Subharmonic Response of Linear Vibroimpact System with Fractional Derivative Damping to a Randomly Disrobed Periodic Excitation

The subharmonic response of single-degree-of-freedom vibroimpact oscillator with fractional derivative damping and one-sided barrier under narrow-band random excitation is investigated. With the help of a special Zhuravlev transformation, the system is reduced to one without impacts, thereby permitting the applications of asymptotic averaging over the period for slowly varying random process. The analytical expression of the response amplitude is obtained in the case without random disorder, while only the approximate analytical expressions for the steady-state moments of the response amplitude are obtained in the case with random disorder. The effects of the fractional order derivative term, damping term, random disorder, and the coefficient of restitution and other system parameters on the system response are discussed. Theoretical analyses and numerical simulations show that fractional derivative makes both the system damping and stiffness coefficients increase, such that it changes the system parameters region at which the response amplitude reaches the maximum. The system energy loss in collision is equivalent to increasing the damping coefficient of the system. System response amplitude will increase when the excitation frequency is close to the resonant frequency and will decay rapidly when the excitation frequency gradually deviates from the resonance frequency

Report / Institute für Physik

The 2016 Report of the Physics Institutes of the Universität Leipzig presents a hopefully interesting overview of our research activities in the past year. It is also testimony of our scientific interaction with colleagues and partners worldwide. We are grateful to our guests for enriching our academic year with their contributions in the colloquium and within our work groups

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

Theoretical and experimental studies of the dynamics and acoustics of forced ordered granular networks

Ordered arrays of granular particles (beads) have attracted considerable attention in recent years due to their rich dynamical behaviors and interesting properties. Depending on the ratio of static to dynamic deformations between particles the dynamics of granular media is highly tunable ranging from being strongly nonlinear and non-smooth in the absence of static pre-compression, to reducing to weakly nonlinear and smooth for large static pre-compression. The nonlinearity in uncompressed granular media arises from two sources: First, nonlinear Hertzian interactions, which can be modeled mathematically, between beads in contact, and second, bead separations in the absence of compressive forces between them leading to collisions between adjacent beads. When no applied pre-compression exists there is complete absence of linear acoustics in ordered granular media, which results in zero speed of sound as defined in the sense of linear acoustics through the classical wave equation; thus, these media have been characterized as “sonic vacua”. However, various nonlinear waves can still propagate in these media with energy tunable properties. The first part of this dissertation aims to study the frequency responses of a single homogenous granular chain. We consider a one-dimensional uncompressed granular chain composed of a finite number of identical spherical elastic beads with Hertzian interactions. The chain is harmonically excited by an amplitude- and frequency-dependent boundary drive at its left end and has a fixed boundary at its right end. We computationally and experimentally detect time-periodic, strongly nonlinear resonances whereby the particles (beads) of the granular chain respond at integer multiples of the excitation period, and which correspond to local peaks of the maximum transmitted force at the chain’s right, fixed end. In between these resonances we detect local minima of the maximum transmitted forces corresponding to anti-resonances, where chimera states (i.e., coexistence of different stationary and nonstationary waveforms) are noted, in the steady-state dynamics. Furthermore, we construct a mathematical model which can completely capture the rich and complex dynamics of the system. The second part of the study is primarily concerned with the propagatory dynamics of geometrically coupled ordered granular media. In particular, we focus on primary pulse transmission in a two-dimensional granular network composed of two ordered chains that are nonlinearly coupled through Hertzian interactions. Impulsive excitation is applied to one of the chains (denoted as “excited chain”), and the resulting transmitted primary pulses in both chains are considered, especially in the non-directly excited chain (denoted as “absorbing chain”). A new type of mixed nonlinear solitary pulses – shear waves is predicted for this system, leading to primary pulse equi-partition between chains, indicating strong energy exchange between two chains through the geometric