Simulation of the nonlinear vibration of a string using the cellular automation method

In this study, the nonlinear dynamic responses of a string were simulated using the cellular automaton (CA) method. The local rules were set for the amplitude of vibration and the decay rate of amplitude. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. Thus, a new treatment of the time step was proposed, i.e., the time step in the CA method is adjusted to real time by considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic were simulated and a typical resonance curve could be obtained. Secondly the dynamic responses of a string with nonlinear characteristic were simulated. Some characteristic types of vibration could be obtained. It was concluded that the linear and nonlinear dynamic responses of a string could be simulated using the CA method.     

The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis

A newly developed phase-unwrapping algorithm, which is termed Tapestry Cellular Automata, are presented. Fundamental restrictions of traditional path-dependent phase unwrapping algorithms such as noise propagation and inconsistent data reconstruction are discussed first. The advantages and drawbacks of a path-independent algorithm, Cellular Automata, are then examined. The parallel and distributed processing nature of Tapestry Cellular Automata is shown to be able to keep the merits of traditional Cellular Automata algorithm while taking advantage of the rapid advancement of personal computers such as distributed computing over internet or intranet and multi-tasks operating environment. Both numerical simulation and experiments used to examine the effectiveness of this newly developed algorithm are presented in detail as well.     

Analysis of energy dissipation in an elastic moving string with a viscous damper at one end

In this paper transverse vibration of an axially moving viscoelastic string with a viscous damper at one end is investigated analytically. The string is assumed to be travelling with constant velocity and the length of string is constant or time varying. The linear and nonlinear mathematical models are derived using the Lagrangian function and implemented using a finite element method. The method considers a time varying state space function applied to the linear model, the Newmark-Beta method is used to solve the response for the nonlinear problem numerically. The case of energy dissipated by a viscoelastic damper at one end of the string for different axial string velocities is considered. When a disturbance arrives at the boundary an exact value for the damper which provides maximum energy dissipation is investigated. Finally, numerical simulations are presented to establish the feasibility of the method.     

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

We investigate the acoustic wave propagation in bubbly liquid inside a pilot sonochemical reactor which aims to produce antibacterial medical textile fabrics by coating the textile with ZnO or CuO nanoparticles. Computational models on acoustic propagation are developed in order to aid the design procedures. The acoustic pressure wave propagation in the sonoreactor is simulated by solving the Helmholtz equation using a meshless numerical method. The paper implements both the state-of-the-art linear model and a nonlinear wave propagation model recently introduced by Louisnard (2012), and presents a novel iterative solution procedure for the nonlinear propagation model which can be implemented using any numerical method and/or programming tool. Comparative results regarding both the linear and the nonlinear wave propagation are shown. Effects of bubble size distribution and bubble volume fraction on the acoustic wave propagation are discussed in detail. The simulations demonstrate that the nonlinear model successfully captures the realistic spatial distribution of the cavitation zones and the associated acoustic pressure amplitudes.     

On the one-dimensional acoustic propagation in conical ducts with stationary mean flow

This paper proposes a direct time-domain calculation of the time-domain responses of anechoic conical tubes with steady weak mean flow. The starting point is the approximated linear one-dimensional wave equation governing the velocity potential for the case of steady flow with low Mach number. A traveling solution with general space-dependent propagation velocity is then proposed from which the inward and outward pressure and velocity impulse responses can be obtained. The results include the well-known responses of conical and cylindrical ducts with zero mean flow.     

次声波在非均匀运动大气中非线性传播特性的研究

基于有限时域差分方法将大气中近似到二阶的非线性波动方程进行离散化,得到了数值模拟所采用的差分方程. 在此基础上,对线阵列辐射的脉冲声波在非均匀运动大气中的垂直和斜向传播进行了二维数值模拟,模拟了武汉地区(114:20°E, 30:37°N)在夏季和冬季UT=29000 s时开始传播的脉冲声波在不同时刻的声压分布. 模拟时通过采用Msise00和HWM93 两个大气模型,考虑了由于大气温度和密度变化以及大气风场存在所引起的大气不均匀性和运动性. 通过研究上述两季有风与无风条件下的声压差值p_r,可以发现:风场对次声波在传播中声压分布的影响较大;由于不同季节和不同传播距离上"有效声速"的不同,导致了两季p_r分布波形存在差异;风场对声波非线性传播的影响要远大于其对线性传播的影响. 关键词： 次声波传播 非均匀运动大气 有效声速     

Infrared image enhancement using Cellular Automata

Image enhancement is a crucial technique for infrared images. The clear image details are important for improving the quality of infrared images in computer vision. In this paper, we propose a new enhancement method based on two priors via Cellular Automata. First, we directly learn the gradient distribution prior from the images via Cellular Automata. Second, considering the importance of image details, we propose a new gradient distribution error to encode the structure information via Cellular Automata. Finally, an iterative method is applied to remap the original image based on two priors, further improving the quality of enhanced image. Our method is simple in implementation, easy to understand, extensible to accommodate other vision tasks, and produces more accurate results. Experiments show that the proposed method performs better than other methods using qualitative and quantitative measures.     

