Dissertations / Theses on the topic 'Damped oscillation'

This work deals with the power supply of wireless sensors. When using a wireless sensor is desirable application of alternative energy sources, because the primary cells or batteries may reduce the extent or length of service of the sensor itself. Ambient energy can be used as a suitable alternative source. This energy must be in an appropriate form, which allows its conversion to electric energy. These appropriate, already used types include: solar en., temperature gradient en., en. of flowing liquids, vibration, etc. The advantage of vibrations is its presence in almost all mechanical systems. One of the possibilities for using the vibration of machine systems for power supply wireless sensors is using the vibration power generator with oscillating component. The generator must be designed so that its resonance frequency coincides with the frequency of vibration in the machine system. This method can be used only if the machinery system vibrations at least partially constant. Another option is to use the vibrations caused by, for example, transit transport, or different step acting factor. In this case, it is desirable that the generator is designed with variable resonant frequency, which can partly be achieved, for example, integrating several oscillating component in the body of generator. After the general analysis of the problem, graduation theses will be concerned with the possibility of use of energy from the short damped oscillation and step impulse. Focusing on a proposal of multi-element structures.

Energy dissipation due to sloshing liquid in torus shaped nutation dampers is studied using the potential flow model with nonlinear free surface conditions in conjunction with the boundary layer correction. Special consideration is given to the case of resonant interactions which were found to yield interesting damping characteristics. An extensive test program with the dampers undergoing steady-state oscillatory translation is then undertaken to establish the optimal damper parameters. Low liquid heights and large diameter ratios with the system operating at the liquid sloshing resonance are shown to result in increased damping, while low Reynolds numbers and presence of baffles tend to reduce the peak efficiency by restricting the action of the free surface. Tests with two-dimensional as well as three-dimensional models in laminar flow and boundary layer wind tunnels suggest that the dampers can successfully control both the vortex resonance and galloping types of instabilities. Applicability of the concept to vertically oscillating structures such as transmission lines is also demonstrated with dampers undergoing a rotational motion about their horizontal axis.
Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate

This thesis examines a new method of detecting the presence of structural cracks in wing-like structures at an incipient stage. This method is based on the analysis of the dynamics of damaged structures with bonded piezoelectric strips executing flexural oscillations. Such oscillations can be generated by mechanical loads, piezoelectric actuators, or unsteady aerodynamic loads in certain flight conditions of the aircraft. The proposed method of crack detection uses pairs of piezoelectric strip sensors bonded on the opposite sides of the structure and is based on the fact that the presence of a crack causes a difference between the strains measured by the two sensors of a given pair. The structural analysis presented in this thesis uses a nonlinear model for the cracks and a finite element formulation for the piezoelectric strips coupled with the structure. A 3D panel method is used to determine the unsteady aerodynamic loads acting on the oscillating wing. This study includes the dynamic analysis in time domain of cracked wing-like structures undergoing forced flexural vibrations in a range of frequencies generated by a pair of piezoelectric actuators, as well as the analysis of the oscillating wings with piezoelectric strips subjected to unsteady aerodynamic loads. The numerical simulations have shown that the presence of a crack in wing-like structures can be efficiently detected at an early stage by monitoring the response of the piezoelectric sensor pairs.
Cette thèse étudie une nouvelle méthode de détection de la présence de fissures structurelles à un stade précoce dans une structure de type aile. Cette méthode est basée sur l'analyse des oscillations en flexion des structures endommagées munies de bandes piézoélectriques collées. Ces oscillations peuvent être générées par des charges mécaniques, des actionneurs piézoélectriques, ou des charges aérodynamiques instationnaires dans certaines conditions de vol de l'avion. La méthode de détection des fissures proposée utilise des paires de capteurs piézoélectriques collés sur les côtés opposés de la structure et est basée sur le fait que la présence d'une fissure entraîne une différence entre les déformations mesurées par les deux capteurs d'une paire donnée. L'analyse structurale présentée dans cette thèse utilise un modèle non linéaire pour les fissures et une formulation par éléments finis pour les bandes piézoélectriques couplées avec la structure. Une méthode de panneau tridimensionnelle est utilisée pour déterminer les charges aérodynamiques instationnaires agissant sur l'aile oscillante. Cette étude comprend l'analyse dynamique dans le domaine temporel de structure de type aile fissurée subissant des vibrations en flexion forcées dans une gamme de fréquences générées par une paire d'actionneurs piézoélectriques, ainsi que l'analyse des ailes oscillantes équipées de bandes piézoélectriques soumises à des charges aérodynamiques instationnaires. Les simulations numériques ont montré que la présence d'une fissure dans ces structures peut être efficacement détectée à un stade précoce en surveillant la réponse des capteurs piézoélectriques.

