Nonlinear Fluid Damping In Structure-Wake Oscillators In Modeling Vortex-Induced Vibrations

A Nonlinear Fluid Damping (NFD) in the form of the square-velocity is applied in the response analysis of Vortex-induced Vibrations (VIV). Its nonlinear hydrodynamic effects oil the coupled wake and structure oscillators are investigated. A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics, such as the amplification of body displacement at lock-in and frequency lock-ill, both at high and low mass ratios. Particularly, the predicted peak amplitude of the body in the Griffin plot is ill good agreement with experimental data and empirical equation, indicating the significant effect of the NFD on the structure motion.

Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.

A perturbation procedure for nonlinear oscillations (The dynamics of two oscillators with weak nonlinear coupling)

This thesis considers in detail the dynamics of two oscillators with weak nonlinear coupling. There are three classes of such problems: non-resonant, where the Poincaré procedure is valid to the order considered; weakly resonant, where the Poincaré procedure breaks down because small divisors appear (but do not affect the O(1) term) and strongly resonant, where small divisors appear and lead to O(1) corrections. A perturbation method based on Cole's two-timing procedure is introduced. It avoids the small divisor problem in a straightforward manner, gives accurate answers which are valid for long times, and appears capable of handling all three types of problems with no change in the basic approach.

One example of each type is studied with the aid of this procedure: for the nonresonant case the answer is equivalent to the Poincaré result; for the weakly resonant case the analytic form of the answer is found to depend (smoothly) on the difference between the initial energies of the two oscillators; for the strongly resonant case we find that the amplitudes of the two oscillators vary slowly with time as elliptic functions of ϵ t, where ϵ is the (small) coupling parameter.

Our results suggest that, as one might expect, the dynamical behavior of such systems varies smoothly with changes in the ratio of the fundamental frequencies of the two oscillators. Thus the pathological behavior of Whittaker's adelphic integrals as the frequency ratio is varied appears to be due to the fact that Whittaker ignored the small divisor problem. The energy sharing properties of these systems appear to depend strongly on the initial conditions, so that the systems not ergodic.

The perturbation procedure appears to be applicable to a wide variety of other problems in addition to those considered here.

7.3 W of single-frequency output power at 2.09 μm from an Ho:YAG monolithic nonplanar ring laser

Single-frequency output power of 7.3 W at 2.09 mu m from a monolithic Ho:YAG nonplanar ring oscillator (NPRO) is demonstrated. Resonantly pumped by a Tm-doped fiber laser at 1.91 mu m, the Ho:YAG NPRO produces 71% of slope efficiency with respect to absorbed pump power and nearly diffraction-limited output with a beam quality parameter of M-2 approximate to 1.1. (c) 2008 Optical Society of America

Dynamical behavior of damped driven coupled single electron simple harmonic oscillators

Coherent coupling between a large number of qubits is the goal for scalable approaches to solid state quantum information processing. Prototype systems can be characterized by spectroscopic techniques. Here, we use pulsed-continuous wave microwave spectroscopy to study the behavior of electrons trapped at defects within the gate dielectric of a sol-gel-based high-k silicon MOSFET. Disorder leads to a wide distribution in trap properties, allowing more than 1000 traps to be individually addressed in a single transistor within the accessible frequency domain. Their dynamical behavior is explored by pulsing the microwave excitation over a range of times comparable to the phase coherence time and the lifetime of the electron in the trap. Trap occupancy is limited to a single electron, which can be manipulated by resonant microwave excitation and the resulting change in trap occupancy is detected by the change in the channel current of the transistor. The trap behavior is described by a classical damped driven simple harmonic oscillator model, with the phase coherence, lifetime and coupling strength parameters derived from a continuous wave (CW) measurement only. For pulse times shorter than the phase coherence time, the energy exchange between traps, due to the coupling, strongly modulates the observed drain current change. This effect could be exploited for 2-qubit gate operation. The very large number of resonances observed in this system would allow a complex multi-qubit quantum mechanical circuit to be realized by this mechanism using only a single transistor.