圆孔非线性声阻抗三维时域仿真与特性分析

为研究有限振幅声波作用下圆孔的非线性声学特性,提出了基于三维时域计算流体动力学(CFD)仿真的圆孔非线性声阻抗提取方法,通过求解层流方程来模拟声信号在圆孔及上下游的传播,以及采用横向周期性边界条件来考虑高穿孔率时圆孔之间相互作用的影响。研究了不同幅值声波作用下孔径、厚度和穿孔率对声阻抗的影响规律,通过对质点振速幅值、频率和板厚等组成的无量纲参量进行非线性回归分析,得到了圆孔非线性声阻抗的拟合公式,并将其转换为可考虑多频声波影响的时域模型。最后结合声阻抗时域模型和有限差分方法计算了直通穿孔管消声器在小振幅和有限振幅声波作用下的传递损失,通过与实验测量结果的比较,验证了拟合公式的准确性和实用性。     

用细胞自动机方法构造非平衡相变模型

阐述了一旦给定细胞自动机方法的法则,将如何构造实际问题的物理学模型的方法。并用此法构造出非平衡相变模型。同时对类平均场近似方法进行了讨论,并将其预言与非平衡相变模型的精确的数值结果进行了比较。 关键词：     

A derating method for therapeutic applications of high intensity focused ultrasound

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. A new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal wave-forms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue.     

On the Evolution Equations of Nonlinearly Permissible,Coherent Hole Structures Propagating Persistently in Collisionless Plasmas

A fundamental study describing nonlinear plasma wave propagation is presented. Elementary linear wave theory describes small-amplitude random waves, but lacks information about coherent structures. This improved wave model arises from the fact that structure formation is inevitably associated with particle trapping, which can only be properly addressed by the pseudo-potential method instead of Bernstein, Greene, and Kruskal (BGK) - likemethods. Only by using this method can legitimate nonlinear dispersion relations be obtained and reconciled with trapping scenarios. This privilege is used to derive evolution equations for five structures, the derivation being simplified by the acoustic nature of the permitted modes. The focus is on a special structure, the solitary electron hole of negative polarity, with which it can explain a spacecraft observation for the first time. Furthermore, it is shown that an intrinsically nonlinear structure can become macroscopically linear and thus harmonic by suitably adjusting the trapping scenario. An example is the monochromatic ion acoustic wave that propagates at ion sound velocity without dispersion. In this literature research, it also takes a critical look at a recently awarded work.     

Prediction condensed models adapted to the nonlinear structures in time domain

This paper deals with a method to study closely the stationary solution of nonlinear dynamic systems in time domain. This method is based on the exploitation of Karhunen-Loève decomposition with or without parametric modifications as well as on the characteristics of localized nonlinearities. With the application of this method at first on linear models initially condensed by Karhunen-Loève, the predictions of nonlinear responses can be obtained rapidly. This method is adapted to a condensed linear model used in the first optimization procedure of the nonlinear dynamic behaviour. This robust basis will be used as condensation basis of the modified model local per zone, which leads to a prediction of vibratory responses of complex structures modified and affected by localized nonlinearities.     

基于法布里-珀罗腔反射光相位特性设计的梳状滤波器

提出了一种用于设计密集波分复用全光网络中梳状滤波器的方法，该器件利用法布里-珀罗腔反射光相位的非线性性质，结合光的相位在一定光程差下随频率呈线性周期变化的特点，通过使这样两束相位匹配的光发生干涉，得到所需滤波特性。运用江膜特征矩阵对模型进行了模拟计算，并分析了计算结果，论证了这种结构的可行性。     

Robust Multiplexer Design and Analysis Using Quantum Dot Cellular Automata

Quantum Dot Cellular Automata (QCA) is an alternate version of the existing conventional CMOS technology due to its low power intake, faster speed, and smaller size. A multiplexer is a very important logical block in VLSI designs. In this paper, a 2:1 multiplexer (MUX) architecture is proposed, analyzed and compared with related existing architectures. The kink energy of proposed circuit has been calculated and hazard analysis has been completed successfully. All designs in this paper are simulated, checked, and verified using the popular QCADesigner tool. The comparisons of the proposed design with respect to different parameters of the existing MUX(s) along with their corresponding graphical representations prove the robustness of the proposed multiplexer.

     

A novel cellular automata based technique for visual multimedia content encryption

This paper proposes a new method for visual multimedia content encryption using Cellular Automata (CA). The encryption scheme is based on the application of an attribute of the CLF XOR filter, according to which the original content of a cellular neighborhood can be reconstructed following a predetermined number of repeated applications of the filter.The encryption is achieved using a key image of the same dimensions as the image being encrypted. This technique is accompanied by the one-time pad (OTP) encryption method, rendering the proposed method reasonably powerful, given the very large number of resultant potential security keys. The method presented here makes encryption possible in cases where there is more than one image with the use of just one key image. A further significant characteristic of the proposed method is that it demonstrates how techniques from the field of image retrieval can be used in the field of image encryption. The proposed method is further strengthened by the fact that the resulting encrypted image for a given key image is different each time. The encryption result depends on the structure of an artificial image produced by the superposition of four 1-D CA time-space diagrams as well as from a CA random number generator.A semi-blind source separation algorithm is used to decrypt the encrypted image. The result of the decryption is a lossless representation of the encrypted image. Simulation results demonstrate the effectiveness of the proposed encryption method. The proposed method is implemented in C# and is available online through the img(Rummager) application.     