Les actionneurs multi-axes sont de plus en plus prisés par les concepteurs de systèmes de nanopositionnement car ils permettent une réduction de l'espace occupé et de l'énergie consommée, une dextérité plus grande et une modularité avec peu de contraintes pour les applications. Certains de ces actionneurs et systèmes multi-axes sont cependant caractérisés par des oscillations mal-amorties qui compromettent de manière drastique leurs performances générales. Cette thèse concerne l'exploitation des techniques de commande en boucle-ouverte input-shaping classiquement utilisées pour amortir de manière sans capteurs les oscillations dans les systèmes mono-axes et les étendent pour qu'ils soient utilisables pour les systèmes multi-axes. Les résultats proposés dans la thèse qui sont des techniques input-shaping multivariables sont ensuite appliquées sur des actionneurs piézoélectriques classiquement dédiés pour les applications de nanopositionnement
Multi-axes actuators are becoming more and more tempting to nanopositioning system designers as they enable them to save space, reduce energy consumption, increase dexterity and offer more modularity and freedom with fewer constraints to their applications. Some of these multi-axes actuators and systems exhibit however badly damped vibrations which strongly compromise their global performances. This thesis work exploits the advantages of the well-known feedforward input shaping techniques usually used to damp vibrations in monovariable (SISO) systems to present a new multivariable (MIMO) input shaping technique that can be used to damp vibrations in multi-axes systems. The approach that was used in this study is to extend a previous work that was done on multiple-input single-output (MISO) systems and generalize it for MIMO systems. The study demonstrates also the application of this newly developed technique on different piezoelectric actuators commonly used in nanopositioning systems

