Optimum design of structures with both natural frequency and frequency response constraints

An efficient method is developed to compute the sensitivities of eigenvalues, eigenvectors and frequency responses in a reduced approximate rnodel. The reanalyses of a modified structure for those dynamic responses are also derived in the approximate model. An optimization process utilizing the efficiently calculated sensitivities and reanalyses of the modified structure is formed. The difficulties of finding eigenvector sensitivities for repeated modes have also been addressed and averted in the approximate model. Two numerical examples show satisfactory outcomes by using this proposed approach.     

主动结构动力学特征与频响特性研究

对主动结构动力学特征进行理论分析,从不同角度对其分类、讨论代表性范例。分析主动结构与非自伴随结构之关系。探讨其频域特性、阐述其与被动结构频响函数之关系。通过数值算例揭示主、被动结构频响函数间差异,展示仿真系统左右特征向量。通过实验及数据处理,获得由自由-自由梁构造的主动结构频响函数,验证主动结构的频域特性。     

Quantitative determination of dynamical properties using coherent spatial frequency domain imaging

Laser speckle imaging (LSI) is a fast, noninvasive method to obtain relative particle dynamics in highly light scattering media, such as biological tissue. To make quantitative measurements, we combine LSI with spatial frequency domain imaging, a technique where samples are illuminated with sinusoidal intensity patterns of light that control the characteristic path lengths of photons in the sample. We use both diffusion and radiative transport to predict the speckle contrast of coherent light remitted from turbid media. We validate our technique by measuring known Brownian diffusion coefficients (D(b)) of scattering liquid phantoms. Monte Carlo (MC) simulations of radiative transport were found to provide the most accurate contrast predictions. For polystyrene microspheres of radius 800 nm in water, the expected and fit D(b) using radiative transport were 6.10E-07 and 7.10E-07 mm2/s, respectively. For polystyrene microspheres of radius 1026 nm in water, the expected and fit D(b) were 4.7E-07 and 5.35 mm2/s, respectively. For scattering particles in water-glycerin solutions, the fit fractional changes in D(b) with changes in viscosity were all found to be within 3% of the expected value.     

Multiscale topology optimization for frequency domain response with bi-material interpolation schemes

In areas that require high performance components, such as the automotive, aeronautics and aerospace industries, optimization of the dynamic behavior of structures is sought through different approaches, such as the design of materials specific to the application, for instance through structural topology optimization. The bi-directional evolutionary structural optimization (BESO) method, in particular, has been used for the simultaneous design of hierarchical structures, which means that the structural domain consists not only of the macrostructure but also of the microstructural topology of the materials employed. The purpose of this work is to apply the BESO method to solve two-dimensional multiscale problems in order to minimize the response of structures subjected to forced vibrations in a given frequency range. The homogenization method is applied to integrate the different scales of the problem. In particular, the material interpolation model for two materials is used. The BESO method is applied to different cases of optimization, in macroscale, microscale, and multiscale structural domains. Numerical examples are presented to validate the optimization and demonstrate the potential of this approach. The numerical examples show that the multiscale bi-material topology optimization method implemented here is able to produce structures and microstructures for optimization of the frequency domain response, satisfying prescribed volume constraints.

     

The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates

The uniaxial compressive responses of silicone rubber (B452 and Sil8800) and pig skin have been measured over a wide range of strain rates (0.004–4000 s⁻¹). The uniaxial tensile response of the silicone rubbers was also measured at low strain rates. The high strain rate compression tests were performed using a split-Hopkinson pressure bar made from AZM magnesium alloy. High gain semi-conductor strain gauges were used to detect the low levels of stress (1–10 MPa), and a pulse shaper increased the rise time of dynamic loading on the specimen. The experiments reveal that pig skin strain hardens more rapidly than silicone rubbers and has a greater strain rate sensitivity: pig skin stiffens and strengthens with increasing strain rate over the full range explored, whereas silicone rubber stiffens and strengthens at strain rates in excess of 40 s⁻¹. A one term Ogden strain energy density function adequately describes the measured constitutive response of each solid, and a strategy is outlined for determining the associated material constants (strain hardening exponent and a shear modulus). The strain rate sensitivities of the pig skin and two silicone rubbers are each quantified by an increase in the shear modulus with increasing strain rate, with no attendant change in the strain hardening exponent. It is shown that the Mooney-Rivlin model is unable to describe the strong strain hardening capacity of these rubber-like solids.     

