Experimental verification of Foreman dislocation model

We present a strain analysis of an edge dislocation core, and a detailed discussion of the Foreman dislocation model. In order to examine the model, the quantitative measurement of strain field around an edge dislocation in aluminum is performed, and high-resolution transmission electron microscopy and geometric phase analysis are employed to map the strain field of the edge dislocation core in aluminum. The strain measurements are compared with the Foreman dislocation model, showing that they are in good agreement with each other when 0.7 ≤ a ≤ 1.5.     

Dynamic response of an insonified sonar window interacting with a Tonpilz transducer array

This paper derives and evaluates an analytical model of an insonified sonar window in contact with an array of Tonpilz transducers operating in receive mode. The window is fully elastic so that all wave components are present in the analysis. The output of the model is a transfer function of a transducer element output voltage divided by input pressure versus arrival angle and frequency. This model is intended for analysis of sonar systems that are to be built or modified for broadband processing. The model is validated at low frequency with a comparison to a previously derived thin plate model. Once this is done, an example problem is studied so that the effects of higher order wave interaction with acoustic reception can be understood. It was found that these higher order waves cause multiple nulls in the region where the array detects acoustic energy and that their locations in the arrival angle-frequency plane can be determined. The effects of these nulls in the beam patterns of the array are demonstrated.     

Data assimilation and numerical forecasting with imperfect models: The mapping paradigm

Errors in numerical forecasts arise due to errors in the initial conditions and the discrepancies between the model and nature (and may amplify due to chaos). In a quest to reduce forecast errors, initial conditions for forecast integrations are traditionally chosen to be as close to nature as possible. When such an initial condition (analysis) is used to initialize an imperfect model that is systematically different from nature, the model will drift from a state on or near the attractor of nature to a state near the model’s attractor. Such a drift will induce forecast errors.

To reduce drift-induced errors, a mapping paradigm is proposed where a link (i.e., mapping vector) is established between states of nature and corresponding states on (or near) the model attractor. Observations from near the attractor of nature are moved with the mapping vector to the vicinity of the model attractor. Data assimilation is performed with the mapped observations and the mapped initial conditions are then used to initialize model forecasts to be used in the next assimilation cycle. For practical applications, the mapped initial conditions as well as the forecasts are “remapped” back to be close to nature using the mapping vector with an opposite sign.

The mapping paradigm is demonstrated in a setting where a simple Lorenz model is used to generate “nature” and a modified version is used as an imperfect model. The mapping vector is first estimated as the difference between the climate mean of nature and the model. Model related errors in the Lorenz system with the mapping algorithm are reduced by 67%, leading to improvements in the quality of both the numerical forecasts made with the imperfect model and the analyses produced with the forecasts. Considering that the mapping vector may be a function of phase space location or no long-term climatology for nature or the model may be available, an adaptive approach that can be used with a relatively small amount of data was also introduced and successfully tested.     

PREDICTION OF DYNAMIC CHARACTERISTICS USING UPDATED FINITE ELEMENT MODELS

Model updating techniques are used to update a finite element model of a structure so that an updated model predicts the dynamics of a structure more accurately. The application of such an updated model in dynamic design demands that it also predict the effects of structural modifications with a reasonable accuracy. This paper deals with updating of a finite element model of a structure and its subsequent use for predicting the effects of structural modifications. Updated models have been obtained by a direct model updating method and by an iterative method of model updating based on the frequency response function (FRF) data. The suitability of updated models for predicting the effect of structural modifications is evaluated by some computer and laboratory experiments. First a study is performed using a simulated fixed-fixed beam. Cases of complete, incomplete and noisy data are considered. Updated models are obtained by the direct and the FRF-based method in each of these cases. These models are then used for predicting the changes in the dynamic characteristics brought about due to a mass and a beam modification. The simulated study is followed by a study involving actual measured data for the case of an F-shape test structure. The updated finite element models for this structure are obtained again by the direct and the FRF-based method. Structural modifications in terms of mass and beam modifications are then introduced to evaluate the updated model for its usefulness in dynamic design. It is found that the predictions based on the iterative method based updated model are reasonably accurate and, therefore, this updated model can be used with reasonable accuracy to perform dynamic design. The predictions on the basis of the direct method based updated model are found to be reasonably accurate in the lower portion of the updating frequency range but the predictions are in a significant error in the remaining portion of the updating frequency range. It is concluded that the updated models that are closer to the structure physically are likely to perform better in predicting the effects of structural modification.     

