Physical mechanisms of phonation onset: a linear stability analysis of an aeroelastic continuum model of phonation

In an investigation of phonation onset, a linear stability analysis was performed on a two-dimensional, aeroelastic, continuum model of phonation. The model consisted of a vocal fold-shaped constriction situated in a rigid pipe coupled to a potential flow which separated at the superior edge of the vocal fold. The vocal fold constriction was modeled as a plane-strain linear elastic layer. The dominant eigenvalues and eigenmodes of the fluid-structure-interaction system were investigated as a function of glottal airflow. To investigate specific aerodynamic mechanisms of phonation onset, individual components of the glottal airflow (e.g., flow-induced stiffness, inertia, and damping) were systematically added to the driving force. The investigations suggested that flow-induced stiffness was the primary mechanism of phonation onset, involving the synchronization of two structural eigenmodes. Only under conditions of negligible structural damping and a restricted set of vocal fold geometries did flow-induced damping become the primary mechanism of phonation onset. However, for moderate to high structural damping and a more generalized set of vocal fold geometries, flow-induced stiffness remained the primary mechanism of phonation onset.     

QCD plasma parameters in axial gauge

Within the framework of imaginary time formalism we investigate the structure of the gluon polarization tensor and relate its structure functions to the dispersion relation of plasma eigenmodes. To one loop order, we calculate the transversal structure function to leading order in the high temperature expansion as well as the first subleading order contribution in the long wavelength limit. The result is used to express the dynamical mass and the damping constant for transversal plasma eigenmodes. The aim of our present paper is a systematic discussion of the gauge fixing vector dependence of the damping constant. In the limit of temporal axial gauge we encounter a negative damping constant contradicting previous results.     

Eigenvalue density of linear stochastic dynamical systems: A random matrix approach

Eigenvalue problems play an important role in the dynamic analysis of engineering systems modeled using the theory of linear structural mechanics. When uncertainties are considered, the eigenvalue problem becomes a random eigenvalue problem. In this paper the density of the eigenvalues of a discretized continuous system with uncertainty is discussed by considering the model where the system matrices are the Wishart random matrices. An analytical expression involving the Stieltjes transform is derived for the density of the eigenvalues when the dimension of the corresponding random matrix becomes asymptotically large. The mean matrices and the dispersion parameters associated with the mass and stiffness matrices are necessary to obtain the density of the eigenvalues in the frameworks of the proposed approach. The applicability of a simple eigenvalue density function, known as the Marenko–Pastur (MP) density, is investigated. The analytical results are demonstrated by numerical examples involving a plate and the tail boom of a helicopter with uncertain properties. The new results are validated using an experiment on a vibrating plate with randomly attached spring–mass oscillators where 100 nominally identical samples are physically created and individually tested within a laboratory framework.     

The Taylor-Couette eigenvalue problem with independently rotating cylinders

The eigenvalue problem for disturbances of the laminar Couette flow with co- or counterrotating cylinders of infinite height is considered. We solve the eigenvalue equation numerically and also give some analytical approximations for the eigenvalues and eigenmodes. Flow field patterns and spectra are offered.     

Aeroelastic flutter of a disk rotating in an unbounded acoustic medium

The linear aeroelastic stability of an unbaffled flexible disk rotating in an unbounded fluid is investigated by modeling the disk-fluid system as a rotating Kirchhoff plate coupled to the irrotational motions of a compressible inviscid fluid. A perturbed eigenvalue formulation is used to compute systematically the coupled system eigenvalues. Both a semi-analytical and a numerical method are employed to solve the fluid boundary value problem. The semi-analytical approach involves a perturbation series solution of the dual integral equations arising from the fluid boundary value problem. The numerical approach is a boundary element method based on the Hadamard finite part. Unlike previous works, it is found that a disk with zero material damping destabilizes immediately beyond its lowest critical speed. Upon the inclusion of small disk material damping, the flutter speeds become supercritical and increase with decreasing fluid density. The competing effects of radiation damping into the surrounding fluid and disk material damping control the onset of flutter at supercritical speed. The results are expected to be relevant for the design of rotating disk systems in data storage, turbomachinery and manufacturing applications.     

Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform

Based on the nonlinear Schr?dinger equation(NLSE) with damping, detuning, and driving terms describing the evolution of signals in a Kerr microresonator, we apply periodic nonlinear Fourier transform(NFT) to the study of signals during the generation of the Kerr optical frequency combs(OFCs). We find that the signals in different states, including the Turing pattern, the chaos, the single soliton state, and the multi-solitons state, can be distinguished according to different distributions of the eigenvalue spectrum. Specially, the eigenvalue spectrum of the single soliton pulse is composed of a pair of conjugate symmetric discrete eigenvalues and the quasi-continuous eigenvalue spectrum with eye-like structure.Moreover, we have successfully demonstrated that the number of discrete eigenvalue pairs in the eigenvalue spectrum corresponds to the number of solitons formed in a round-trip time inside the Kerr microresonator. This work shows that some characteristics of the time-domain signal can be well reflected in the nonlinear domain.     