Two-dimensional distributed strain sensing with an Archimedean spiral arrangement in optical frequency domain reflectometry

We demonstrate a distributed two-dimensional(2D)strain-sensing system in optical frequency domain reflectometry(OFDR)with an Archimedean spiral arrangement of the sensing fiber.The Archimedean spiral describes a simple relationship between the radial radius and polar angle,such that each circle(the polar angle from0 to 2π)can sense the 2D strain in all directions.The strain between two adjacent circles can also be easily obtained because an Archimedean spiral facilitates sensing of every angle covering the full 2D range.Based on the mathematical relation of Archimedean spirals,we deduce the relationship between the one-dimensional position of the sensing fiber and 2D distribution in polar coordinates.The results of the experiment show that an Archimedean spiral arrangement system can achieve 2D strain sensing with different strain load angles.     

一种海上浮式风电基础频域动力响应分析新技术

提出一种风、浪联合作用下的海上浮式风电基础频域动力响应分析新技术。该技术将浮式风电基础的动力方程从时域转换到Laplace域,推导并获得新的浮式风电基础传递函数,解决了现有技术其延迟函数在Laplace域中无法直接获得的技术不足。其优势在于新的传递函数能够与傅里叶变换技术相结合,实现了海上浮式风电基础的频域动力响应计算。相比于传统时域方法,该算法将延迟函数卷积项在Laplace域上转换为乘积项,计算效率得到提高;较传统频域算法,该方法提供了新的传递函数,为浮式风电基础频域动力响应计算提供一种新的技术手段。文中采用安装三台3MW风力发电机的三浮筒浮式风电模型进行研究,结果证实:所提出的频域动力响应算法可以准确得到浮式风电基础在风、浪联合作用下的频域动力响应,为海上浮式风电基础的动力响应计算提供一种更为高效的技术手段。     

Analysis of structures subjected to random wind loading by simulation in the frequency domain

The closely related methods of transfer matrices and direct numerical integration have been extensively used in the analysis of free standing structures. In case of structures subjected to dynamic loading, the method is particularly suitable to analysis in the frequency domain, enabling the consideration of arbitrary linear time-dependent material behaviour without additional difficulties. In this paper, a method is proposed to simulate stationary random processes in the frequency domain and it is applied for analysis of structures under along-wind action. The method requires less computational effort than standard procedures to obtain the power spectral density function of response quantities of interest and, since the solutions are obtained by simulation, may be extended to include in the formulation some types of non-linearity. Furthermore, it can be advantageously employed in the dynamic analysis of thin-walled open section beams, for which other alternatives are rarely available. The method proposed is applied to various free-standing towers and chimneys, for which response measurements are available, allowing a direct comparison of theoretical and experimental results.     

浅谈频域和时域

1频域和时域概念 我们经常讲的信号时域分析就是分析信号随时间的变化,比如24小时体温监测图即体温随时间变化,如图1.1;24小时动态血压监测图即血压随时间的变化,如图1.2;心电图即心电信号随收缩期,舒张期的时间变化,如图1.3;超声多普勒频谱图即血流速度随收缩期、舒张期的时间变化,如图1.4.      

Material modeling of frequency,magnetic field and strain dependent response of magnetorheological elastomer

Journal of Materials Science - Accurate modeling of material behavior is very critical for the success of magnetorheological elastomer-based semi-active control device. The material property of...     