Ultrasonic waves in crystals with charged dislocations

A system of equations for charged dislocations, where the quadratic nonlinear terms are taken into account, is derived using the variational principle. This system describes the propagation of ultrasonic (US) waves in crystals with charged dislocations. From the linearized system of equations a linear dispersion equation is derived. Formulas for the phase linear velocity of the wave and the absorption coefficient are obtained, which show essential influence of charged dislocations and electrical properties of media on the mentioned quantities. For a nonlinear US wave an equation for the amplitude of the first harmonic is derived and, as a consequence, expressions are obtained for the nonlinear velocity of the US wave, for the attenuation of the first harmonic's amplitude, and for phase variation.     

Geometrical interpretation of acoustic holography: Adaptation of the propagator and minimum quality guaranteed in the presence of errors

A large number of inverse problems in acoustics consist of a reverse propagation of the acoustic pressure measured with an array of microphones. The goal is usually to identify the acoustic source location and strength or the surface velocity of a vibrating structure. The quality of the results obtained depends on the propagation model, on the accuracy of the pressure measurements and, finally, on the inverse problem conditioning. How to quantify this quality is the issue addressed in this paper. For this purpose, a geometrical interpretation of the inverse acoustic problem is proposed. The main application will, eventually, be near-field acoustic holography (NAH), but it is expected that the proposed approach will also apply to other types of inverse acoustic problems. First, the geometrical representation of the inverse problem is proposed. The inverse problem is stated from a direct linear problem in the frequency domain. For each frequency, an overdetermined system of linear complex algebraic equations must be inverted. The concept of quality is discussed and a quality index is proposed based upon the residue of the inverse problem, solved in a mean square sense. Then, a simple one-dimensional (plane wave) acoustic example consisting of a source and two pressure measurements is used to illustrate the proposed geometrical representation of the inverse problem and the quality criterion inspired by it. In the simple example, the propagation model can be improved by searching for a reflection coefficient at the origin of the simulated hologram. This reflection coefficient is used to simulate the presence of a hidden source placed behind the source. An artificial attenuation is introduced to simulate the effect of geometrical attenuation present in real NAH problems. Again, using the geometrical representation, it is shown how, from an improved propagation model together with a given measurement noise level in the hologram, one can guarantee a certain quality level of the inverse procedure. Finally, numerical results show, in a preliminary way, how the identified source strength converges towards the exact velocity when the estimated propagation model tends to the exact propagation model.     

On variable length induced vibrations of a vertical string

The purpose of this paper is to study the free lateral responses of vertically translating media with variable length, velocity and tension, subject to general initial conditions. The translating media are modeled as taut strings with fixed boundaries. The problem can be used as a simple model to describe the lateral vibrations of an elevator cable, for which the length changes linearly in time, or for which the length changes harmonically about a constant mean length. In this paper an initial-boundary value problem for a linear, axially moving string equation is formulated. In the given model a rigid body is attached to the lower end of the string, and the suspension of this rigid body against the guide rails is assumed to be rigid. For linearly length variations it is assumed that the axial velocity of the string is small compared to nominal wave velocity and the string mass is small compared to car mass, and for the harmonically length variations small oscillation amplitudes are assumed and it is also assumed that the string mass is small compared to the total mass of the string and the car. A multiple-timescales perturbation method is used to construct formal asymptotic approximations of the solutions to show the complicated dynamical behavior of the string. For the linearly varying length analytic approximations of the exact solution are compared with numerical solution. For the harmonically varying length it will be shown that Galerkin?s truncation method cannot be applied in all cases to obtain approximations valid on long timescales.     

Damage identification in plates using finite element model updating in time domain

A response sensitivity-based approach is presented for identifying the local damages in isotropic plate structures from the measured structural dynamic responses. The local damage is simulated by a reduction in the elemental Young's modulus of the plate. In the forward analysis, the forced vibration responses of the plate under external force are obtained from Newmark direct integration. In the inverse analysis, a response sensitivity-based finite element model updating approach is used to identify local damages of the plate in time domain. The damage identification results are obtained iteratively with the penalty function method with Tikhonov regularization using the measured structural dynamic responses. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Both single damage and multiple damages cases are studied. The effects of measurement noise and measurement point on the identification results are investigated. Studies in this paper indicate that the proposed method is efficient and robust for both single and multiple damages for plate structures. Good identified results can be obtained from the short time histories of a few number of measurement points.     

On the orthogonalised reverse path method for nonlinear system identification

The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673–708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach – the orthogonalised reverse path (ORP) method – is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.