Wind power has emerged as one of the most promising renewable energy sources. The very penetration levels of wind energy in power systems have altered several aspects of power system operation, such as system stability. Owing to the large penetration of wind power, transmission system operators (TSOs) have established special grid codes for wind farms connection. These grid codes require wind farms to provide ancillary services to the grid such as frequency and voltage regulation. In the near future, the capability of damping power system oscillations will be required. As a result of the development of such requirements, the concept of wind power plant (WPP) arises being de ned as a wind farm which is expected to behave similarly to a conventional power plant in terms of power generation, control and ancillary services. As future grid codes will require power oscillation damping contribution from wind power, the thesis is mainly focused on the analysis of the power system stabilizer (PSS) capability of wind power plants. The change produced by wind power plants based on di erent wind turbine technologies on power system small signal dynamics is analysed to determine their possible contribution to damp oscillations. The eff ect of the distance from the tie line to the wind power plant on the controller response and the influence of wind power plants proximity to synchronous generators are demonstrated to be critical factors. At this point several questions are raised as: What are the most critical factors? How can be ensure a proper contribution, at least the best possible response? Can it be ensured to be independent to the power system and the controller selected? To answer these questions, this thesis conducts research on proper selection of input-output signal pairs to damp out electromechanical oscillations using wind power plants without drawing attention to a particular control design. This is necessary conclusions about the power system independently of a particular controller. The capability to damp is an intrinsic characteristic of the system and should not be a ected by a particular controller (PSS). Firstly, di erent analysis techniques are compared, considering both controllability and observability measures and input-output interactions. This enables recommendations to be drawn so as to the selection of the the best signal pairs to damp power system oscillations considering di erent approaches, such as single-input single-output (SISO) and multivariable control (MIMO). Second, a new criterion to select the best input-output signals used by a PSS based on WPPs is presented, considering explicitly local and remote signals in the analysis. Taking into account fundamental design limitations and using controllability and observability concepts, the criterion is able to identify the most suitable pair of input-output local signals without consider any particular controller. Finally, due to the increase of wind power generation - including o shore locations - and the concept of an interconnected Pan-European network, a new o shore wind power plant AC network similar in design to the European SuperGrid \SuperNode", is analyzed. The cost e ect of choosing a nonstandard operating frequency on the o shore AC network is investigated. As the o shore AC network is isolated from onshore networks through the use of HVDC links, it may be operated in an asynchronous fashion and at a suitable frequency. The cost associated with operating the network at a fixed frequency in the range 20 to 120 Hz is investigated, focusing on the frequency-cost-scalings of electrical devices (such as cables, transformers and reactive compensation) and the related o shore infrastructures,
L'energia e olica s'ha convertit en una de les fonts d'energia renovable m es prometedores. Actualment, l'elevat nivell de penetraci o de l'energia e olica a la xarxa el ectrica ha conduï t a la modi caci o del comportament de diversos aspectes d'aquesta, com per exemple, l'estabilitat. Degut a aquesta gran penetraci o, els operadors de xarxes de transmissi o (TSOs) han establert procediments d'operaci o especials per a la connexi o de grans parcs e olics. Aquests codis requereixen als parcs elics que realitzin serveis auxiliars al sistema el ectric com, per exemple, la regulaci o de freqü encia i la regulaci o de la pot encia reactiva. En un futur proper, la capacitat dels parcs e olics per esmorteir les oscil lacions del sistema de pot encia es requerir a (en l'actualitat ja existeixen esborranys de nous procediments d'operaci o que ho inclouen). A causa d'aquest requeriments, el concepte de central de generaci o d'energia e olica es de neix com un parc e olic que s'espera que es comporti de manera similar a una central de generaci o el ectrica convencional en termes de poder realitzar tasques tals com generaci o, control i serveis auxiliars. Ja que un futur requeriment dels operadors de xarxa ser a la contribuci o de l'energia e olica en l'esmorteiment de les oscil lacions de pot encia, en aquesta tesi s'estudia la capacitat de les centrals e oliques per actuar com estabilitzador dels sistemes el ectrics de pot encia. A m es a m es, s'analitza l'efecte de les centrals d'energia e olica al comportament din amic del sistema el ectric considerant l'estabilitat de petita senyal, per a determinar quina podr a ser la possible contribuci o proporcionada per aquestes tecnologies. S'ha estudiat que l'efecte de la dist ancia des d'el punt de connexi o amb la central d'energia e olica a la resposta del control estabilitzant i la influ encia de la proximitat de les centrals e oliques als generadors s ncrons s on factors cr tics. D'aquest fet surgeixen algunes preguntes com: Es aquest el factor m es cr tic? Com es pot assegurar una contribuci o adequada, si m es no la millor resposta possible, per ajudar a estabilitzar el sistema el ectric? Es poden asegurar quina ser a la contribuci o a l'estabilitat del sistema el ectric independentment de la xarxa i l'esquema de control escollit? Per respondre a aquestes preguntes, aquesta tesi ha realitzat investigacions sobre l'adequada selecci o de parells de senyals d'entrada-sortida per esmorteir les oscil lacions electromec aniques amb centrals e oliques evitant dissenyar el controlador i propossant met odes f acilment adaptables a qualsevol sistema el ectric. En primer lloc, s'han comparat diferents t ecniques d'an alisi tenint en compte tant les mesures de controlabilitat i observabilitat com les interaccions entre les senyals d'entrada i sortida. D'aquesta comparaci o, certes recomanacions es donen a l'hora de seleccionar els millors parells de senyals per esmorteir les oscil lacions del sistema el ectric de pot encia considerant diferents esquemes de control com ara entrada unica sortida unica (SISO) i control multivariable (MIMO). En segon lloc, s'ha proposat un nou criteri per seleccionar les senyals d'entrada i sortida utilitzades per un control estabilitzador per centrals d'energia e olica. On, a difer encia amb anteriors met odes de selecci o proposats, el criteri presentat considera expl citament tant senyals locals com senyals remotes dins el seu an alisi. Aquest criteri es capa c d'identi car la parella de senyals locals d'entrada i sortida m es adequada sense realitzar el disseny del controlador, considerant tant les limitacions fonamentals del disseny del controlador imposades per el sistema com els conceptes de controlabilitat i observabilitat. Finalment, a causa del augment de la generaci o d'energia e olica, principalment en localitzacions marines, i al concepte d'una xarxa el ectrica comuna Pan-Europea, s'ha realitzat l'an alisi d'un nou concepte de xarxa en corrent altern (AC) dins de les centrals d'energia e olica marina, amb un disseny similar al concepte investigat a la Super-Xarxa Europea \Supernode". En aquest treball s'ha investigat l'efecte que t e en els costos la tria una freqüencia nominal d'operaci o no est andard en dita xarxa en corrent altern. La xarxa en AC que es forma entre les turbines e oliques i el convertidor de transmissi o es aï llada tant de les xarxes terrestres per l' us d'enlla cos en corrent continu (HVDC) com de la pr opia de les turbines per el convertidor que porten incorporat. Aquest fet implica que aquesta xarxa pot ser operada sense sincronitzar a qualsevol freqüencia. En aquesta tesi, s'ha estudiat quin es el cost associat amb l'operaci o de la xarxa a una freqü encia fi xa dins del rang de 20-120 Hz, focalitzant principalment en l'escalat del costos dels diferents elements el ectrics (com ara cables, transformadors i compensaci o reatviva i infraestructures necessaris en instal lacions marines respecte la freqüencia.