Bayesian estimation of simultaneous musical notes based on frequency domain modelling

This paper proposes a Bayesian method for polyphonic music description. The method first divides an input audio signal into a series of sections called snapshots, and then estimates parameters such as fundamental frequencies and amplitudes of the notes contained in each snapshot. The parameter estimation process is based on a frequency domain modelling and Gibbs sampling. Experimental results obtained from audio signals of test note patterns are encouraging; the accuracy is better than 80% for the estimation of fundamental frequencies in terms of semitones and instrument names when the number of simultaneous notes is two.

Electrically coupled MEMS oscillators

In this paper, we demonstrate synchronization of two electrically coupled MEMS oscillators incorporating nearly identical silicon tuning fork microresonators. It is seen that as the output of the oscillators are coupled, they exhibit a synchronized response wherein the output amplitudes and signal-to-noise ratios of the two oscillators are improved relative to the case where the two oscillators are uncoupled. The observed output frequency of each oscillator before coupling is 219402.4 Hz and 219403.6 Hz respectively. In contrast, when the oscillators are driven simultaneously, they lock at a common output frequency of 219401.3 Hz and their outputs are found to be out-of-phase with respect to each other. A 6 dBm gain in output power and a reduction in the phase fluctuations of the output signal are observed for the coupled oscillators compared to the case when the oscillators are uncoupled. © 2011 IEEE.

Modeling nonlinearities in MEMS oscillators

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude¿frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier-based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases. © 1986-2012 IEEE.

Synchronization in a coupled architecture of microelectromechanical oscillators

There has been much recent interest in engineering the phenomenon of synchronization in coupled micro-/nano-scale oscillators for applications ranging from precision time and frequency references to new approaches to information processing. This paper presents descriptive modelling detail and further experimental validation of the phenomenon of mutual synchronization in coupled MEMS oscillators building upon recent experimental validation of this concept by the present authors. In particular, the underlying dependence of the observation of synchronization on system parameters is studied through numerical and analytical modelling while considering essential nonlinearities in both the resonator and circuit domain. Experimental results demonstrating synchronized response are elaborated based on the realization of electrically coupled MEMS resonator based square-wave oscillators. The experimental results on frequency entrainment are found to be in general agreement with results obtained through analytical modeling and numerical simulation. The concept presented here is scalable and could be used to investigate the dynamics of large-arrays of coupled MEMS oscillators. © 2014 AIP Publishing LLC.

Novel hybrid voltage controlled ring oscillators using single electron and MOS transistors

This paper proposes two kinds of novel hybrid voltage controlled ring oscillators (VCO) using a single electron transistor (SET) and metal-oxide-semiconductor (MOS) transistor. The novel SET/MOS hybrid VCO circuits possess the merits of both the SET circuit and the MOS circuit. The novel VCO circuits have several advantages: wide frequency tuning range, low power dissipation, and large load capability. We use the SPICE compact macro model to describe the SET and simulate the performances of the SET/MOS hybrid VCO circuits by HSPICE simulator. Simulation results demonstrate that the hybrid circuits can operate well as a VCO at room temperature. The oscillation frequency of the VCO circuits could be as high as 1 GHz, with a -71 dBc/Hz phase noise at 1 MHz offset frequency. The power dissipations are lower than 2 uW. We studied the effect of fabrication tolerance, background charge, and operating temperature on the performances of the circuits.

Effect of polymeric properties on the operation of gel-type audio transducers.