On the tuning of variable piezoelectric transducer circuitry network for structural damage identification

The concept of using piezoelectric transducer circuitry with tunable inductance has been recently proposed to enhance the performance of frequency-shift-based damage identification method. While this approach has shown promising potential, a piezoelectric circuitry tuning methodology that can yield the optimal damage identification performance has not been synthesized. This research aims at advancing the state-of-the-art by exploring the characteristics of inductance tuning such that the enrichment of frequency measurements can be effectively realized to highlight the damage occurrence. Analysis shows that when the inductance is tuned to accomplish eigenvalue curve veering, the change of system eigenvalues induced by structural damage will vary significantly with respect to the change of inductance. Therefore, by tuning the inductance near the curve-veering range, one may obtain a family of frequency response functions that could effectively reflect the damage occurrence. When multiple tunable piezoelectric transducer circuitries are integrated to the mechanical structure, multiple eigenvalue curve veering can be simultaneously accomplished, and a series of inductance tunings can be formed by accomplishing curve veering between different pairs of system eigenvalues. It will then be shown that, to best characterize the damage occurrence, the favorable inductance tuning sequence should be selected as that leads to a “comprehensive” set of eigenvalue curve veering, i.e., all measurable natural frequencies undergo curve veering at least once. An iterative second-order perturbation-based algorithm is used to identify the locations and severities of the structural damages based on the frequency measurements before and after the damage occurrence. Numerical analyses on benchmark beam and plate structures have been carried out to examine the system performance. The effects of measurement noise on the effectiveness of the proposed damage identification method are also evaluated. It is demonstrated that the damage identification results can be significantly improved by using the variable piezoelectric transducer circuitry network with the favorable inductance-tuning scheme proposed in this research.     

壳模型哈密顿量本征值的美与奇

本征值问题是自然科学中基本运算之一，对于超大矩阵的对角化是当今许多科学问题的瓶颈。在应用原子核壳模型理论研究较重的原子核结构时，因为壳模型组态太大，通常的方法是基于各种物理考虑做某些组态截断，另一个思路是利用新的算法和飞速发展的计算机资源对这些大矩阵对角化或者近似对角化。总结了本课题组近年来在壳模型哈密顿量本征值近似方面研究的主要结果，包括最低本征值半经验公式及多种外推方法、本征值与对角元的相关性等。The eigenvalue problem is one of the fundamental issues of sciences. Many research fields have been challenged by diagonalizing huge matrices. The nuclear structure theorists face this problem in studies of medium-heavynuclei in terms of the nuclear shell model, in which the configuration space is too gigantic to handle. Thus one usually truncates the nuclear shell model configuration space based on various considerations. Another approach is to make use of super computers by various algorithms, and/or to obtain approximate eigenvalues. In this paper we review our recent efforts in obtaining approximate eigenvalues of the nuclear shell model Hamiltonian, with the focus on our semi-empirical approach and a number of extrapolation approaches towards predicting the lowest eigenvalue, as well as strong correlation between the sorted eigenvalues and the diagonal matrix elements, and so on.     

Actuator saturation control of uncertain structures with input time delay

This paper presents a robust saturation control approach for active vibration attenuation of building structures involving parameter uncertainties and input time delay. The parameter uncertainties are described in both polytopic and norm-bounded forms and represent the variations of floor masses, stiffnesses and damping coefficients. The input time delay can be time-varying within a known bound. In terms of the feasibility of certain delay-dependent linear matrix inequalities (LMIs), a state feedback controller can be designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties, actuator saturation, and input time delay. The effectiveness of the proposed approach is investigated by numerical simulations on the vibration control of a three-storey building structure subject to seismic excitation. It is validated that the designed robust saturation controller can effectively suppress the structural vibration and keep the system stability when there are parameter uncertainties and input time delay.     

Quantum field theoretical description of unstable behavior of trapped Bose-Einstein condensates with complex eigenvalues of Bogoliubov-de Gennes equations

The Bogoliubov-de Gennes equations are used for a number of theoretical works on the trapped Bose-Einstein condensates. These equations are known to give the energies of the quasi-particles when all the eigenvalues are real. We consider the case in which these equations have complex eigenvalues. We give the complete set including those modes whose eigenvalues are complex. The quantum fields which represent neutral atoms are expanded in terms of the complete set. It is shown that the state space is an indefinite metric one and that the free Hamiltonian is not diagonalizable in the conventional bosonic representation. We introduce a criterion to select quantum states describing the metastablity of the condensate, called the physical state conditions. In order to study the instability, we formulate the linear response of the density against the time-dependent external perturbation within the regime of Kubo’s linear response theory. Some states, satisfying all the physical state conditions, give the blow-up and damping behavior of the density distributions corresponding to the complex eigenmodes. It is qualitatively consistent with the result of the recent analyses using the time-dependent Gross-Pitaevskii equation.     