Dielectric response of Li0.4K0.6NbO3 crystal in the frequency domain

Complex impedance and dielectric constants of ferroelectric crystals Li_0.4K_0.6NbO₃ have been studied in the frequency domain at several temperatures. A strong low-frequency dielectric dispersion below 1 kHz was revealed in the high temperature range. The normalized behaviour of the complex dielectric constants satisfies the universal dynamic response with its power exponent n=0.04. In the high frequency region, the complex impedance was described by a modified Cole-Cole arc. An equivalent circuit for the transport process of high frequency region has been examined. The temperature-dependent exponent has its minimum at the ferro- to para-electric phase transition point and relaxation frequencies do not satisfy the Arrhenius law in the ferroelectric region     

Effect of bimodularity on frequency response of cylindrical panels using Galerkin time domain approach

The forced vibration analysis of bimodulus material laminated structures is a challenging problem due to non-smooth nonlinear nature of governing equations. The most commonly used direct time integration schemes show numerical instability and do not predict steady state response except for limited number of cases without considering in-plane inertia. This is due to the sudden change of restoring force from positive/negative half cycle to negative/positive half cycle exciting higher modes/harmonics at every instant of a cycle change leading to numerical instability in the time marching scheme. In the present work, Galerkin time domain approach is successfully used for the forced vibration analysis of bimodular cylindrical panels. The effect of bimodularity ratio on the frequency response of cylindrical panels for few typical geometrical and lamination parameters is studied for the first time. It is found that the positive half cycle amplitude is greater than the negative half cycle amplitude for E _2t /E _2c < 1 and is smaller for E _2t /E _2c > 1. Further, the percentage difference of positive and negative half cycle amplitudes decreases with the increase in E _2t /E _2c . The stresses under dynamic loading are different for positive and negative half of a vibration cycle.     

Multi-objective design optimization of antenna structures using sequential domain patching with automated patch size determination

In this article, a simple yet efficient and reliable technique for fully automated multi-objective design optimization of antenna structures using sequential domain patching (SDP) is discussed. The optimization procedure according to SDP is a two-step process: (i) obtaining the initial set of Pareto-optimal designs representing the best possible trade-offs between considered conflicting objectives, and (ii) Pareto set refinement for yielding the optimal designs at the high-fidelity electromagnetic (EM) simulation model level. For the sake of computational efficiency, the first step is realized at the level of a low-fidelity (coarse-discretization) EM model by sequential construction and relocation of small design space segments (patches) in order to create a path connecting the extreme Pareto front designs obtained beforehand. The second stage involves response correction techniques and local response surface approximation models constructed by reusing EM simulation data acquired in the first step. A major contribution of this work is an automated procedure for determining the patch dimensions. It allows for appropriate selection of the number of patches for each geometry variable so as to ensure reliability of the optimization process while maintaining its low cost. The importance of this procedure is demonstrated by comparing it with uniform patch dimensions.     