A novel design of a moving-coil transducer coupled with a low-hardness elastomer called “the gel surround” is presented in this thesis. This device is termed a “gel-type audio transducer”. The gel-type audio transducer has been developed to overcome the problems that conventional loudspeakers have suffered - that is, the problem with size of the audio device against the quality of sound at low frequency range. Therefore the research work presented herein aims to develop the “gel-type audio transducer” as a next-generation audio transducer for miniaturized woofers. The gel-type audio transducer consists of the magnetic and coil-drive plate assembly, and these parts are coupled by the gel surround. The transducer is driven by the electromagnetic conversion mechanism (a moving-coil transducer) and its output driving force can be greatly enhanced by applying the novel mechanism of the gel surround especially at low frequency range, resulting in the enhanced acoustic efficiency. The transducer can be attached to a stiff and light panel with both the optimized impedance matching and minimised wave collisions. The performance of the gel-type audio transducer is greatly influenced by the mass of the magnetic assembly and compliance of the “gel surround”. But as the size of the magnet and its weight have to be kept minimal for a miniaturisation of the device, the focus of the research is on the effect of the of the gel surround. As a result, the effect of the gel surround, made of the RTV (room-temperature vulcanising) silicone elastomer, TPE (thermoplastic elastomer), and the silicone foam, on generation of the output driving force, the energy transfer from the transducer to a panel to which the transducer is attached, and sound radiation from the vibrating panel, was investigated. This effect was studied by COMSOL multiphysics (FE analysis) and thereby, the simulated results were verified by experiments such as the laser scanning measurement, DMA (dynamic mechanical analyzer), and the acoustic test. Successful development of prototypes of the gel-type audio transducers, with an enhanced acoustic efficiency at reduced size and weight, was achieved. Implementation of the transducers into consumer applications was also demonstrated with their commercial values.

A pll based frequency synthesizer in 0.13 um sige bicmos for mb-ofdm uwb systems

With the growing demand for high-speed and high-quality short-range communication, multi-band orthogonal frequency division multiplexing ultra-wide band (MB-OFDM UWB) systems have recently garnered considerable interest in industry and in academia. To achieve a low-cost solution, highly integrated transceivers with small die area and minimum power consumption are required. The key building block of the transceiver is the frequency synthesizer. A frequency synthesizer comprised of two PLLs and one multiplexer is presented in this thesis. Ring oscillators are adopted for PLL implementation in order to drastically reduce the die area of the frequency synthesizer. The poor spectral purity appearing in the frequency synthesizers involving mixers is greatly improved in this design. Based on the specifications derived from application standards, a design methodology is presented to obtain the parameters of building blocks. As well, the simulation results are provided to verify the performance of proposed design.

Modeling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations

A new method for modeling-frequency-dependent boundaries in finite-difference time-domain (FDTD) and Kirchhoff variable digital waveguide mesh (K-DWM) room acoustics simulations is presented. The proposed approach allows the direct incorporation of a digital impedance filter (DIF) in the Multidimensional (2D or 3D) FDTD boundary model of a locally reacting surface. An explicit boundary update equation is obtained by carefully constructing a Suitable recursive formulation. The method is analyzed in terms of pressure wave reflectance for different wall impedance filters and angles of incidence. Results obtained from numerical experiments confirm the high accuracy of the proposed digital impedance filter boundary model, the reflectance of which matches locally reacting surface (LRS) theory closely. Furthermore a numerical boundary analysis (NBA) formula is provided as a technique for an analytic evaluation of the numerical reflectance of the proposed digital impedance filter boundary formulation.

A frequency measure robust to linear filtering

It is noted that the determination of an oscillation frequency by used of the power spectrum of measured time series is susceptible to filtering of the signal. Similarly, frequency measurements made by period counting can yield different, results depending on how the signal is filtered for noise reduction. In an attempt to eliminate these ambiguities, a new measure of frequency, based on an approximate reconstruction of the phase-space trajectory of the oscillator from the signal, is introduced. This measure is shown to be invariant under linear filtering. For this reason, it is also inaccessible by spectral methods. The effect of filtering on frequency for weakly nonlinear, noisy oscillators, to which this definition applies only imperfectly, is quantified. This work provides the theoretical basis for frequency measurements employing MIRVA filtering.