Reconstruction of dynamic displacement and velocity from measured accelerations using the variational statement of an inverse problem

This paper presents two types of finite impulse response (FIR) filters to reconstruct dynamic displacement induced by structural vibration from measured acceleration. The governing equation for the reconstruction is derived by taking the variation of a minimization problem, which defines an inverse problem on displacement. A regularization function for overcoming the ill-posedness of the inverse problem is included in the minimization problem. The governing equation of the inverse problem becomes the same type of differential equation as that of a beam on an elastic foundation. The conventional FIR (CFIR) filter directly approximates the transfer function of the governing equation, while the FEM-based FIR (FFIR) filter is formulated by the discretization of the minimization problem with the finite element method. For the finite element discretization, the Hermitian shape function is utilized. The proposed FFIR filter is capable of reconstructing displacement and velocity simultaneously. The fundamental characteristics of the proposed filters are investigated in the frequency domain using the transfer and accuracy functions. It is shown that the proposed FIR filters suppress low frequency noise components in measured accelerations effectively, and reconstruct physically meaningful displacement accurately. The validity of the proposed filters is demonstrated through a numerical simulation study, a field experiment and an evaluation of flutter derivatives using measurements taken from a wind tunnel test.     

A hybrid formulation for mid-frequency analysis of assembled structures

A new formulation able to predict the behaviour of structures in the mid-frequency range is presented in this paper. The mid-frequency field is a hybrid domain for which assembled structures exhibit simultaneously low- and high-frequency behaviours, depending on the material and geometrical properties of different subsystems. Thus, dealing with the mid-frequency field requires simulation methods which are able to account the differences in behaviour of different subsystems. The hybrid formulation is based on the coupling of two different formulations, the finite elements for the low-frequency behaving subparts and a probabilistic formulation, the smooth integral formulation, applied to the high-frequency subsystems. The hybrid method enables to correctly predict the deterministic response of the low-frequency parts which is not affected by randomness, and the smooth trend of the contributions of the high-frequency parts. The paper is concluded with several numerical examples computed for coupled one- and two-dimensional structures.     

一种适合基于原子尺度有限元方程的低通滤波边界条件

发展一种基于原子尺度的有限元动力学方程,其动态行为跨越了从原子尺度到宏观尺度.理论计算该方程的色散关系和动力学散射特征.在此基础上,基于滤波器的概念,设计低通滤波边界条件用于减少网格增大带来的高频反射波,同时又保证低频振动波传播不受影响.通过一维数值模拟,计算了能量反射和透射系数,展示低通滤波边界条件可以吸收高频反射波而不影响低频波的传播.     

LOCAL-MODE RESONANCE AND ITS STRUCTURAL EFFECTS UNDER HORIZONTAL GROUND SHOCK EXCITATIONS

The dynamic response of building structures has been studied extensively for relatively low-frequency seismic actions, and it is established that the seismic response generally is governed by the global-mode vibration, i.e., the vibration in terms of the floor movement. Much less fundamental study has been done regarding the structural response to ground shock excitations with principal frequencies many times of the fundamental frequency of the structural system. Most of the existing code provisions on ground shock control have U001remained empirical. In this paper, it is demonstrated through numerical study and laboratory model testing that the structural response to high-frequency ground shocks have distinctive characteristics as compared to the seismic response, and most significant is the participation of the vibration at the local elemental level. Local-mode resonance could occur when the shock frequency is sufficiently high, and to a large extent it can be uncoupled from the global floor vibration. As a result, large force effects can develop at relatively small floor displacement, rendering the conventional displacement-based criteria inapplicable, while more focus on the stress-strain response is deemed necessary. The results pave a way for further development of more rational criteria for this category of the structural vibration problems.     