Bounding-surface plasticity: Stress space versus strain space

Summary A bounding-surface plasticity model is formulated in stress space in a general enough manner to accommodate a considerable range of hardening mechanisms. Conditions are then established under which this formulation can be made equivalent to its strain-space analogue. Special cases of the hardening law are discussed next, followed by a new criterion to ensure nesting. Finally, correlations with experimental data are investigated.Notation (a) centre of the stress-space (strain-space) loading surface; i.e., backstress (backstrain) - ^* (a ^*) centre of the stress-space (strain-space) bounding surface - (a ) target toward which the centre of the stress-space (strain-space) loading surface moves under purely image-point hardening - (b) parameter to describe how close the loading surface is to nesting with the bounding surface in stress (strain) space; see (H10) - (c) elastic compliance (stiffness) tensor - (d) parameter to describe how close the stress (strain) lies to its image point on the bounding surface; see (H10) - (D) generalised plastic modulus (plastic compliance); see (1) - function expressing the dependence of the generalised plastic modulus on (plastic complianceD ond) - ^* (D ^*) analogue to (D) for the bounding surface - function expressing the dependence of ^* on (D ^* ond) - () strain (stress) - ' (') deviatoric strain (stress) - ^P ( ^R ) plastic strain (stress relaxation); see Fig. 1 - () image point on the bounding surface corresponding to the current strain (stress) - _iso (f _iso) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change of radius; i.e., fraction of isotropic hardening in the stress-space theory - _kin (f _kin) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change in the backstress (backstrain); i.e., fraction of kinematic hardening in the stress-space theory - _nor (f _nor) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - _ima (f _ima) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - function relating _iso to , , and (f _iso tob,d, andl) - function relating _kin to , , and (f _kin onb,d, andl) - function relating _nor to , , and (f _nor onb,d, andl) - function relating _ima to , , and (f _ima onb,d, andl) - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change of radius - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change in the centre - function relating _iso ^* to (f _iso ^* tod) - function relating _kin ^* to (f _kin ^* tod) - (l) parameter to describe the full extent of plastic loading up to the present, giving the arc length of plastic strain (stress relaxation) trajectory; see (H10) - function relating the direction for image-point translation of the loading surface to various other tensorial directions associated with the current state; see (H5). With 6 Figures     

Thin-film thickness and density determination from x-ray reflectivity data using a conventional power diffractometer

The determination of thin-film thickness and density from X-ray specular and off-specular reflectivity data obtained using a conventional powder diffractometer has been investigated. An analysis of specular reflectivity data for a 565.9 Å Pt film showed that the results were determined precisely and agreed with those obtained previously from a high-resolution reflectometer. A systematic study of the effect of film-surface misalignment revealed that the values of thickness were insensitive to the alignment. A precision of about 1% or less was obtained from off-specular reflectivity data with a surface misalignment of 0.20° or less. The insensitivity makes conventional powder diffractometers attractive for film thickness determination and opens this technique to many laboratories. The values of density were found to be relatively more sensitive to surface alignment. Nevertheless, densities with a precision of 3% and better were obtained when the film surfaces were aligned to within the effective divergence of the incident X-ray beam.     

Design of couplers for traveling wave RF structures using 3D electromagnetic codes in the frequency domain

In this paper, a simple equivalent circuit model of a traveling wave RF structure with input and output couplers is introduced. A few properties related to evaluating the reflection coefficient of the single coupler are then obtained and discussed. From these properties, a general procedure to design couplers for traveling wave structures using 3D electromagnetic codes in the frequency domain is derived. Finally, an example of coupler design for a 2π/3 X band accelerating structure is illustrated.     

植物微弱电波信号的时、频域分析

在时域和频域上对植物电波信号进行了分析.植物电波信号的幅值处于μV级量级,是一种微弱信号;随时间变化剧烈,在不同时刻的取值关系松散;植物电波信号属于低频信号,其功率谱主要分布在小于5 Hz这一频段.     

复杂机械结构中高频动响应能量有限元方法研究

从理论研究和应用研究两个方面追踪了国内外关于能量有限元的发展现状,并指出能量有限元已趋向于预示越来越复杂的结构动响应;接下来介绍本课题组近年来利用能量有限元方法针对实际复杂结构及复杂载荷环境中的高频动响应问题所做的研究工作,主要包括3个部分:一是在考虑多种传递波功率流耦合的情况下,发展了圆柱壳、截锥壳等复杂结构的高频响应能量有限元方法,从而得到了此类结构的中高频局部动响应特性;二是考虑在脉动载荷、混响室等复杂环境中,利用能量有限元方法并结合能量边界元方法预示了结构的高频振动特性和声振耦合特性;三是开发了能量有限元的计算软件,为其大规模应用奠定了基础。最后指出了能量有限元方法目前存在的问题和进一步研究的方向。