Time-domain simulation of damped impacted plates. I. Theory and experiments

A time-domain formulation for the flexural vibrations in damped rectangular isotropic and orthotropic plates is developed, in order to investigate transient excitation of plates by means of sound synthesis. The model includes three basic mechanisms of damping (thermoelasticity, viscoelasticity and radiation) using a general differential operator. The four rigidity factors of the plate are modified by perturbation terms, each term corresponding to one specific damping mechanism. The first damping term is derived from the coupling between the thermoelastic stress-strain relations and the heat diffusion equation. The second term is obtained from the general differential formulation of viscoelasticity. The third term is obtained through a Pade approximation of the damping factor which governs the coupling of the plate with the surrounding air. The decay factors predicted by the model reproduce adequately the dependence on both dimensions and frequency of the decay factors measured on rectangular plates of various sizes and thicknesses made of four different materials (aluminum, glass, carbon fiber, and wood). The numerical resolution of the complete problem, including initial and boundary conditions, and the comparison between real and simulated sounds are presented in a companion paper.     

复杂结构冲击声合成及实验验证

以复杂结构受击振动响应的时域计算为目的, 讨论了结构阻尼的计算方法, 给出一种用于冲击声合成的综合数值方法, 并进行了实验验证. 首先, 考虑到阻尼是影响瞬态振动时变特性的重要因素, 详细讨论了两种模态阻尼的计算方法; 其次, 对阻尼板的受击振动和声辐射进行了时域仿真, 并与时域有限差分法的计算结果进行对比, 显示出两种声音合成方法的计算结果具有高度的一致性; 最后, 针对有限长圆柱壳的受击振动, 将合成声与实验录音进行了对比研究. 结果表明, 合成声与实际录音的时域包络、频谱结构以及衰减趋势基本一致, 证明了采用数值方法进行冲击声合成的有效性. 关键词： 声音合成 模态阻尼 冲击声 数值方法     

Acoustical wave propagator for time-domain flexural waves in thin plates

In this paper, an explicit acoustical wave propagator technique is introduced to describe the time-domain evolution of acoustical waves in two-dimensional plates. A combined scheme with Chebyshev polynomial expansion and fast Fourier transformation is used to implement the operation of the acoustical wave propagator. Through this operation, the initial wave packet at t = 0 is mapped into the wave packet at any instant t > 0. By comparison of the results of the exact analytical solution and the Euler numerical method, we find that this new Chebyshev-Fourier scheme is highly accurate and computationally effective in predicting the acoustical wave propagation in thin plates. This method offers an opportunity for future study of dynamic stress concentration and time-domain energy flow in coupled structures.     

Prediction method for sound from passing vehicle transmitted through building façade

This study proposes a prediction method for assessing the sound of a passing vehicle that is transmitted through a glass plate, which employs the vibro-acoustic finite-difference time-domain (FDTD) method. The noise that is transmitted through the glass in a building façade, which is affected by the sound-insulation characteristics of its glass plates, can have a psychological influence such as a sleep disorder on the residents. In this study, a prediction method for the spectral characteristics of the transmitting sound through glass plates is proposed. The sound-insulation characteristics of glass plates are obtained using a vibro-acoustic FDTD method, and are then synthesized with the sound of passing vehicles obtained by in situ measurement. Firstly, the sound transmitted through several kinds of glass plates is simulated using the proposed method. Then, in order to confirm the validity of this method, the simulated results are compared to measured sounds transmitted by passing vehicles into a room near the street.     