An experimental study of acoustoelectric transducers with nonuniform distribution of the piezoelectric coefficient

In this paper, an experimental test of a theoretical model published previously is presented that describes the behavior of an acoustoelectric transducer with a nonuniform distribution of the piezoelectric coefficient within its bulk. Results of this theoretical model are first reviewed. Uniform and nonuniform piezoelectric transducers were fabricated, following a procedure described herein. The receive transfer functions of the transducers were recorded experimentally, and a comparison is made with the theoretical transfer functions predicted by the model, which shows good agreement. The transmit transfer functions of the uniform and nonuniform transducers were also measured and are reported. Numerical calculations of the different transfer functions given by the theoretical model for a uniform transducer associated with different backing materials are also presented, and the results are shown to be equivalent to the results following from the Mason equivalent circuit. Comparisons with experimental results and with Mason's equivalent circuit verified the new theoretical model.     

An ensemble source spectra model for merchant ship-radiated noise

This paper presents an evaluation of the classical model for determining an ensemble of the broadband source spectra of the sound generated by individual ships and proposes an alternate model to overcome the deficiencies in the classical model. The classical model, proposed by Ross [Mechanics of Underwater Noise (Pergamon, New York, 1976)] postulates that the source spectrum for an individual ship is proportional to a baseline spectrum with the constant of proportionality determined by a power-law relationship on the ship speed and length. The model evaluation, conducted on an ensemble of 54 source spectra over a 30-1200-Hz to 1200-Hz frequency band, shows that this assumption yields large rms errors in the broadband source level for the individual ships and significantly overestimates the variability in the source level across the ensemble of source spectra. These deficiencies are a consequence of the negligible correlation between the source level and the ship speed and the source level and the ship length. The alternate model proposed here represents the individual ship spectra by a modified rational spectrum where the poles and zeros are restricted to the real axis and the exponents of the terms are not restricted to integer values. An evaluation of this model on the source spectra ensemble indicates that the rms errors are significantly less than those obtained with any model where the frequency dependence is represented by a single baseline spectrum. Furthermore, at high frequencies (400 to 1200 Hz), a single-term rational spectrum model is sufficient to describe the frequency dependence and, at the low frequencies (30 to 400 Hz), there is only a modest reduction in the rms error for a higher order model. Finally, a joint probability density on the two parameters of the single term model based on the measured histograms of these parameters is proposed. This probability density provides a mechanism for generating an ensemble of ship spectra.     

基于小关联时间两相湍流色噪声的近似模型及数值模拟

从一般高斯型色噪声模型出发,通过泛函导数,应用小关联时间,近似计算多维色噪声,得到有效Fokker-Planck方程.将其应用到两相湍流中得到颗粒相的概率密度函数输运方程,从而得到颗粒相的二阶矩模型.将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,并将求解结果与实验结果进行对比分析.     

Substructure methods for structural condition assessment

It is commonly known that an accurate analysis of a large structure requires an accurate analytical model. This is also true for the inverse analysis of a structural system where measured structural responses are used as input to assess the structural conditions. However, an accurate model of the structure is always not available in practice. Two substructural identification methods are presented in this paper with the structure divided into substructures and with one substructure assessed at one time. In the first method, an accurate finite element model of the whole structure is assumed known. A state space method is applied to identify the external forces acting on the structure, and a damage identification method is then applied to identify the local damages using time domain information. Iterative model updating method based on the measured acceleration in the selected substructure is employed for the assessment. The second identification method requires only the finite element model of the substructure. The interface forces and the external forces acting on the target substructure are all taken as excitations and they are identified in state space. The substructure is then assessed similar to the first method. Since the target substructure for updating consists of a much reduced number of components and the identification problem is more efficient. The validation of the proposed methods is demonstrated by a truss structure with polluted measured accelerations with promising results.     

