The GMMBS Method for Time-temperature Superposition of Viscoelastic Materials

Using the time-temperature superposition principle, the dynamic properties of viscoelastic materials can be shifted to obtain a master curve. A shifting method based on the Generalized Maxwell Model （ GMMBS ） , is proposed for the time-temperature superposition process of thermo-rheological simple, linear viscoelastic materials. Experimental data points under different temperatures are all considered as a whole and expressed with one unified representation by the GMMBS, which utilizes the feature that the Generalized Maxwell Model can describe a large class of viscoelastic materials with needed accuracy. Compared with traditional overlapping window based shifting methods, the proposed constitutive model based method needn＇t judge the size or existence of the overlapping window first, and computes shift factors with useful information contained in all experimental data points. The effectiveness of the proposed method is verified by simulated data, generated from published test results, with various experimental noise levels, densities of data points and sizes of overlapping windows. It has been shown that the GMMBS is robust and accurate.

Extension of sound field reconstruction based on element radiation superposition method in a sparsity framework

Nearfield acoustic holography(NAH)is a powerful tool for realizing source identification and sound field reconstruction.The wave superposition(WS)-based NAH is appropriate for the spatially extended sources and does not require the complex numerical integrals.Equivalent source method(ESM),as a classical WS approach,is widely used due to its simplicity and efficiency.In the ESM,a virtual source surface is introduced,on which the virtual point sources are taken as the assumed sources,and an optimal retreat distance needs to be considered.A newly proposed WS-based approach,the element radiation superposition method(ERSM),uses piston surface source as the assumed source with no need to choose a virtual source surface.To satisfy the application conditions of piston pressure formula,the sizes of pistons are assumed to be as small as possible,which results in a large number of pistons and sampling points.In this paper,transfer matrix modes(TMMs),which are composed of the singular vectors of the vibro-acoustic transfer matrix,are used as the sparse basis of piston normal velocities.Then,the compressive ERSM based on TMMs is proposed.Compared with the conventional ERSM,the proposed method maintains a good pressure reconstruction when the number of sampling points and pistons are both reduced.Besides,the proposed method is compared with the compressive ESM in a mathematical sense.Both simulations and experiments for a rectangular plate demonstrate the advantage of the proposed method over the existing methods.

APPLICATION OF TIME-TEMPERATURE SUPERPOSITION PRINCIPLE TO EVALUATION OF SCATTERING INTENSITY EVOLUTION IN PHASE SEPARATION FOR PMMA/SAN BLENDS

Spinodal phase separation behavior of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) (PMMA/SAN) blends was investigated by the time-resolved small angle light scattering (SALS) technique. It was found that the influence of temperature on the scattering intensity evolution followed the time-temperature superposition principle. The relationship between temperature and the relaxation ti me of scattering intensity I(t) can be well described by the Williams-Landel-Ferry (WLF) function.

WAVE SUPERPOSITION METHOD BASED ON VIRTUAL SOURCE BOUNDARY WITH COMPLEX RADIUS VECTOR FOR SOLVING ACOUSTIC RADIATION PROBLEMS

By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.

Superposition formulas of multi-solution to a reduced(3+1)-dimensional nonlinear evolution equation

We gave the localized solutions,the interaction solutions and the mixed solutions to a reduced(3+1)-dimensional nonlinear evolution equation.These solutions were characterized by superposition formulas of positive quadratic functions,the exponential and hyperbolic functions.According to the known lump solution in the outset,we obtained the superposition formulas of positive quadratic functions by plausible reasoning.Next,we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory.These two kinds of solutions contained superposition formulas of positive quadratic functions,which were turned into general ternary quadratic functions,the coefficients of which were all rational operation of vector inner product.Then we obtained linear superposition formulas of exponential and hyperbolic function solutions.Finally,for aforementioned various solutions,their dynamic properties were showed by choosing specific values for parameters.From concrete plots,we observed wave characteristics of three kinds of solutions.Especially,we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.

On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.

First-Arrival Picking Method for Active Source Data with Ocean Bottom Seismometers Based on Spatial Waveform Variation Characteristics

The precision and reliability of first-arrival picking are crucial for determining the accuracy of geological structure inversion using active source ocean bottom seismometer(OBS)refraction data.Traditional methods for first-arrival picking based on sample points are characterized by theoretical errors,especially in low-sampling-frequency OBS data because the travel time of seismic waves is not an integer multiple of the sampling interval.In this paper,a first-arrival picking method that utilizes the spatial waveform variation characteristics of active source OBS data is presented.First,the distribution law of theoretical error is examined;adjacent traces exhibit variation characteristics in their waveforms.Second,a label cross-correlation superposition method for extracting highfrequency signals is presented to enhance the first-arrival picking precision.Results from synthetic and field data verify that the proposed approach is robust,successfully overcomes the limitations of low sampling frequency,and achieves precise outcomes that are comparable with those of high-sampling-frequency data.