阻尼受击板的时域建模及声音合成

为满足声源辨识中对合成冲击声的迫切需求,建立了球-板撞击的时域模型,提出一种时域快速求解方法,并进行了实验验证.首先给出一种将时域有限差分法(FDTD)和模态展开法(MEM)相结合的时域混合方法,求解板的振动方程,并解决了混合方法中MEM的模态截断和初值问题,及两种方法中阻尼的一致性问题;随后,给出了简支矩形板的冲击声计算结果,通过与FDTD方法的运算量进行对比,验证了混合方法的高效性;最后,针对自由边界下的L形板进行了实验验证.结果表明,与传统FDTD方法相比,时域混合方法在保证合成冲击声精度的前提下可将计算效率提高100至1200倍。      

A finite element model for sandwich viscoelastic beams: Experimental and numerical assessment

Among the passive control systems for attenuation of vibrations in structures, those that use viscoelastic materials as a damping core in laminated-plate-like components are focused herein. In the present work an assessment of a time-domain formulation for numerical modelling of viscoelastic materials is made. This formulation, which is called Golla–Hughes method (GHM), is based on a second-order time-domain realization of Laplace-domain motion equations. The GHM parameters used in the characterization of a viscoelastic material are experimentally determined and a sandwich GHM-based finite element model is presented and validated through numerical comparisons with classic formulation results. Finally, a time-domain simulation of an experimentally tested sandwich beam is carried out.     

Time-Domain Numerical Solutions of Maxwell Interface Problems with Discontinuous Electromagnetic Waves

This paper is devoted to time domain numerical solutions of two-dimensional (2D) material interface problems governed by the transverse magnetic (TM) and transverse electric (TE) Maxwell's equations with discontinuous electromagnetic solutions. Due to the discontinuity in wave solutions across the interface, the usual numerical methods will converge slowly or even fail to converge. This calls for the development of advanced interface treatments for popular Maxwell solvers. We will investigate such interface treatments by considering two typical Maxwell solvers – one based on collocation formulation and the other based on Galerkin formulation. To restore the accuracy reduction of the collocation finite-difference time-domain (FDTD) algorithm near an interface, the physical jump conditions relating discontinuous wave solutions on both sides of the interface must be rigorously enforced. For this purpose, a novel matched interface and boundary (MIB) scheme is proposed in this work, in which new jump conditions are derived so that the discontinuous and staggered features of electric and magnetic field components can be accommodated. The resulting MIB time-domain (MIBTD) scheme satisfies the jump conditions locally and suppresses the staircase approximation errors completely over the Yee lattices. In the discontinuous Galerkin time-domain (DGTD) algorithm – a popular Galerkin Maxwell solver, a proper numerical flux can be designed to accurately capture the jumps in the electromagnetic waves across the interface and automatically preserves the discontinuity in the explicit time integration. The DGTD solution to Maxwell interface problems is explored in this work, by considering a nodal based high order discontinuous Galerkin method. In benchmark TM and TE tests with analytical solutions, both MIBTD and DGTD schemes achieve the second order of accuracy in solving circular interfaces. In comparison, the numerical convergence of the MIBTD method is slightly more uniform, while the DGTD method is more flexible and robust.     

Subjective evaluations of sound radiated by impacted plates, using the design of experiments method

This study combines physical and subjective approaches to evaluate the sound quality of impacted plates. A numerical model, based on the Hertz law of contact, has been used to determine the sound pressure level at any point in space resulting from an impact. Sounds synthesized using this model and those from experiments can then be exploited in a physical analysis and/or a subjective analysis of the effects associated with variations in parameters. Here the influence of certain physical parameters on the sound perception of impacted plates is evaluated through a design of experiments method and a subjective test of preference. The subjective test is based on an estimate of preference between two pairs of synthetic sounds by varying several structural parameters at the same time. This differs from other studies that vary only one parameter at a time and fix the other parameters.     

On the quality of plate reverberation

Metallic plates are used in recording studios to create artificial reverberation. In this paper, the flexural vibrations of such plates are analysed in order to better understand the influence of geometry and materials on the quality of plate reverberation. A comparison is made with acoustic reverberation, both in the time and frequency domain. This comparison is supported by objective criteria such as modal density and density of reflections. From a physical point of view, the internal and external damping mechanisms are examined in detail since they determine the frequency dependence of the reverberation time. Theoretical results are validated through comparison with experiments performed on an EMT140 reverberation plate. The underlying model is aimed at developing numerical simulations of plates (virtual reverberators) allowing a large variety of reverberations based on variations of geometry and materials as input parameters.     