Les mécanismes volontaires (V) et involontaires (I) de l’attention reposent sur les réseaux dorsal et ventral, convergeant dans le cortex préfrontal latéral (lPFC). La distractibilité accrue liée au vieillissement ou à une lésion frontale pourrait être due à une altération de l’équilibre entre ces mécanismes V et I, essentiel mais rarement étudié. Notre objectif est de tester, dans la modalité auditive, si (1) les oscillations alpha coordonnent l'activité du réseau dorsal, (2) les oscillations gamma celle du réseau ventral, (3) le couplage oscillatoire dans le lPFC maintient l’équilibre entre les deux réseaux. Ce travail vise également à étudier les corrélats oscillatoires de la distractibilité accrue liée au vieillissement ou à une atteinte frontale. Des données MEEG ont été enregistrées alors que des participants réalisaient le Competitive Attention Test, qui permet d’étudier simultanément les mécanismes V et I de l’attention. Nous avons montré que les oscillations alpha reflètent l’activation des mécanismes facilitateurs et suppresseurs de l’attention V, et la communication au sein du réseau dorsal ; alors que les oscillations gamma indexent l’activation du réseau ventral. De plus, le lPFC serait impliqué dans la communication au sein des deux réseaux, et le PFC médian dans l’équilibre attentionnel V/I. Nous avons également montré que la distractibilité accrue était liée à un déficit d’attention V au cours du vieillissement, et à une altération des processus V et I après lésion frontale. Ce travail de thèse offre donc une meilleure compréhension de la dynamique cérébrale oscillatoire sur laquelle repose l'équilibre attentionnel V/I, et donc la distractibilité
Top-down (TD) and bottom-up (BU) mechanisms of attention are supported by dorsal and ventral networks that mainly overlap in the lateral prefrontal cortex (lPFC). A balance between these mechanisms is essential, yet rarely investigated. Increased distractibility observed during ageing or after frontal damage could result from jeopardizing this balance. It has been proposed that distinct oscillatory frequencies support the activation of these two attention networks. Our main aim was to test, in the auditory modality, whether (1) alpha oscillations would coordinate activity within the dorsal TD network, (2) gamma activity would index the activation of the ventral BU network, (3) the lPFC would support the balance between these networks through oscillatory coupling. We also aimed to investigate the oscillatory correlates of the increased distractibility associated with ageing or frontal damage. MEEG data were recorded while participants performed the Competitive Attention Test, which enables simultaneous investigation of BU and TD attention mechanisms. We showed that alpha oscillations indexed facilitatory and suppressive mechanisms of TD attention, and communication within the dorsal network; while gamma oscillations indexed the ventral network activation. Moreover, the lPFC subtended communication in the two networks; with the TD/BU interaction occurring in the medial PFC. We also showed that ageing-related distractibility was of TD deficit origin. Finally, preliminary results suggest that lPFC damage can impact both TD and BU attention. This thesis provides novel insights into the brain oscillatory dynamics of the TD/BU attentional balance supporting distractibility

This thesis deals with mathematical modeling of multiphysics FSI (fluid-structure interaction) problem, describing mutual interaction of pressure pulsations and vibrations of indirect pipe in a 2D region. Firstly, physical partial differential equations are derived separately for both media, which are in turn coupled and solved analytically. Results of mentioned models include natural frequency values, amplitude-frequency characteristics and both natural and driven damped oscillations of pipe and liquid.