Nonequilibrium model for the contact process in an ensemble of constant particle number.

We introduce and analyze numerically a nonequilibrium model with a conserved dynamics which is a realization of the contact process in an ensemble of constant particle number. The model possesses just one process in which particles jump around landing only on empty sites next to an existing particle. Particles are not allowed to land on a vacant site surrounded by empty sites. In contrast with the ordinary contact process, the present model does not have an absorbing state. In spite of lacking an absorbing state, the model displays properties that, in the thermodynamic limit, are identical to those of the ordinary contact process.     

Algebraic Description of Anharmonic Stretching Vibrations

A U(2) algebraic model is presented to describe stretching vibrations of XYn (n = 2, 3, and 4) systems, where anharmonic interactions between the bond modes are considered. This model in a limit corresponds to an anharmonically coupled local-mode model. As an example, the model for a molecule XY4 is applied to recently observed spectra of methane in both gas and liquid phases, and the results obtained are in good agreement with the experiments. Copyright 1999 Academic Press.     

An Efficient Three-Dimensional Coupled Normal Mode Model and Its Application to Internal Solitary Wave Problems

We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.     

The fictitious force method for efficient calculation of vibration from a tunnel embedded in a multi-layered half-space

This paper presents an extension of the Pipe-in-Pipe (PiP) model for calculating vibrations from underground railways that allows for the incorporation of a multi-layered half-space geometry. The model is based on the assumption that the tunnel displacement is not influenced by the existence of a free surface or ground layers. The displacement at the tunnel–soil interface is calculated using a model of a tunnel embedded in a full space with soil properties corresponding to the soil in contact with the tunnel. Next, a full space model is used to determine the equivalent loads that produce the same displacements at the tunnel–soil interface. The soil displacements are calculated by multiplying these equivalent loads by Green?s functions for a layered half-space. The results and the computation time of the proposed model are compared with those of an alternative coupled finite element–boundary element model that accounts for a tunnel embedded in a multi-layered half-space. While the overall response of the multi-layered half-space is well predicted, spatial shifts in the interference patterns are observed that result from the superposition of direct waves and waves reflected on the free surface and layer interfaces. The proposed model is much faster and can be run on a personal computer with much less use of memory. Therefore, it is a promising design tool to predict vibration from underground tunnels and to assess the performance of vibration countermeasures in an early design stage.     

A complex of analytical models for predicting noise in an aircraft cabin

A series of analytical calculated models for predicting the noise in an aircraft cabin is developed: an orthotropic model, a model with discrete frames, a model with discrete stringers, a model with isolated cells, and a model with a cross system of discrete ribs. The analytical solution is constructed on the basis of the method of space harmonic expansion. Vibrations are represented in the form of double trigonometric series. Strict periodicity allows dividing the series into a large number of independent groups, which makes it possible to effectively perform calculations for large fragments of the fuselage in the entire frequency region both for deterministic and random external force fields.     

气泡成核过程的格子Boltzmann方法模拟

利用精确差分格子Boltzmann模型探讨水在特定温度下的亚稳态及不稳定平衡态, 获得等温相变过程中形成气泡和液滴的条件, 模型预测结果与理论解符合良好. 在该等温模型的基础上耦合能量方程, 通过调节流体-壁面相互作用力获得不同的气泡与固壁间接触角, 从而建立了一种新的描述气液相变的格子Boltzmann理论模型. 利用该新模型模拟不同流体-壁面相互作用力下凹坑气泡成核过程, 再现了气泡成核过程中的三阶段特性; 探讨了接触角、曲率半径及气泡体积随气泡成核过程的变化关系, 获得了与文献结果定性符合的曲率-气泡体积关系曲线. 关键词： 格子Boltzmann方法 气泡成核过程 气液相变 接触角     

Dynamic modeling and simulation of a real world billiard

Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic billiard for arbitrary boundaries. Simulations of the model are applied to parabolic, wedge and hyperbolic billiards that are driven sinusoidally. Direct comparisons are made between the model?s predictions and previously published experimental data. It is shown that the data can be successfully modeled with a simple set of parameters without an assumption of exotic energy dependence.     

