Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

Analysis of nonlinear steady state vibration of a multi-degree-of-freedom system using component mode synthesis method

In this paper, an analytical approach for nonlinear forced vibration of a multi-degree-of-freedom system is proposed using the component mode synthesis method. The whole system is divided into some components and a nonlinear modal equation of each component is derived using the free-interface vibration modes. The modal equations of all components and the conjunction conditions are solved simultaneously, and then the modal responses of components are derived. Finally, the dynamic responses of the whole system can be obtained. The degrees of freedom of modal equations can be reduced when the lower vibration modes are only adopted in each component. As a numerical example, a nine-degree-of-freedom system is considered, in which all spring have cubic type nonlinearity. As a result, it is shown that when there are no rigid modes in components, the compliance by the proposed method agrees very well with the exact one even if the lower vibration modes of components are only adopted. The other hand, in the case with rigid modes in components, the compliance has a little error compared with the exact result. It is recognized that the method proposed is very effective in the case without rigid modes in components for the actual application.     

Three methods for analyzing forced vibration of a fluid-filled cylindrical shell

The forced vibration of an infinite elastic circular cylindrical shell filled with fluid is studied. Three methods are employed to analyze the forced vibration problem of this shell-fluid coupled system, that is, wave propagation approach (wave mode superposition), theorem of residues and a numerical integral method. In order to explain these methods more explicitly, before being used to investigate the vibration of an infinite fluid-filled elastic circular cylindrical shell, all these three methods are employed firstly to analyze the forced vibration problem of an infinite beam and an infinite elastic circular cylindrical shell in vacuo. Advantage and disadvantage of these three methods are discussed and their interesting relationship is revealed. That is, to any circumferential wavenumber and frequency of the external force, there is an unchangeable relationship between the general coordinates of various waves in the wave propagation approach and the residuals in the theorem of residues.     

An improved cellular automaton model with the consideration of a multi-point tollbooth

Based on the classical Nagel–Schreckenberg model, we in this paper propose an improved cellular automaton (CA) model to study the influences of a multi-point tollbooth on traffic flow. The numerical results show that the multi-point tollbooth can be looked at as a bottleneck and that it can improve the road capacity compared with other tolling stations, which shows that the proposed model is more effective than other traffic flow models. In addition, the results can help readers to better understand the effects of a multi-point tollbooth on traffic flow and help traffic engineers to reasonably design the tolling station.     

The kink of cellular automaton rule 18 performs a random walk

We give an exact characterization of the movement of a single kink in the elementary cellular automaton Rule 18. It is a random walk with independent increments as well as independent delay times. Its statistical parameters are computed to confirm the earlier simulation results by Grassberger.     

基于元胞自动机方法的定向凝固枝晶竞争生长数值模拟

通过耦合温度场模型、溶质扩散方程以及枝晶生长动力学方程等重要因素,建立了一种改进的元胞自动机模型.该模型通过采用偏心算法消除网格各向异性,实现了二维尺度上任意角度枝晶生长的模拟,同时适用于模拟三维尺度上枝晶的生长过程.利用建立的模型开展了定向凝固枝晶竞争生长过程的数值模拟.为了体现本模型的有效性,模拟了透明合金的竞争生长过程,并与实验结果符合良好.镍基高温合金汇聚竞争和发散竞争的模拟结果清楚地展现了不同抽拉速度和枝晶优先生长角度下枝晶的竞争生长过程,并且模拟结果与理论模型相符合.三维枝晶生长的模拟结果表明本模型可以用来模拟三维枝晶一次臂间距的调整过程.     