The objective of this work is to design a damping controller for a thyristor controlled series capacitor (TCSC) to damp robustly inter-area oscillations in power systems with an immunity against sub-synchronous resonance (SSR) oscillations which may lead to torsional oscillations. The new control strategy has two main loops; an SSR mitigation loop and a bang-bang loop, the latter is designed with the aim of damping inter-area oscillations with a settling time 8-10 sec. The appropriate selection of the bang-bang series compensation component, ∆KC, is addressed by considering the Eigen analysis of the generators’ shafts and an impedance scan of the series compensated line for different compensation levels. The SSR mitigation loop is designed with the aim of providing a fine tune control signal to be added to the main value of the inserted series compensation (KC), to damp SSR oscillations and related torsional mode of oscillations. To address this issue, a new observer-based multiple model adaptive control algorithm is designed to control a multi-stage TCSC. The SSR modelling challenges associated with the load dynamics and with the insertion of the series compensation into the transmission system are overcome by a fine tuning control loop, which adjusts the resultant series compensation (KC). Considering the integration and coordination of oscillation damping and distance protection in the transmission system, a new adaptive technique must be designed to control the distance relay (DR) to prevent its mal operation (during the damping process). The new strategy is illustrated through an 11-bus 4-machine 2-area benchmark power system. The performance and advantages of the new algorithm are validated using time domain simulation via PSCAD software.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
Neste trabalho analisamos as soluÃÃes para a equaÃÃo de movimento para os osciladores de Lane-Emden, onde a massa à dada por m(t)=t^α, onde α>0. Os osciladores de Lane-Emden sÃo osciladores harmÃnicos amortecidos, onde o fator de amortecimento depende do tempo, γ(t)=α/t. Obtivemos as expressÃes analÃticas de q(t), dq(t)/dt, and p(t)=m(t)(dq(t)/dt) para α=2 e α=4. Discutimos as diferenÃas entre as expressÃes da hamiltoniana e da energia para sistemas dependentes do tempo. TambÃm, comparamos nossos resultados com aqueles do oscilador de Caldirola-Kanai. Usamos o mÃtodo dos invariantes quÃnticos e uma transformaÃÃo unitÃria para obter a funÃÃo de onda exata de SchrÃdinger, ψn (q,t), e calcular para n=0 a entropia conjunta (entropia de Leipnik) dependente do tempo e as informaÃÃes Fisher para posiÃÃo (Fq) e para o momento (Fp) para duas classes de osciladores harmÃnicos quÃnticos amortecidos. Observamos que a entropia de Leipnik nÃo varia no tempo para o oscilador Caldirola-Kanai, enquanto diminui e tende a um valor constante (ln(e/2)) para tempos assintÃticos para o oscilador de Lane-Emden. Isto à devido ao fato de que, para este Ãltimo, o fator de amortecimento diminui à medida que o tempo aumenta. Os resultados mostram que a dependÃncia do tempo da entropia de Leipnik à bastante complexa e nÃo obedece a uma tendÃncia geral de aumento monotonicamente com o tempo e que Fq aumenta enquanto Fp diminui com o aumento do tempo. AlÃm disso, FqFp aumenta e tende a um valor constante (4/ℏ^2 ) no limite em que t->∞. NÃs comparamos os resultados com os do bem conhecido oscilador de Caldirola-Kanai.
In this work we analyze the solutions of the equations of motions for two Lane-Emden-type Caldirola-Kanai oscillators. For these oscillators the mass varies as m(t)=t^α, where α>0.We obtain the analytical expression of q(t), dq(t)/dt, and p(t)=m(t)(dq(t)/dt) for α=2 and α=4. These are damped-like harmonic oscillators with a time-dependent damping factor given by γ(t)=α/t. We discuss the differences between the expressions for the hamiltonian and the mechanical energy for time-dependent systems. We also compared our results to those of the well-known Caldirola-Kanai oscillators. We use the quantum invariant method and a unitary transformation to obtain the exact SchrÃdinger wave function, ψn (q,t), and calculate for n=0 the time-dependent joint entropy (LeipnikÂs entropy) and the position (Fq) and momentum (Fp) Fisher information for two classes of quantum damped harmonic oscillators. We observe that the joint entropy does not vary in time for the Caldirola-Kanai oscillator, while it decreases and tends to a constant value (ln(e/2)) for asymptotic times for the Lane-Emden ones. This is due to the fact that for the latter, the damping factor decreases as time increases. The results show that the time dependence of the joint entropy is quite complex and does not obey a general trend of monotonously increase with time and that F_q increases while F_p decreases with increasing time. Also, FqFp increases and tends to a constant value (4/ℏ^2 ) in the limit t->∞.We compare the results with those of the well-known Caldirola-Kanai oscillator.