coupling. Then, an analytical reduced model for primary pulse transmission is derived to study the strongly nonlinear acoustics in the small-amplitude approximation. In contrast to the full equations of motion the simplified model is re-scalable with energy and parameter-free, and is asymptotically solved by extending the one-dimensional nonlinear mapping technique. The nonlinear maps, which are derived for this two-dimensional system and governing the amplitudes of the mixed-type waves, accurately capture the primary pulse propagation in this system and predict the first occurrence of energy or pulse equi-partition in the network. Moreover, to confirm the theoretical results we experimentally test a series of two-dimensional granular networks, and prove the occurrence of strong energy exchanges leading to eventual pulse equi-partition between the excited and absorbing chains, provided that the number of beads is sufficiently large. Then we analyze the dynamics of a granular network composed of two semi-infinite, ordered homogeneous granular chains mounted on linear elastic foundations and coupled by weak linear stiffnesses under periodic excitation. We first review the acoustic filtering properties of linear and nonlinear semi-infinite periodic media containing two attenuation zones (AZs) and one propagation zone (PZ) in the frequency domain. In both linear and nonlinear systems, under suddenly applied, high-frequency harmonic excitations, “dynamic overshoot” phenomena are realized whereby coherent traveling responses are propagating to the far fields of these media despite the fact that the high frequencies of the suddenly applied excitations lie well within the stop bands of these systems. For the case of the linear system we show that the transient dynamic overshoot can be approximately expressed in terms of the Green’s function at its free end. A different type of propagating wave in the form of a “pure” traveling breather, i.e., of a single propagating oscillatory wavepacket with a localized envelope, is realized in the transient responses of a nonlinear granular network. The pure breather is asymptotically studied by a complexification/averaging technique, showing nearly complete but reversible energy exchanges between the excited and absorbing chains as the breather propagates to the far field. We analytically prove that the reason for this dynamic overshoot phenomenon in both linear and nonlinear networks is the high rate of application of the high-frequency harmonic excitation, which, in essence, amounts approximately to an impulsive excitation of the periodic medium. Verification of the analytical approximations with direct numerical simulations is performed. We further study passive pulse redirection and nonlinear targeted energy transfer in the aforementioned weakly coupled granular network. Periodic excitation in the form of repetitive half-sine pulses is applied to the excited chain. The frequency of excitation is within the pass band of the granular system. At the steady state nearly complete but reversible energy exchanges between the two chains are noted. We show that passive pulse redirection and targeted energy transfer from the excited to the absorbing chain can be achieved by macro-scale realization of the spatial analog of the Landau-Zener quantum tunneling effect. This is realized by finite stratification of the elastic foundation of the excited chain, and depends on the system parameters (e.g., the percentage of stratification) and on the parameters of the periodic excitation. We detect the existence of two distinct nonlinear phenomena in the periodically forced network; namely, (i) energy localization in the absorbing chain due to sustained 1:1 resonance capture leading to irreversible pulse redirection from the excited chain, and (ii) continuous energy exchanges in the form of nonlinear beats between the two chains in the absence of resonance capture. Our results demonstrate that steady state passive pulse redirection in these networks can be robustly achieved under periodic excitation. The final part of present work is concerned with propagating breathers in granular networks under impulsive excitation. We apply a complexification-averaging methodology leading to smooth slow flow reduced models of the dynamics to reveal the nature of 1:1 resonance at fundamental steady-state responses of the system. The primary aim of this analytical study is to provide a predictive way to excite the system at its resonance conditions. In addition to the fundamental resonance we numerically verify the occurrences of subharmonic steady-state responses in such granular networks. We experimentally detect the propagating breathers in a single chain mounted on elastic foundations. Our experimental measurements show good correspondence with the computational results which validate our previous theoretical predications. The results of this work contribute to the design of practical nonlinear acoustic metamaterials and provide a new avenue for understanding ofthe complex nonlinear dynamics of granular media