Surface effect on the nonlinear forced vibration of cantilevered nanobeams

The nonlinear forced vibration behavior of a cantilevered nanobeam is investigated in this paper, essentially considering the effect due to the surface elastic layer. The governing equation of motion for the nano-cantilever is derived, with consideration of the geometrical nonlinearity and the effects of additional flexural rigidity and residual stress of the surface layer. Then, the nonlinear partial differential equation (PDE) is discretized into a set of nonlinear ordinary differential equations (ODEs) by means of the Galerkin’s technique. It is observed that surface effects on the natural frequency of the nanobeam is of significance, especially for the case when the aspect ratio of the nanobeam is large. The nonlinear resonant dynamics of the nanobeam system is evaluated by varying the excitation frequency around the fundamental resonance, showing that the nanobeam would display hardening-type behavior and hence the frequency-response curves bend to the right in the presence of positive residual surface stress. However, with the negative residual surface stress, this hardening-type behavior can be shifted to a softening-type one which becomes even more evident with increase of the aspect ratio parameter. It is also demonstrated that the combined effects of the residual stress and aspect ratio on the maximum amplitude of the nanobeam may be pronounced.     

金属基复合结构粘接强度的非线性超声混频检测

采用非线性超声混频方法对金属基复合结构的粘接强度进行表征研究。以不同固化剂含量的铝合金丙烯酸酯粘接结构作为检测对象,基于非线性超声混频的共振条件及其作用机制,并结合粘接固化机理,开展了非线性超声混频实验。非线性超声混频模式选取两列横波生成和频纵波的方式,实验测量并计算不同基频周期数下的超声非线性参量。通过拉伸实验标定粘接结构的粘接强度,并采用扫描电镜分析拉伸断面微观结构,进而分析超声非线性参量与粘接强度的关系。从实验结果可以看出在不同周期的基频信号激励下,超声非线性参量随着粘接强度的增大均呈现出减小的趋势。研究表明非线性超声混频信号对金属基复合结构粘接强度的变化比较敏感,可以适用于类似结构件粘接强度状态弱化的表征。     

Analysis of femtosecond optical pulse propagation in one-dimensional nonlinear photonic crystals using finite-difference time-domain method

In this paper, we have used the finite-difference time-domain (FDTD) method to analyze the optical pulse propagation in a nonlinear, one-dimensional photonic crystal (1DPC). Hyperbolic secant pulses with various carrier wavelengths are utilized in this study. In a nonlinear regime, a 1DPC introduces a photonic band-gap whose central wavelength and width depend on the input pulse intensity. In the present work, three different cases are considered. These correspond to the carrier wavelengths of the incident pulses being out of, near to, and partially in the band-gap. For each case, the effect of nonlinearity on pulse propagation is investigated. Also, we have analyzed the two-frequency regime, in which each of the two pulses has a different carrier frequency (wavelength). This kind of study can be done directly with FDTD without any further computational burden but it is somewhat complicated using nonlinear coupled-mode equations (NLCME) and nonlinear Schrödinger equation (NLSE), which require separate treatments for each carrier wavelength.     

Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method

In the present work, effect of von Kàrmàn geometric nonlinearity on the vibration behavior of a single-walled boron nitride nanotube (SWBNNT) is investigated based on nonlocal piezoelasticity theory. The SWBNNT is considered as a nanobeam within the framework of Timoshenko beam (TB). Loading is composed of a temperature change and an imposed axially electric potential throughout the SWBNNT. The interactions between the SWBNNT and its surrounding elastic medium are simulated by Winkler and Pasternak foundation models. The higher order governing equations of motion are derived using Hamilton's principle and the numerical solution of equations is obtained using Differential Quadrature (DQ) method. The effects of geometric nonlinearity, elastic foundation modulus, electric potential field, temperature change and nonlocal parameter on the frequency of the SWBNNT are studied in detail.     

On the low vibration modes observed in a sphere submitted to a tangential contact force

In this paper we discuss the existence of translational and rotational displacements of a sphere submitted to a tangential contact force. On the basis of the Bogdanov and Skvortsov’s works [A.N. Bogdanov, A.T. Skvortsov, Sov. Phys. Acoust. 38 (1992) 224–226.] the dispersion equation has been established and solved for any value of the frequency in the case of the linear approximation. The present experimental analysis confirms that it exists two branches: an upper branch associated to the translation of the sphere and a lower branch characteristic of the rotation of the bead.     