The possibility to save energy in synchronous machines operation by dismissing d-axis damping bars and surrogating them with active excitation current control in sectored field winding is proved. In particular a way to recover the energy of rotor oscillations during power regulation is shown by means of a studycase generator whereas a self-starting machine is analytically and numerically designed in view of its next construction and test. Principal design requirements and limits for both applications are presented and discussed.

The aim of this thesis is to find out the influence of eccentricity of crank mechanism on the duration of the force between the piston and the cylinder liner. At the same time I wanted to find out its influence on the balance of the whole system. It is important to design the balance for the selected value of the eccentricity and subsequently put through the crank shaft to stress analysis with torsional vibrations. I got so interested in this problem that in addition to the whole topic I designed a torsional vibration damper.

The aim of this diploma is to design a crankshaft for a six-cylinder commercial vehicle, which is one of the unified motors. The main parts are the design of the crankshaft configuration, the crankshaft balancing method for forces and moments, the crankshaft design documentation, and the crankshaft strength verification. The design of torsional vibration damping characteristics is also made and its effect on torsional vibration and crankshaft strength is determined.

After decades of routine operation, the hydropower industry faces new challenges. Large-scale integration of other renewable sources of generation in the power system accentuates the role of hydropower as a regulating resource. At the same time, an extensive reinvestment programme has commenced where many old components and apparatus are being refurbished or replaced. Introduction of new technical solutions in existing power plants requires good systems knowledge and careful consideration. Important tools for research, development and analysis are suitable mathematical models, numerical simulation methods and laboratory equipment. This doctoral thesis is devoted to studies of the electromechanical interaction between hydropower units and the power system. The work encompasses development of mathematical models, empirical methods for system identification, as well as numerical and experimental studies of hydropower generator and power system interaction. Two generator modelling approaches are explored: one based on electromagnetic field theory and the finite element method, and one based on equivalent electric circuits. The finite element model is adapted for single-machine infinite-bus simulations by the addition of a network equivalent, a mechanical equation and a voltage regulator. Transient simulations using both finite element and equivalent circuit models indicate that the finite element model typically overestimates the synchronising and damping properties of the machine. Identification of model parameters is performed both numerically and experimentally. A complete set of equivalent circuit parameters is identified through finite element simulation of standard empirical test methods. Another machine model is identified experimentally through frequency response analysis. An extension to the well-known standstill frequency response (SSFR) test is explored, which involves measurement and analysis of damper winding quantities. The test is found to produce models that are suitable for transient power system analysis. Both experimental and numerical studies show that low resistance of the damper winding interpole connections are vital to achieve high attenuation of rotor angle oscillations. Hydropower generator and power system interaction is also studied experimentally during a full-scale startup test of the Nordic power system, where multiple synchronised data acquisition devices are used for measurement of both electrical and mechanical quantities. Observation of a subsynchronous power oscillation leads to an investigation of the torsional stability of hydropower units. In accordance with previous studies, hydropower units are found to be mechanically resilient to subsynchronous power oscillations. However, like any other generating unit, they are dependent on sufficient electrical and mechanical damping. Two experimentally obtained hydraulic damping coefficients for a large Francis turbine runner are presented in the thesis.

碩士
國立臺灣大學
統計碩士學位學程
104
In financial economics, the efficient-market hypothesis is well known for stating market behavior. Under this hypothesis, asset prices fully reflect all historical information, which implies that only new relevant information affects market prices. Investors’ reactions to the information is random and in a normally distributed pattern so that the change on the market price is also normally distributed. This is a strong argument for the use of geometric Brownian motion (GBM) on modeling stock prices. However, GBM is not a completely realistic model, in particular it fails to describe some properties of stock prices. One is that GBM is a continuous path through time, but in real life, stock price often show jumps. The other is the mean-reverting property. When stock price is far from its equilibrium due to some shocks, it will have a high chance to be adjusted to its equilibrium nearby, but GBM will still follow the trend even in an unreasonable price level. There have been several models conducted to modify GBM, some examples like Ornstein-Uhlenbeck model for mean-reverting property, jump-diffusion model for discontinuity, and affine jump-diffusion model for both. Recently, more and more economists believes the inefficiency of the market. Investors predictably overreact to new information, creating a large effect on the stock price, making the price oscillate. This kind of oscillation has not been described by those classical models. My thesis is to discuss the dynamic of the oscillation, and introducing a process in the framework of damped harmonic oscillation.