FDTD Analysis of Magnetized Plasma with Arbitrary Magnetic Declination

In this paper, the frequency-dependent finite-difference time-domain (FDTD) method employing the piecewise linear recursive convolution (PLRC) scheme is applied to the numerical analysis of magnetized plasma with arbitrary magnetic declination. The PLRC-FDTD equations are derived in detail and are checked through practical examples. Excellent agreement between the numerical results and the exact analytical solutions is demonstrated.     

Time-domain prediction of impact noise from wheel flats based on measured profiles

Railway impact noise is caused by discrete rail or wheel irregularities, such as wheel flats, rail joints, switches and crossings. In order to investigate impact noise generation, a time-domain wheel/rail interaction model is needed to take account of nonlinearities in the contact zone. A nonlinear Hertzian contact spring is commonly used for wheel/rail interaction modelling but this is not sufficient to take account of actual surface defects which may include large geometry variations. A time-domain wheel/rail interaction model with a more detailed numerical non-Hertzian contact is developed here and used with surface roughness profiles from field measurements of a test wheel with a flat. The impact vibration response and noise due to the wheel flat are predicted using the numerical model and found to be in good agreement with the measurements. Moreover, compared with the Hertzian theory, a large improvement is found at high frequencies when using the detailed contact model.     

高阶辛算法的稳定性与数值色散性分析

利用Maxwell方程的哈密尔顿函数,导出对应的欧拉-哈密尔顿方程.利用辛积分技术与高阶交错差分技术,建立求解三维时域Maxwell方程的高阶辛算法;结合电磁场中的物理概念,借助矩阵分析和张量分析理论,获得高阶时域方法及高阶辛算法的稳定性和数值色散性的统一处理新方法.用数值结果证实方法的正确性,与FDTD算法和其它时域高阶方法相比,高阶辛算法具有较大的计算优势,为电磁计算提供了新的途径.     

Recent advances on a DGTD method for time-domain electromagnetics

During the last ten years, the discontinuous Galerkin time-domain (DGTD) method has progressively emerged as a viable alternative to well established finite-difference time-domain (FDTD) and finite-element time-domain (FETD) methods for the numerical simulation of electromagnetic wave propagation problems in the time-domain. In this paper, we review the historical development of the DGTD method and emphasize its recent adoption by the nanophotonic research community. In addition, we discuss about some of our recent efforts aiming at improving the accuracy, flexibility and efficiency of a non-dissipative order DGTD method, and also report on some preliminary works towards its extension to the numerical treatment of physical models and problems that are relevant to nanophotonics.     

Acoustical wave propagator

In this paper, an explicit acoustical wave propagator (AWP) is introduced to describe the time-domain evolution of acoustical waves. To implement its operation on an initial state of wave motion, the acoustical wave propagator is approximated as a Chebyshev polynomial expansion, which converges to machine accuracy. The spatial gradient in each polynomial term is evaluated by a Fourier transformation scheme. Analysis and numerical examples demonstrated that this Chebyshev-Fourier scheme is highly accurate and computational effective in predicting time-domain acoustical wave propagation and scattering.     

Geometrically nonlinear vibrations of rectangular plates carrying a concentrated mass

Nonlinear forced vibrations of rectangular plates carrying a central concentrated mass are studied. The plate is assumed to have immovable edges and rotational springs; numerical results are presented for clamped plates. The Von Kármán nonlinear plate theory is used, but in-plane inertia in both the plate and the mass is retrained. The problem is discretized into a multi-degree-of-freedom (dof) system by using an energy approach and Lagrange equations taking damping into account. A pseudo-arclength continuation method is used in order to obtain numerical solutions. Results are presented as both (i) frequency-amplitude curves and (ii) time domain responses. The effect of gravity and the effect of the consequent initial plate deflection are also investigated.     