贴片晶振在冲击环境下的损伤边界

贴片式石英晶体振荡器广泛应用于各类电子和通信设备系统中。针对晶振在冲击环境中容易出现结构破坏而导致系统工作异常的问题,通过分析单自由度系统在不同频率冲击载荷作用下的响应特点,建立了结构的应力响应水平与相关冲击响应谱谱值之间的联系,获得了较已有结论更合理的损伤边界形式。根据典型晶振结构易损组件的力学特性建立对应的简化分析模型,得到了贴片晶振在大频率范围内的结构损伤边界。利用有限元仿真软件,对晶振结构在0.5~30 kHz频率范围内冲击载荷下的响应进行仿真分析,验证了该损伤边界的有效性。这也为以贴片晶振为代表的微小元器件在冲击环境下的可靠性研究提供了一种可行的方法。     

Three-dimensional experimental spatial dynamics modelling of a reciprocating Freon compressor housing

Experimental spatial dynamics modelling encompasses the modelling, postprocessing, and visualization of 3D spatial dynamic response of structures as statistically-qualified complex-valued continuous vector fields derived from experimental structural dynamics testing. A weighted least-squares discrete finite element formulation has been developed to reconstruct the continuous 3D velocity response fields from experimental dynamics data. Dynamic 3D rotations, displacements, and accelerations were naturally derived from the full field velocity response model. Also, dynamic strain and stress fields across the shell elements were extracted by directly postprocessing the dynamic response. A Scanning Laser Doppler Vibrometer (SLDV) was used to measure a single frequency of the 3D dynamic response in an in situ test of an operating reciprocating Freon compression. The SLDV measured the velocity response at thousands of locations on the compressor housing from multiple, positionally-registered locations. The geometry from a preexisting finite element model provided the shape model of the compressor. An experimentally derived spatial dynamics model of the compressor housing was solved and postprocessed results were obtained.     

Influence of ballast models in the dynamic response of railway viaducts

This paper presents an investigation of the numerical, dynamic response of medium-span railway viaducts by taking into account the influence of the ballasted track and the loadmodelling methodologies. Three models for the track and two loading procedures (the Moving Forces procedure and the Train-Structure Interaction procedure) were used. The comparison was made using three case studies. Model calibration using available response-acceleration measurements showed that time variation of the first natural frequency must be assumed to reproduce the measured time histories. The influence of track models was detectable in the time domain for only the maximum accelerations. When response is analysed in the frequency domain, results show that track models act as a filter for the high-frequency components. When the Moving Forces load model was used, the effect of the track models was less significant but consistent with the previous conclusion.     

Self-oscillations of electronic and nuclear polarization during optical excitation of an Si/CaF2 nanostructure in a transverse magnetic field

We examine theoretically low-frequency and high-frequency self-oscillations of electronic and nuclear polarization in an Si/CaF₂ nanostructure in a transverse magnetic field. We show that the low-frequency self-oscillations are stable in zero field, and the analogous high-frequency oscillations are stable beyond the region of the maximum on the Hanle curve. The frequency of the low-frequency oscillations is 0.001–0.500 of the reciprocal nuclear longitudinal relaxation time; the frequency of the high-frequency oscillations is 10⁸–10⁹ Hz, and their amplitude reaches 50% of the initial electronic spin polarization. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 3, pp. 363–369, May–June, 2006.     

基于高级统计能量分析的周期加筋板振动特性研究

统计能量分析(statistical energy analysis, SEA)是复杂耦合系统中、高频动力学特性计算的有力工具. 本文以波传播理论和SEA的基本原理为基础, 研究周期加筋板中弯曲波传播特性. 分析了周期结构的频率带隙特性和加强筋对板上弯曲波的滤波特性对SEA计算结果的影响规律, 发现经典SEA由于忽视了加筋板中物理上不相邻子系统间存在的能量隧穿效应, 而导致响应预测结果产生最高近 40 dB的误差. 为了解决这一问题, 本文应用高级统计能量分析(advanced statistical energy analysis, ASEA)方法, 考虑能量在不相邻子系统间的传递、转移和转化的物理过程, 从而大幅提高子系统响应的预测精度, 将误差在大部分频段降低至小于5 dB. 设计了模拟简支边界条件的加筋板振动测试实验装置, 实验测试结果与有限元结果符合较好, 对理论模型进行了验证.     

Numerical and experimental validation of a hybrid finite element-statistical energy analysis method

The finite element (FE) and statistical energy analysis (SEA) methods have, respectively, high and low frequency limitations and there is therefore a broad class of "mid-frequency" vibro-acoustic problems that are not suited to either FE or SEA. A hybrid method combining FE and SEA was recently presented for predicting the steady-state response of vibro-acoustic systems with uncertain properties. The subsystems with long wavelength behavior are modeled deterministically with FE, while the subsystems with short wavelength behavior are modeled statistically with SEA. The method yields the ensemble average response of the system where the uncertainty is confined in the SEA subsystems. This paper briefly summarizes the theory behind the method and presents a number of detailed numerical and experimental validation examples for structure-borne noise transmission.     

