CACSD, GUI's, and the multivariable frequency domain toolbox

This talk describes a new version of the Multivariable Frequency Domain Toolbox for Matlab. The intellectual issue which arises here is whether there is a role for Matlab-4 GUI facilities in a Toolbox which provides relatively low-level functionality, with a correspondingly random pattern of user interaction. My belief is that there is a role, but it is very restricted: in effect only for providing convenient 'viewing' facilities for low-level objects (which are multivariable frequency responses in the case of the MFD Toolbox). There is a more obvious role for a GUI with higher-level functions, such as frequency domain identification or parametric controller optimisation.

An efficient frequency-domain algorithm for wave scattering problems with application to jet noise

This paper presents a pseudo-time-step method to calculate a (vector) Green function for the adjoint linearised Euler equations as a scattering problem in the frequency domain, for use as a jet-noise propagation prediction tool. A method of selecting the acoustics-related solution in a truncated spatial domain while suppressing any possible shear-layer-type instability is presented. Numerical tests for 3-D axisymmetrical parallel mean flows against semi-analytical reference solutions indicate that the new iterative algorithm is capable of producing accurate solutions with modest computational requirements.

Adjoint linearised Euler solver in the frequency domain for jet noise modelling

The paper is devoted to extending the new efficient frequency-domain method of adjoint Green's function calculation to curvilinear multi-block RANS domains for middle and farfield sound computations. Numerical details of the method such as grids, boundary conditions and convergence acceleration are discussed. Two acoustic source models are considered in conjunction with the method and acoustic modelling results are presented for a benchmark low-Reynolds-number jet case.

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.

A three-dimensional tunnel model for calculation of train-induced ground vibration

The frequency range of interest for ground vibration from underground urban railways is approximately 20 to 100 Hz. For typical soils, the wavelengths of ground vibration in this frequency range are of the order of the spacing of train axles, the tunnel diameter and the distance from the tunnel to nearby building foundations. For accurate modelling, the interactions between these entities therefore have to be taken into account. This paper describes an analytical three-dimensional model for the dynamics of a deep underground railway tunnel of circular cross-section. The tunnel is conceptualised as an infinitely long, thin cylindrical shell surrounded by soil of infinite radial extent. The soil is modelled by means of the wave equations for an elastic continuum. The coupled problem is solved in the frequency domain by Fourier decomposition into ring modes circumferentially and a Fourier transform into the wavenumber domain longitudinally. Numerical results for the tunnel and soil responses due to a normal point load applied to the tunnel invert are presented. The tunnel model is suitable for use in combination with track models to calculate the ground vibration due to excitation by running trains and to evaluate different track configurations. © 2006 Elsevier Ltd. All rights reserved.

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.

HEAVY VEHICLE VIBRATION - A CASE STUDY.

A method is presented for the digital simulation of multiple degrees-of-freedom lumped parameter vibrating systems with arbitrary constitutive elements in an inertial frame of reference. The geometry of the system is treated independently of the constitutive elements and as a result nonlinear (time domain) or linearised (frequency domain) calculations may be performed using a single input description. The method is used to simulate a 3-axle rigid heavy commercial vehicle for harsh vibrating conditions. Some of the assumptions to which the calculations are sensitive are examined. Agreement between the response of a 3-dimensional whole vehicle model and measurements on the test vehicle is satisfactory.

Multivariable toolbox for use with MATLAB.

The authors describe a toolbox for the frequency-domain analysis and design of multivariable feedback systems, to be used with PC-Matlab, or Pro-Matlab. The principal model representations used by the toolbox are described. Its capabilities are illustrated by a worked design example, which shows the use of a Nyquist array method. Other design techniques supported by the toolbox are briefly reviewed.

Decay of vibrations along deepwater mooring lines

Model tests for global design verification of deepwater floating structures cannot be made at reasonable scales. An overview of recent research efforts to tackle this challenge is given first, introducing the concept of line truncation techniques. In such a method the upper sections of each line are modelled in detail, capturing the wave action zone and all coupling effects with the vessel. These terminate to an approximate analytical model, that aims to simulate the remainder of the line. The rationale for this is that in deep water the transverse elastic waves of a line are likely to decay before they are reflected at the seabed. The focus of this paper is the verification of this rationale and the ongoing work, which is considering ways to produce a truncation model. Transverse dynamics of a mooring line are modelled using the equations of motion of an inextensible taut string, submerged in still water, one end fixed at the bottom the other assumed to follow the vessel response, which can be harmonic or random. Nonlinear hydrodynamic damping is included; bending and VIV effects are neglected. A dimensional analysis, supported by exact benchmark numerical solutions, has shown that it is possible to produce a universal curve for the decay of transverse vibrations along the line, which is suitable for any kind of line with any top motion. This has a significant engineering benefit, allowing for a rapid assessment of line dynamics - it is very useful in deciding whether a truncated line model is appropriate, and if so, at which point truncation might be applied. Initial efforts in developing a truncated model show that a linearized numerical solution in the frequency domain matches very closely the exact benchmark. Copyright © 2011 by ASME.