一种简化的分析光纤布拉格光栅的时域有限差分束传输法

提出了一种便于分析光纤布拉格光栅(FBG)、基于强制边界条件的简化TD-FD-BPM模型.采用交替隐式法(ADIM)和综合道格拉斯(GD)法,离散化时域束传输方程,获得比普通差分格式低二阶的误差。提出并采用强制边界条件,简化了光波导分析中边界处理问题.重点讨论和确定了在此条件下激励源位置、脉冲形状和径向分布函数、连续波激励条件等.在修正的正弦脉冲激励情况下,通过离散傅利叶变换,直接得到较为理想的短FBG反射谱.此法可减少数值计算时间,直观反映光脉冲传输.     

Numerical Analysis of Electromagnetic Fields in Multiscale Model

Modeling technique for electromagnetic fields excited by antennas is an important topic in computational electromagnetics, which is concerned with the numerical solution of Maxwell's equations. In this paper, a novel hybrid technique that combines method of moments(MoM) with finite-difference time-domain(FDTD) method is presented to handle the problem. This approach employed Huygen's principle to realize the hybridization of the two classical numerical algorithms. For wideband electromagnetic data, the interpolation scheme is used in the MoM based on the dyadic Green's function. On the other hand, with the help of equivalence principle, the scattered electric and magnetic fields on the Huygen's surface calculated by MoM are taken as the sources for FDTD. Therefore, the electromagnetic fields in the environment can be obtained by employing finite-difference time-domain method. Finally, numerical results show the validity of the proposed technique by analyzing two canonical samples.     

Dynamics of fractional-order sinusoidally forced simplified Lorenz system and its synchronization

In this paper, dynamical behaviors of the fractional-order sinusoidally forced simplified Lorenz are investigated by employing the time-domain solution algorithm of fractional-order calculus. The system parameters and the fractional derivative orders q are treated as bifurcation parameters. The range of the bifurcation parameters in which the system generates chaos is determined by bifurcation, phase portrait, and Poincaré section, and different bifurcation motions are visualized by virtue of a systematic numerical analysis. We find that the lowest order of this system to yield chaos is 3.903. Based on fractional-order stability theory, synchronization is achieved by using nonlinear feedback control method. Simulation results show the scheme is effective and a chaotic secure communication scheme is present based on this synchronization.     

MRTD算法在集成平面光波导组件分析中的应用

将基于Daubechies紧支集尺度函数的时域多分辨分析（MRTD）算法用于集成平面光波导组件的时域分析中,实现了MRTD算法的各向异性理想匹配层（APML）吸收边界条件,并对平行介质带定向耦合器进行了数值模拟和验证,所得结果与解析解非常一致.与传统的FDTD算法相比,MRTD算法在不牺牲计算精度的前提下能够大大节省计算资源.     

NON-LINEAR FORCED VIBRATIONS OF PLATES BY AN ASYMPTOTIC-NUMERICAL METHOD

Non-linear forced vibrations of thin elastic plates have been investigated by an asymptotic-numerical method (ANM). Various types of harmonic excitation forces such as distributed and concentrated are considered. Using the harmonic balance method and Hamilton's principle, the equation of motion is converted into an operational formulation. Based on the finite element method a starting point corresponding to a non-linear solution associated to a given frequency and amplitude of excitation is computed. Applying perturbation techniques in the vicinity of this solution, the non-linear governing equation obtained is transformed into a sequence of linear problems having the same stiffness matrix. Employing one matrix inversion, a large number of terms of the perturbation series of the displacement and frequency can be easily computed with a small computation time. Iterations of this method lead to a powerful path-following technique. Comprehensive numerical tests for forced vibrations of plates subjected to time-harmonic lateral excitations are reported.