On the definition of the natural frequency of oscillations in nonlinear large rotation problems

Computational multibody system algorithms allow for performing eigenvalue analysis at different time points during the simulation to study the system stability. The nonlinear equations of motion are linearized at these time points, and the resulting linear equations are used to determine the eigenvalues and eigenvectors of the system. In the case of linear systems, the system eigenvalues remain the same under a constant coordinate transformation; and zero eigenvalues are always associated with rigid body modes, while nonzero eigenvalues are associated with non-rigid body motion. These results, however, cannot in general be applied to nonlinear multibody systems as demonstrated in this paper. Different sets of large rotation parameters lead to different forms of the nonlinear and linearized equations of motion, making it necessary to have a correct interpretation of the obtained eigenvalue solution. As shown in this investigation, the frequencies associated with different sets of orientation parameters can differ significantly, and rigid body motion can be associated with non-zero oscillation frequencies, depending on the coordinates used. In order to demonstrate this fact, the multibody system motion equations associated with the system degrees of freedom are presented and linearized. The resulting linear equations are used to define an eigevalue problem using the state space representation in order to account for general damping that characterizes multibody system applications. In order to demonstrate the significant differences between the eigenvalue solutions associated with two different sets of orientation parameters, a simple rotating disk example is considered in this study. The equations of motion of this simple example are formulated using Euler angles, Euler parameters and Rodriguez parameters. The results presented in this study demonstrate that the frequencies obtained using computational multibody system algorithms should not in general be interpreted as the system natural frequencies, but as the frequencies of the oscillations of the coordinates used to describe the motion of the system.     

Statistics of the Jones matrix of fibers affected by polarization mode dispersion

We carry out a statistical characterization of Jones matrix eigenvalues and eigenmodes to gain deeper insight into recently proposed fiber models based on Jones matrix spectral decomposition. A set of linear dynamic equations for the Pauli coordinates of the Jones matrix is established. Using stochastic calculus, we determine the joint distribution of the retardation angle of the eigenmodes and, indirectly, their autocorrelation function. The correlation bandwidth of the eigenmodes is found to be radical2/3 that of the polarization mode dispersion vector. The results agree well with simulations performed with the standard retarded plate model.     

Optimization of Quantum Correlation in Cascaded Four-Wave Mixing

We propose a measurement strategy that can be used to optimize quantum correlation for a cascaded four-wave mixing (FWM) structure. By calculating the covariance matrix of a cascaded FWM structure, we can get all the correlations between any two parties in the outputs. We then calculate the eigenvalues and corresponding eigenmodes of the covariance matrix to find the squeezing degrees of the squeezed modes. Our theoretical model can explain our previous experimental results very well and is useful to optimize the squeezing degree in the cascaded FWM structure.     

Delocalization of Slowly Damped Eigenmodes on Anosov Manifolds

We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with damping parameters which are asymptotically close enough to the real axis. We prove that such modes cannot be completely localized on subsets satisfying a condition of negative topological pressure. As an application, one can deduce the existence of a ??strip?? of logarithmic size without eigenvalues below the real axis under this dynamical assumption on the set of undamped trajectories.     

Suppression of brake squeal noise applying finite element brake and pad model enhanced by spectral-based assurance criteria

An enhanced dynamic finite element (FE) model with friction coupling is applied to analyze the design of disc brake pad structure for squeal noise reduction. The FE model is built-up from the individual brake component representations. Its interfacial structural connections and boundary conditions are determined by correlating to a set of measured frequency response functions using a spectral-based assurance criterion. The proposed friction coupling formulation produces an asymmetric system stiffness matrix that yields a set of complex conjugate eigenvalues. The analysis shows that eigenvalues possessing positive real parts tend to produce unstable modes with the propensity towards the generation of squeal noise. Using a proposed lumped parameter model and eigenvalue sensitivity study, beneficial pad design changes can be identified and implemented in the detailed FE model to determine the potential improvements in the dynamic stability of the system. Also, a selected set of parametric studies is performed to evaluate numerous design concepts using the proposed dynamic FE model. The best pad design attained, which produces the least amount of squeal response, is finally validated by comparison to a set of actual vehicle test results.     