天然源超低频频谱的曲波分解与分析

由于天然源超低频电磁探测仪器接收的是宽频段多源信号,如何进行信号的分解以将干扰信号滤除,是利用天然源超低频电磁探测技术进行实际探测应用的关键。北京大学自主研发的天然源超低频电磁探测仪器,以山西沁水盆地煤层气探测数据为研究对象,将曲波变换的方法应用在超低频电磁探测频谱的分解上。分解结果表明,曲波变换分解出的高频信息主要是探测仪器直接接收的大气层雷电产生的干扰信号,而低频信息层则主要包含了地下的探测目标信息。基于此,以低频信息为基础重构后的探测频谱曲线相对于原始探测曲线来说,更有利于探测目标的解释。但是对于由于人工工频所引起的干扰信号,该方法并不能有效去除,在实际应用中需要结合其他数据处理方法一同进行。     

铁镓单晶Janus-Helmholtz换能器

针对深水、低频、宽带换能器的技术需求,结合Janus-Helmholtz换能器的结构特点和铁镓单晶材料低场应变大及机械强度高的特性,提出了铁镓单晶Janus-Helmholtz换能器设计方案。采用永磁偏磁场和环形闭合磁路,建立了一系列铁镓单晶磁致伸缩换能器理论分析模型,包括对磁致伸缩材料参数进行线性化处理,设计了换能器最佳工作点,结合静态磁场和动态磁场分布情况分段细化换能器驱动等效参数,以及利用全阻抗模型通过电感损耗等效计算换能器静态阻抗,然后通过二维有限元分析等效模型,优化分析了换能器的结构参数与电声性能。最后制作了换能器样机,并进行了测试与分析。对比仿真和测试结果表明:全阻抗模型得到的阻抗曲线与样机测试结果相一致,有限元等效模型计算的发送电流响应与样机测试结果良好吻合。换能器样机水中谐振基频为1000 Hz,谐振频率下发送电流响应176.4 dB;在875～2300 Hz频率范围内,发送电流响应起伏不大于6 dB;增加驱动电流有效值到16.2 A,最大声源级可以达到196.2 dB。     

Analyses of contact forces and vibration response for a defective rolling element bearing using an explicit dynamics finite element model

This paper provides insights into the physical mechanism by which defect-related impulsive forces, and consequently, vibrations are generated in defective rolling element bearings. A dynamic nonlinear finite element model of a rolling element bearing with an outer raceway defect was numerically solved using the explicit dynamics finite element software package, LS-DYNA. A hypothesis was developed to explain the numerical noise observed in the predicted vibrations and contact forces, and the noise frequencies were analytically estimated. In-depth analyses of the numerically estimated dynamic contact forces between the rolling elements and the raceways of a bearing, which are not measured in practice, and have not been reported previously, are presented in this paper. Several events associated with the traverse of the rolling elements through the outer raceway defect are elaborated, and the impulsive force generating mechanism is explained. It was found that the re-stressing of the rolling elements that occurs near the end of a raceway defect generates a burst of multiple short-duration force impulses. The modelling results also highlight that much higher contact forces and accelerations are generated on the exit of the rolling elements out of defect compared to when they strike the defective surface. A bearing with a machined outer raceway defect was tested in a controlled experiment; the measured acceleration response compared favourably with the numerically modelled acceleration results, thereby, validating the low- and high-frequency characteristics of the de-stressing and re-stressing of the rolling elements, respectively.     

Mechanically tunable metamaterials terahertz dual-band bandstop filter

We experimentally demonstrate a mechanically tunable metamaterials terahertz(THz) dual-band bandstop filter. The unit cell of the filter contains an inner aluminum circle and an outside aluminum Ohm-ring on high resistance silicon substrate. The performance of the filter is simulated by finite-integration-time-domain(FITD) method. The sample is fabricated using a surface micromachining process and experimentally demonstrated using a THz time-domain-spectroscopy(TDS) system. The results show that, when the incident THz wave is polarized in y-axis, the filter has two intensive absorption peaks locating at 0.71 THz and 1.13 THz, respectively. The position of the high-frequency absorption peak and the amplitude of the low-frequency absorption peak can be simultaneously tuned by rotating the sample along its normal axis.The tunability of the high-frequency absorption peak is due to the shift of resonance frequency of two electrical dipoles,and that of the low-frequency absorption peak results from the effect of rotationally induced transparent. This tunable filter is very useful for switch, manipulation, and frequency selective detection of THz beam.     

