Stoffaustausch herrscht. Die Temperatur und der Feuchtigkeitsgehalt in der Wand sind ursprünglich konstant. Die Oberfläche beix = 0 ist plötzlich einem Gasstrom von verschiedener Temperatur und einer relativen Feuchtigkeit ausgesetzt.Die Erhaltungsgleichungen, die die Wärme- und Feuchtigkeitswanderung beschreiben, werden dadurch vereinfacht, daß die Stoffwerte als konstant angesehen werden. Der Unterschied zwischen der ursprünglichen und der Kühlgrenztemperatur wird benutzt um die Gleichungen dimensionslos zu machen. Die dimensionslosen Temperaturprofile sind dann eine Funktion eines einzigen Parameters - einer zweckmäßig definierten Biotzahl. Die Feuchtigkeitsprofile sind durch vier Parameter bestimmt. Numerische Ergebnisse sind als Profile und als Gradienten der Temperatur und der Feuchtigkeit an der Oberflächex = 0 dargestellt. Der Wärme- und Feuchtigkeitsübergang an der Oberfläche sowie die zur Erreichung des quasistationären Endzustandes benötigte Zeit können damit bestimmt werden.

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Nomenclature Bi ^* modified Biot number, Eq. (30) - c _c composite specific heat (solid + fluid) - c _pa specific heat of air at constant pressure - C _t defined by Eq. (15) - D ^* moisture diffusion coefficient due to temperature gradient - D _c vapor diffusion coefficient through porous medium - h convective heat transfer coefficient - h _m convective mass transfer coefficient - i enthalpy - i _vl heat of evaporation - j diffusive mean flux - k thermal conductivity - k _c composite thermal conductivity (including vapor diffusion) - K moisture diffusion coefficient due to moisture content gradient - K moisture diffusion coefficient due to suction potential gradient - m _a mass flux into air space - P_l,P ₂ dimensionless parameters, Eqs. (46), (47) - q heat flux - t temperature - t _wb wet bulb temperature - w vapor mass fraction (mass of vapor/mass of air) - W moisture content (mass of moisture/mass; of dry medium) - x coordinate Greek symbols _c composite thermal diffusivity (including vapor diffusion) - suction potential - relative humidity - density - time Indices a air - c composite (solid + fluid) - d dry - i initial - l liquid - matrix potential - 0 atx = 0 - s saturated - v vapor     

Numerical study of heat and mass transfer in adsorption porous medium heated by solar energy: Boubnov-Galerkin method

This paper presents the modelization of heat and mass transfer in cubical reactor of solar adsorption cooling machine. The reactor is heated by solar energy and contains a porous medium constituted of activated carbon reacting by adsorption with ammonia. From real solar data, the model computes the performances of the machine and shows the existence of the optimal dimensioning of the reactor. For the resolution of the equations describing the coupling between heat and mass transfer, we have adapted a Boubnov-Galerkin method combined to an iterative process, this method provides a continuous distribution of the temperature and adsorbed mass. The convergence of the method is discussed and the numerical results are compared with the results provided by finite-difference method. Considering the rapidity of convergence and the order of Algebraic system (That is generally inferior to 10), the proposed method appeared to be very effective in solving such problem.