Report / Institute für Physik

The 2016 Report of the Physics Institutes of the Universität Leipzig presents a hopefully interesting overview of our research activities in the past year. It is also testimony of our scientific interaction with colleagues and partners worldwide. We are grateful to our guests for enriching our academic year with their contributions in the colloquium and within our work groups

Excitonic behaviour in polymeric semiconductors : the effect of morphology and composition in heterostructures

La compréhension des interrelations entre la microstructure et les processus électroniques dans les polymères semi-conducteurs est d’une importance primordiale pour leur utilisation dans des hétérostructures volumiques. Dans cette thèse de doctorat, deux systémes diffèrents sont étudiés ; chacun de ces systèmes représente une approche diffèrente pour optimiser les matériaux en termes de leur microstructure et de leur capacité à se mettre en ordre au niveau moléculaire. Dans le premier système, j’ai effectué une analyse complète des principes de fonctionnement d’une cellule photovoltaïque hybride à base des nanocristaux d’oxyde de zinc (ZnO) et du poly (3-hexylthiophène) (P3HT) par absorption photoinduite en régime quasi-stationnaire (PIA) et la spectroscopie PIA en pompage modulé dépendant de la fréquence. L’interface entre le donneur (le polymère P3HT) et l’accepteur (les nanoparticules de ZnO), où la génération de charges se produit, joue un rôle important dans la performance des cellules photovoltaïques hybrides. Pour améliorer le mécanisme de génération de charges du P3H: ZnO, il est indispensable de modifier l’interface entre ses constituants. Nous avons démontré que la modification d’interface moléculaire avec cis-bis (4, 40 - dicarboxy-2, 20bipyridine) ruthénium (II) (N3-dye) et a-Sexithiophen-2 yl-phosphonique (6TP) a améliorée le photocourant et la performance dans les cellules P3HT: ZnO. Le 6TP et le N3 s’attachent à l’interface du ZnO, en augmentant ainsi l’aire effective de la surface donneur :accepteur, ce qui contribue à une séparation de charge accrue. De plus, le 6TP et le N3 réduisent la densité de pièges dans le ZnO, ce qui réduit le taux de recombinaison des paires de charges. Dans la deuxième partie, jai introduit une matrice hôte polymérique de polystyréne à masse molaire ulra-élevée, qui se comporte comme un solide pour piéger et protéger une solution de poly [2-méthoxy, 5- (2´-éthyl-hexoxy) -1,4-phénylènevinylène- PPV] (MEHPPV) pour utilisation dans des dispositifs optoèlectroniques quantiques. Des travaux antérieurs ont montré que MEH-PPV en solution subit une transition de conformation, d’une conformation enroulé à haute température (phase bleue) à une conformation de chaîne étendue à basse température (phase rouge). La conformation de la chaîne étendue de la solution MEH-PPV favorise les caractéristiques nécessaires à l’amélioration des dispositifs optoélectroniques quantiques, mais la solution ne peut pas être incorporées dans le dispositif. J’ai démontré que la caractéristique de la phase rouge du MEH-PPV en solution se maintient dans une matrice hôte polymérique de polystyrène transformé de masse molaire très élevée, qui se comporte comme un solide (gel de MEH-PPV/UHMW PS), par le biais de la spectroscopie de photoluminescence (PL) dépendant de la température (de 290K à 80 K). La phase rouge du gel MEH-PPV/UHMW PS se manifeste par des largeurs de raie étroites et une intensité augmentée de la transition 0-0 de la progression vibronique dans le spectre de PL ainsi qu’un petit décalage de Stokes entre la PL et le spectre d’absorption à basse température. Ces approches démontrent que la manipulation de la microstructure et des propriétés électroniques des polymères semi-conducteurs ont un impact direct sur la performance de dispositifs pour leurs développements technologiques continus.Understanding the interrelations between microstructure and electronic processes in polymeric semiconductors is of great importance for their use in bulk heterostructures, as the active part of power-converting devices such as organic photovoltaic cells or light emitting diodes, as well as for quantum optoelectronics applications. In this doctoral thesis, two different systems are investigated; each of these systems represents a different approach to optimize materials in terms of microstructure and their ability to order on the molecular level. In the first system, by means of quasi-steady-state photoinduced absorption (PIA) and pump-modulation-frequency-dependent PIA spectroscopy, I performed a comprehensive analysis of the working principles of a hybrid photovoltaic cell based on nanocrystals of zinc oxide (ZnO) and poly(3-hexylthiophene) (P3HT). The interface surface area between donor (polymer P3HT) and acceptor (ZnO nanocrystals), where charge generation occurs, plays a significant role in the performance of the hybrid photovoltaic cells. To improve the charge generation mechanism of P3HT: ZnO, it is therefore essential to modify the P3HT: ZnO interface area. We demonstrated that molecular interface modification with cis-bis(4,40-dicarboxy-2,20bipyridine) ruthenium (II) (N3-dye) and a-Sexithiophen-2-yl-phosphonic Acid (6TP) as interface modifiers enhanced the photocurrent and performance in P3HT: ZnO cells. 6TP and N3 attach to the ZnO interface, thus increasing the donor:acceptor interface area that contributes to enhanced charge separation. Furthermore, 6TP and N3 reduce the ZnO traps that reduces recombination. In the second part, I introduced a processed solid-like ultra-high-molecular-weight polystyrene polymeric host matrix to trap and protect poly [2-methoxy, 5-(2’-ethylhexoxy)- 1,4-phenylene vinylene-PPV] (MEH-PPV) solution for use in quantum optoelectronic devices. Previous work by others has shown that MEH-PPV in solution undergoes a conformation transition from coiled conformation at high temperatures (blue-phase) to a chain-extended conformation at low temperatures (red-phase). The chain-extended conformation of MEH-PPV solution favours the characteristics needed to improve quantum optoelectronic devices, however the solution cannot be incorporated into the device. We demonstrated that the red-phase feature of MEH-PPV in solution maintains in a processed solid-like ultra-high-molecular-weight polystyrene polymeric host matrix (MEH-PPV/UHMWPS gels), by means of temperature-dependent photoluminescence (PL) spectroscopy (ranged from 290K down to 80 K). The red-phase of MEH-PPV/UHMW PS gels manifest itself as narrow linewidths and enhanced 0-0 line strength in the PL spectrum as well as a small stokes shifts between the PL and absorption spectra at low temperatures. These approaches demonstrate that microstructure manipulation and electronic properties of polymeric semiconductors have a direct impact on the device performance for their continued technological developments