Parameters identification by a single point free response measurement

When a thin rectangular plate is restrained on the two long edges and free on the remaining edges, the equivalent stiffness of the restraining joints can be identified by the order of the natural frequencies obtained using the free response of the plate at a single location. This work presents a method to identify the equivalent stiffness of the restraining joints, being represented as simply supporting the plate but elastically restraining it in rotation. An integral transform is used to map the autospectrum of the free response from the frequency domain to the stiffness domain in order to identify the equivalent torsional stiffness of the restrained edges of the plate and also the order of natural frequencies. The kernel of the integral transform is built interpolating data from a finite element model of the plate. The method introduced in this paper can also be applied to plates or shells with different shapes and boundary conditions. © 2011 Elsevier Ltd. All rights reserved.

Low-order modelling of ducted flames with temporally varying equivalence ratio in realistic geometries

The interaction between unsteady heat release and acoustic pressure oscillations in gas turbines results in self-excited combustion oscillations which can potentially be strong enough to cause significant structural damage to the combustor. Correctly predicting the interaction of these processes, and anticipating the onset of these oscillations can be difficult. In recent years much research effort has focused on the response of premixed flames to velocity and equivalence ratio perturbations. In this paper, we develop a flame model based on the socalled G-Equation, which captures the kinematic evolution of the flame surfaces, under the assumptions of axisymmetry, and ignoring vorticity and compressibility. This builds on previous work by Dowling [1], Schuller et al. [2], Cho & Lieuwen [3], among many others, and extends the model to a realistic geometry, with two intersecting flame surfaces within a non-uniform velocity field. The inputs to the model are the free-stream velocity perturbations, and the associated equivalence ratio perturbations. The model also proposes a time-delay calculation wherein the time delay for the fuel convection varies both spatially and temporally. The flame response from this model was compared with experiments conducted by Balachandran [4, 5], and found to show promising agreement with experimental forced case. To address the primary industrial interest of predicting self-excited limit cycles, the model has then been linked with an acoustic network model to simulate the closed-loop interaction between the combustion and acoustic processes. This has been done both linearly and nonlinearly. The nonlinear analysis is achieved by applying a describing function analysis in the frequency domain to predict the limit cycle, and also through a time domain simulation. In the latter case, the acoustic field is assumed to remain linear, with the nonlinearity in the response of the combustion to flow and equivalence ratio perturbations. A transfer function from unsteady heat release to unsteady pressure is obtained from a linear acoustic network model, and the corresponding Green function is used to provide the input to the flame model as it evolves in the time domain. The predicted unstable frequency and limit cycle are in good agreement with experiment, demonstrating the potential of this approach to predict instabilities, and as a test bench for developing control strategies. Copyright © 2011 by ASME.

Nonlinear phenomena in thermoacoustics: A comparison between single-mode and multi-mode methods

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies and amplitudes of limit cycles. In frequency domain analyses, a quasi-linear transfer function between acoustic velocity and heat release rate perturbations, called the flame describing function (FDF), is obtained from a flame model or experiments. The FDF is a function of the frequency and amplitude of velocity perturbations but only contains the heat release response at the forcing frequency. While the gain and phase of the FDF provide insight into the nonlinear dynamics of the system, the accuracy of its predictions remains to be verified for different types of nonlinearity. In time domain analyses, the governing equations of the fully coupled problem are solved to find the time evolution of the system. One method is to discretize the governing equations using a suitable basis, such as the natural acoustic modes of the system. The number of modes used in the discretization alters the accuracy of the solution. In our previous work we have shown that predictions using the FDF are almost exactly the same as those obtained from the time-domain using only one mode for the discretization. We call this the single-mode method. In this paper we compare results from the single-mode and multi-mode methods, applied to a thermoacoustic system of a premixed flame in a tube. For some cases, the results differ greatly in both amplitude as well as frequency content. This study shows that the contribution from higher and subharmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Hence multi-mode simulations are necessary, and the single-mode method or the FDF may be insufficient to capture some of the complex nonlinear behaviour in fhermoacoustics.

Nonlinear phenomena in thermoacoustic systems with premixed flames

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies, amplitudes and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, but can be used to calculate the amplitudes of limit cycles, as well as their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modelled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearised momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state, for single- mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitudedependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, as well as twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact resulting in a larger limit cycle amplitude. Multimode simulations show that in some situations the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Copyright © 2012 by ASME.

The dynamic effect of a piled-foundation building on an incident vibration field from an underground railway tunnel

This paper presents a three-dimensional comprehensive model for the calculation of vibration in a building based on pile-foundation due to moving trains in a nearby underground tunnel. The model calculates the Power Spectral Density (PSD) of the building's responses due to trains moving on floating-slab tracks with random roughness. The tunnel and its surrounding soil are modelled as a cylindrical shell embedded in half-space using the well-known PiP model. The building and its piles are modelled as a 2D frame using the dynamic stiffness matrix. Coupling between the foundation and the ground is performed using the theory of joining subsystems in the frequency domain. The latter requires calculations of transfer functions of a half-space model. A convenient choice based on the thin-layer method is selected in this work for the calculations of responses in a half-space due to circular strip loadings. The coupling considers the influence of the building's dynamics on the incident wave field from the tunnel, but ignores any reflections of building's waves from the tunnel. The derivation made in the paper shows that the incident vibration field at the building's foundation gets modified by a term reflecting the coupling and the dynamics of the building and its foundation. The comparisons presented in the paper show that the dynamics of the building and its foundation significantly change the incident vibration field from the tunnel and they can lead to loss of accuracy of predictions if not considered in the calculation.