Vibration characteristic analysis of buried pipes using the wave propagation approach

A theoretical analysis for the free vibration of simply supported buried pipes has been investigated using the wave propagation approach. The pipe modeled as a thin cylindrical shell of linear homogeneous isotropic elastic material buried in a linear isotropic homogeneous elastic medium of infinite extent. The vibrations of the pipe are examined by using Flüggle shell equation. The natural frequencies are obtained for the pipes surrounded by vacuo or elastic medium. The results are compared with those available in the literature and agreement is found with them. It is found that the free vibration frequency of the pipe does not appear for some of the axial or circular vibration modes and the real natural frequencies of the pipe are significantly dependent on the rigidity of the surrounding medium.     

Experimental study of solitary waves in a nonlinear transmission line

Several properties of solitary waves were measured on a nonlinear transmission line. These include the transition from a linear dispersive response into a solitary wave response as the amplitude of a narrow voltage impulse is increased, and an observation of the recurrence phenomena of solitary waves. Supported in part by the National Science Foundation.     

2D photonic crystal complete band gap search using a cyclic cellular automaton refination

We present a refination method based on a cyclic cellular automaton (CCA) that simulates a crystallization-like process, aided with a heuristic evolutionary method called differential evolution (DE) used to perform an ordered search of full photonic band gaps (FPBGs) in a 2D photonic crystal (PC). The solution is proposed as a combinatorial optimization of the elements in a binary array. These elements represent the existence or absence of a dielectric material surrounded by air, thus representing a general geometry whose search space is defined by the number of elements in such array. A block-iterative frequency-domain method was used to compute the FPBGs on a PC, when present. DE has proved to be useful in combinatorial problems and we also present an implementation feature that takes advantage of the periodic nature of PCs to enhance the convergence of this algorithm. Finally, we used this methodology to find a PC structure with a 19% bandgap-to-midgap ratio without requiring previous information of suboptimal configurations and we made a statistical study of how it is affected by disorder in the borders of the structure compared with a previous work that uses a genetic algorithm.     

电磁驱动的固定弦振动的理论分析

对电磁驱动的弦线波动方程进行分析,得到了严格的理论解。很好地解释了实际中出现的几个现象,并且讨论了驻波振幅与磁场和讯号源的依赖关系。结果表明：驻波振劝的振幅与讯号源的电压或电流正比,与磁场的关系依赖于电磁阴尼和空气阻尼的相对大小。     

The local vibration modes due to impact on the edge of a viaduct

This paper describes the vibration responses of a cement viaduct model under impulsive force excitation. The frequencies and mode shapes of resonances can control magnitude of the structure-borne noise radiation. A steel hammer is used to excite the cement viaduct model at the centre and at the supporting edge position of the cross-section separately in order to acquire the vibration responses and mode shape data. From such data the global mode and local modes of the cement viaduct model are identified. It is shown that the edge of section supported by the web may have low impedance in the vertical direction. The results of analysis using a Finite Element Method confirmed the experimental findings of the cross-sectional modes of the cement viaduct model. The findings suggested that the vibrations of local modes are of two types: (1) Centre mode - the centre of top panel can move but the edge is fixed. (2) Edge (web) mode - the centre of panel is fixed but the edge (supported by web) can move.     

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.     

A cellular automaton model based on empirical observations of a driver’s oscillation behavior reproducing the findings from Kerner’s three-phase traffic theory

In this paper, we propose a new cellular automaton model based on the well known three-phase traffic theory. The model takes into account the mechanism of a driver’s oscillation behavior obtained from engineering experiments in real traffic conditions. This mechanism shows the inner competition between speed adaptation and distance adjustment effects. The speed adaptation effect leads to synchronized flow, whereas a pinch region emerges, associated with the spontaneous occurrence of wide moving jams, due to distance over-adjustment. Numerical simulations are carried out both with periodic and with open boundary conditions in order to investigate the spatiotemporal features of traffic flow. The results indicate that our model is able to reproduce the three distinct traffic phases and exhibit the four congested patterns upstream of an isolated on-ramp, which is in good consistency with the results predicted from the three-phase theory.