Transient energy density distribution of a rod under high-frequency excitation

Energy finite element analysis (EFEA) is an efficient way to solve high-frequency structural dynamics response problems. Up to now, EFEA has been used to deal with time-independent vibration problems. However, it is still necessary to understand the time dependent details of energy density distribution of a structure. To study the transient response of a rod under high-frequency sinusoidal excitation, the transient energy density governing equation for a rod is presented. The governing equation is solved, and the solution is verified using an analytical method. Example application to a rod is presented to illustrate the feasibility.     

Auditory filter shapes at 8 and 10 kHz

Auditory filter shapes were derived from notched-noise masking data at center frequencies of 8 kHz (for three spectrum levels, N0 = 20, 35, and 50 dB) and 10 kHz (N0 = 50 dB). In order to minimize variability due to earphone placement, insert earphones (Etymotic Research ER2) were used and individual earmolds were made for each subject. These earphones were designed to give a flat frequency response at the eardrum for frequencies up to 14 kHz. The filter shapes were derived under the assumption that a frequency-dependent attenuation was applied to all stimuli before reaching the filter; this attenuation function was estimated from the variation of absolute threshold with frequency for the three youngest normally hearing subjects in our experiments. At 8 kHz, the mean equivalent rectangular bandwidths (ERBs) of the filters derived from the individual data for three subjects were 677, 637, and 1011 Hz for N0 = 20, 35, and 50 dB, respectively. The filters at N0 = 50 dB were roughly symmetrical, while, at the lower spectrum levels, the low-frequency skirt was steeper than the high-frequency skirt. The mean ERB at 10 kHz was 957 Hz. At this frequency, the filters for two subjects were steeper on the high-frequency side than the low-frequency side, while the third subject showed a slight asymmetry in the opposite direction.     

Modeling vibratory damage with reduced-order models and the generalized finite element method

This paper investigates a coupled computational analysis framework that uses reduced-order models and the generalized finite element method to model vibratory induced stress near local defects. The application area of interest is the life prediction of thin gauge structural components exhibiting nonlinear, path-dependent dynamic response. Full-order finite element models of these structural components can require prohibitively large amounts of processor time. Recent developments in nonlinear reduced-order models have demonstrated efficient computation of the dynamic response. These models are relatively insensitive to small imperfections. Conversely, the generalized finite element method provides the ability to model local defects without geometric dependency on the mesh. A more robust version of the method, with numerically built enrichment functions, provides a multiple-scale modeling capability through direct coupling of global and local finite element models. Replacing the component finite element model with a reduced-order model allows for efficient computation of dynamic response while providing the necessary information to drive local, solid analyses which can zoom in on regions containing stress risers or cracks. This paper describes the coupling of these approaches to enable fatigue and crack propagation predictions. Numerical/experimental examples are provided.     

Dynamical electronic polarizability and the force sum rule

It is shown that a dynamical force sum rule is useful in analyzing the response of a finite electronic system to a uniform electric field that oscillates harmonically in time. The sum rule, which has been used previously in calculations of the response of atoms to electric fields, provides a direct test of electronic polarizability calculations and may lead to useful approximations for the electronic polarizability of metallic microstructures. We apply the sum rule to the case of a small metal sphere in the jellium model, and show that it directly leads to an approximation that is equivalent to the surface-plasmon-pole approximation for the red-shift of the surface plasmon frequency.     

Parametric generation of whistler waves due to the interaction of high-frequency wave beams with a magnetoplasma

The parametric generation of low-frequency whistler waves by a pump wave beam formed by high-frequency whistler waves with close frequencies is studied experimentally. The electromagnetic fields excited by the beats of two co- or counterpropagating high-frequency waves, or by an amplitude-modulated pump are studied. It is shown that the nonlinear currents at the beat (modulation) frequency are generated by a transverse ponderomotive force arising due to the finite width of the high-frequency beam. In this case, the nonlinear azimuthal drift currents enclose the pump beam and can radiate low-frequency whistler waves to the surrounding plasma.