碩士
國立中興大學
機械工程學系
89
A damped oscillation internal model-based LQG design technique is proposed in this thesis to attenuate wide-band noise within 100-200Hz bandwidth in acoustic ducts. The optimal number of damped oscillation modes in the internal model is determined using computer simulation and design procedures are derived. Results of computer simulation show the better effect of noise attenuation than internal model-based LQG design technique. The designed controllers are further implemented in experiments by using a floating-point digital signal processor. Experimental results confirm the results of computer simulation.

In this thesis, we are interested in damped wave models with time-dependent propagation speed and time-dependent damping term both having a time-dependent oscillation term. The main goal of this thesis is to understand the influence of strong time-dependent oscillations on Sobolev solutions to the linear models and consequently, to the semilinear models. Especially, due to the deteriorating influence of oscillations on solutions, a stabilization condition and higher-order regularity of the time-dependent coefficients may compensate 'bad behaviors' arising from oscillations.:1. Introduction 2. The influence of oscillations on linear damped wave equation with time-dependent coefficients 3. Global in time existence results for damped wave models with power nonlinearity 4. Global in time existence results for damped wave models with different power nonlinearities 5. Lp-Lq estimates for wave equations with strong time-dependent oscillations 6. Further research topics A. Basic tools B. List of symbols and abbreviations Bibliography

The response of beams resting on viscoelastically damped foundation under moving SDoF oscillators is scrutinized through a novel state-space formulation, in which a number of internal variables is introduced with the aim of representing the frequency-dependent behaviour of the viscoelastic foundation. A suitable single-step scheme is provided for the numerical integration of the equations of motion, and the Dimensional Analysis is applied in order to define the dimensionless combinations of the design parameters that rule the responses of beam and moving oscillator. The effects of boundary conditions, span length and number of modes of the beam, along with those of the mechanical properties of oscillator and foundation, are investigated in a new dimensionless form, and some interesting trends are highlighted. The inaccuracy associated with the use of effective values of stiffness and damping for the viscoelastic foundation, as usual in the present state-of-practice, is also quantified.

Auxiliary absorbers provide an effective means to attenuate the vibrations of a structural or mechanical system (the "primary structure"). The simplest auxiliary absorber, a tuned mass damper (TMD), provides reliable narrow-band attenuation but is not robust to the effects of detuning. Strongly nonlinear tuned mass dampers (NTMDs) are capable of wide-band, irreversible energy transfer known as "energy pumping" but can also exhibit high amplitude solutions which significantly amplify the response of the primary structure. Semi-active tuned mass dampers (STMDs) incorporate an actuating element in order to achieve real-time tuning adjustment capability. This thesis presents a global dynamic analysis of the response of a primary structure with an NTMD and then explores the performance of a novel absorber configuration consisting of an NTMD and STMD attached to the primary structure in series. The global dynamic analysis is conducted using a new cell mapping method developed by the author and introduced within the thesis: the parallelized multi-degrees-of-freedom cell mapping (PMDCM) method. The benefits of the additional STMD component are explored for two distinct applications: (1) restoring the performance of a linear TMD which develops a weak nonlinearity due to operation outside of the intended range or other means, and (2) acting as a safety device to eliminate or minimize convergence to the detached high-amplitude response. In the weakly nonlinear case, the STMD is shown to reduce the effects of the nonlinearity and improve attenuation capability by constraining the motion of the NTMD. In the strongly nonlinear case, the STMD effectively eliminates the complex response behavior and high amplitude solutions which were present in the original system, resulting in a single low amplitude response. Experimental tests using an adjustable-length pendulum STMD verify the numerical results.

Research report to School of Electrical and Information Engineering
An investigation was conducted into how a variable speed drive can provide a damping torque when mechanical oscillations are present. The modeling of mechanical oscillations via an analogous electrical circuit was performed. Simulation was used to demonstrate how a variable speed drive is able to damp speed oscillations using Direct Torque Control (DTC). Damping of mechanical oscillations is done by means of the variable speed drive providing a damping torque component that is in-phase with the speed deviation. The simulation showed that by applying a small torque component with the speed variation results in torque oscillations being damped by 60% after the initial disturbance. Damping is further improved by applying a torque component equal to the speed variation resulting in the oscillations being damped by 80% when compared to the initial disturbance.
MT2017