Collisional radiative model of helium including response to resonant radiation

A collisional-radiative model of helium has been developed that incorporates the effect of optical pumping with light that is resonant with an atomic transition. A steady-state solution of the collisional- radiative model with no pumping is used as an initial condition. The pumping radiation is switched on, and the population densities of the atomic levels are calculated as a function of time. Results are given for a wide range of plasma parameters and various pumping conditions.     

Conditional velocity statistics in the double scalar mixing layer – A mapping closure approach

In this work we use 3D direct numerical simulations (DNS) to investigate the average velocity conditioned on a conserved scalar in a double scalar mixing layer (DSML). The DSML is a canonical multistream flow designed as a model problem for the extensively studied piloted diffusion flames. The conditional mean velocity appears as an unclosed term in advanced Eulerian models of turbulent non-premixed combustion, like the conditional moment closure and transported probability density function (PDF) methods. Here it accounts for inhomogeneous effects that have been found significant in flames with relatively low Damköhler numbers. Today there are only a few simple models available for the conditional mean velocity and these are discussed with reference to the DNS results. We find that both the linear model of Kutznetzov and the Li and Bilger model are unsuitable for multi stream flows, whereas the gradient diffusion model of Pope shows very close agreement with DNS over the whole range of the DSML. The gradient diffusion model relies on a model for the conserved scalar PDF and here we have used a presumed mapping function PDF, that is known to give an excellent representation of the DNS. A new model for the conditional mean velocity is suggested by arguing that the Gaussian reference field represents the velocity field, a statement that is evidenced by a near perfect agreement with DNS. The model still suffers from an inconsistency with the unconditional flux of conserved scalar variance, though, and a strategy for developing fully consistent models is suggested.     

Optimal design of PZT actuators in active structural acoustic control of a cylindrical shell with a floor partition

Genetic algorithms (GAs) are employed to optimize locations of PZT actuators in an active structural acoustic control (ASAC) system comprising a cylindrical shell with an internal floor partition. The effect of PZT actuators is simulated using a bending model and an in-plane force model, respectively. The characteristics of the optimal placements of both models are discussed and compared. Numerical simulations demonstrate that for the investigated structure, the in-plane force model has a better control performance than the bending model in the low-frequency range. The underlying physics of the control results are analyzed. Considering the practical applicability of optimally designed ASAC systems, the control performance of the optimal configuration obtained at a single frequency is assessed in the low-frequency range between 100 and 500 Hz, with results showing a significant sound attenuation in the whole range of interest.     

Sound propagation between two adjacent rectangular workstations in an open-plan office—part I: mathematical modeling

This paper describes the development of a mathematical model of sound propagation between adjacent workstations in an open-plan office. The model is valid for adjacent rectangular workstations consisting of small enclosures made up of partial-height screens or panels. The new model adds the effects of side and back panels to the primary effect of the common separating screen that was considered in a previous model. In both models, reflections are included using an image source technique and expressions are developed to identify those image sources that represent actual reflection paths. The orientation of openings into the workstations is also considered. Comparisons with measured attenuations of sound propagation between adjacent workstations are included. They verify that the model can quite accurately predict the expected speech privacy between workstations in an open-plan office.     

TRANSVERSE VIBRATION OF ELASTIC-VISCOELASTIC-ELASTIC SANDWICH BEAMS: COMPRESSION-EXPERIMENTAL AND ANALYTICAL STUDY

Experimental and analytical results are presented from an investigation into the compressional vibration of an elastic-viscoelastic-elastic three-layer sandwich beam. Most analytical models make the fundamental assumption that shear deformation in the viscoelastic core yields the largest damping and compressional deformation is negligible. Experimental results from a cantilever beam with a constrained layer viscoelastic damping treatment driven with a sinusoidal input are given which show compressional deformation over a relatively wide driving frequency range. A new analytical model for compressional damping is presented and compared with experimental results, with the Mead and Markus shear damping model, and with the Douglas and Yang compressional damping model. These results indicate that the proposed compressional model is a better predictor of resonance frequencies for the cantilever beams tested and that all models show deficiencies in predicting damping