A local damage detection approach based on restoring force method

Chain-like systems have been studied by many researchers for their simple structure and wide range of application. Previously, the damage in a chain-like system was detected by the reduction of the mass-normalized stiffness coefficient for certain elements as reported by Nayeri et al. (2008 [16]). However, some shortcomings exist in that approach and for overcoming them; an improved approach is derived and presented in this paper. In our improved approach, the mass normalized stiffness coefficients under two states (baseline state and potentially damaged state) are first estimated by a least square method, then these mass-stiffness coupled coefficients are decoupled to derive stiffness and mass relative change ratios for individual elements. These ratios are assembled in a vector, which is defined as damage indication vector (DIV). Each component in DIV is normalized individually to one to get multiple solutions. These solutions are averaged for estimating relative system changes, while abnormal solutions are discarded. The work of judging a solution as normal or abnormal is done by a cluster analysis algorithm. The most intriguing merit of this improved approach is that the relative stiffness and mass changes, which are coupled in the previous approach, can be separately identified. By this approach, the damage (single or multiple) extent and location can be correctly detected under operational conditions, meanwhile the proposed damage index has a clear physical meaning and is directly related to the stiffness reduction of corresponding structural elements. For illustrating the effectiveness and robustness of the improved approach, numerical simulation of a four floor building was carried out and experimental data from a structure tested at the Los Alamos National Laboratory was employed. Identified structural changes with both simulation and experimental data properly indicated the location and extent of actual structural damage, which validated the proposed approach.     

Stability in a general coupled laser array

For the first time we have presented a method to investigate the stability of quiescent state in a coupled laser array. By introducing tiny perturbation, stability of quiescent state can be known by investigating eigenvalues of coefficient matrix of the corresponding linear differential equations. Only when real parts of the eigenvalues were all negative or zero, the corresponding quiescent state is stable. Two tapes of coupled laser array with loop and linear topological structure were studied respectively. It was found that there were innumerable quiescent states and they could be divided into several types based on phase relation. Some types were stable and others were unstable. Topological structure affects the stability of quiescent state in a coupled laser array.     

A damage identification technique based on embedded sensitivity analysis and optimization processes

A vibration based structural damage identification method, using embedded sensitivity functions and optimization algorithms, is discussed in this work. The embedded sensitivity technique requires only measured or calculated frequency response functions to obtain the sensitivity of system responses to each component parameter. Therefore, this sensitivity analysis technique can be effectively used for the damage identification process. Optimization techniques are used to minimize the difference between the measured frequency response functions of the damaged structure and those calculated from the baseline system using embedded sensitivity functions. The amount of damage can be quantified directly in engineering units as changes in stiffness, damping, or mass. Various factors in the optimization process and structural dynamics are studied to enhance the performance and robustness of the damage identification process. This study shows that the proposed technique can improve the accuracy of damage identification with less than 2 percent error of estimation.     

Damage Detection of Regular Civil Buildings Using Modified Multi-Scale Symbolic Dynamic Entropy

Based on the examination of the fundamental characteristics of structures, structural health monitoring (SHM) has received increased attention in recent years. Studies have shown that the SHM method using entropy analysis can precisely identify the damaged location of the structure, which is very helpful for the daily inspection or maintenance of civil structures. Although entropy analysis has shown excellent accuracy, it still consumes too much time and too many resources in terms of data processing. To improve the dilemma, in this study, modified multi-scale symbolic dynamic entropy (MMSDE) is adopted to identify the damaged location of the civil structure. A damage index (DI) based on the entropy diagram is also proposed to clearly indicate the damage location. A seven-story numerical model was created to verify the efficiency of the proposed SHM system. The results of the analysis of each case of damage show that the MMSDE curve for the damaged floor is lower than that for the healthy floor, and the structural damage can be correctly diagnosed by the damage index. Subsequently, a scaled-down steel benchmark experiment, including 15 damage cases, was conducted to verify the practical performance of the SHM system. The confusion matrix was used to further evaluate the SHM system. The results demonstrated that the MMSD-based system can quickly diagnose structural safety with reliability and accuracy. It can be used in the field of long-term structural health monitoring in the near future.     

A note on perfect revivals in finite waveguide arrays

We propose a simple and algorithmic method for designing finite waveguide arrays capable of diffractionless transmission of arbitrary discrete beams by virtue of perfect revivals. Our approach utilises an inverse matrix eigenvalue theorem published by Hochstadt in 1974, which states that the Jacobi matrix, describing the system's discrete evolution equations, is uniquely determined by its eigenvalues and the eigenvalues of its largest leading principal submatrix, as long as the two sets of eigenvalues interlace. It is further shown that, by arranging the two sets of eigenvalues symmetrically with respect to zero, the resulting Jacobi matrix has zero diagonal elements. Therefore, arrays with arbitrary revival lengths can be obtained by engineering only the inter-waveguide couplings.