Range of applicability of real mode superposition approximation method for seismic response calculation of non-classically damped industrial buildings

An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.

Possible Linear Superpositions for Special Solutions of the Fifth-Order KdV-Type Equations

Using Lou and Ni's deformation and mapping idea in nonlinear equations to a set of fifth order KdV type equations, it is found that some types of solitary wave solutions and periodic solutions with special velocities can be linearly superposed to new exact solutions.

Superposition solitons in two-component Bose-Einstein condensates

We develop the Hirota bilinear method and obtain the exact one and two superposition soliton solutions for two- component Bose-Einstein condensates. The conversion of three kinds of solitons including the superposition solitons, bright-bright solitons, and dark-bright solitons is discussed. With the energy analysis, we find that the superposition soliton state is an excitation state for this system. Moreover, the collision of two superposition solitons is found to be elastic.

Application of modified superposition model to viscoelastic behavior of periodontal ligament

The periodontal ligament (PDL) is a soft bio-logical tissue which shows a strongly nonlinear and time dependent mechanical behavior. Re-cent experiments on rabbit PDL revealed that the rate of stress relaxation is strain dependent. This nonlinear behavior of PDL cannot be de-scribed well by the separable quasi linear vis-coelasticity theory which is usually used in tis-sue biomechanics. Therefore, PDL requires a more general description which considers this nonlinearity and time dependency. The purpose of this study was to model strain dependent stress relaxation behavior of PDL using modi-fied superposition method. It is shown herein that modified superposition method describes viscoelastic nonlinearties well and shows a good compatibility with available experimental PDL data. Hence, the modified superposition model is suggested to describe periodontal ligament data, because it can suitably demon-strate both elastic nonlinearity and strain-dependent stress relaxation behavior of PDL.

Examples of Application of Principle of Superposition in the Design of Structural Systems and in Static Analyses

The paper presents general description of combined structural system and initial analysis of an innovative system proposed as the main support structure for tall or heavy loaded buildings located on subsoil of very small load-carrying ability or in earthquake areas. Moreover there is presented also an innovative two-stage method of the approximate calculation of the statically indeterminate trusses. Both are invented by the author by application of the principles of the superposition method.

地磁异常识别技术在松原5.7级地震前的应用研究

运用地磁异常识别技术对2018年5月28日松原5.7级地震前的地磁异常展开研究。采用加卸载响应比法、逐日比法、日变化空间相关法、异常叠加法对吉林省三岗台、通化台及东北地区邻近的大连台、营口台、朝阳台、铁岭台等台站,运用松原5.7级地震前18个月内的地磁预处理分钟值数据进行计算分析和异常判定识别。研究结果表明:在加卸载响应比法、逐日比法和日变化空间相关法的基础上,运用异常叠加法提取的地磁异常,其预测的位置与真实值更加接近,预测结果对省内地震具有重要的指示意义。

考虑加载历史的小半径曲线桥梁梁轨相互作用分析

目前,大部分考虑加载历史的梁轨相互作用研究都集中在直线桥梁上,针对曲线桥梁,尤其是小半径曲线桥梁,梁轨相互作用的研究相对较少。采用理想弹塑性滞回阻力模型模拟扣件纵向阻力,运用有限元软件,建立以城东特大桥为研究对象的钢轨-桥梁-墩台三维有限元空间力学计算模型,研究曲线半径对于梁轨相互作用的影响,探究了多荷载耦合作用、往复荷载作用以及循环荷载作用下考虑加载历史效应的曲线桥梁梁轨相互作用情况,并提出“拉力百分比”以及“压力百分比”的概念以便分析曲线半径对传统线性叠加法误差的影响。结果表明,曲线桥梁中梁轨纵、横向相互作用分别与曲线半径成正、反比,相关数据改变幅度与曲线半径成反比且当曲线半径超过800 m时基本收敛,此时可采用“以直代曲”的简化算法;曲线半径对于横向梁轨相互作用影响程度大于纵向,相较于挠曲、制动工况,伸缩工况受曲线半径影响更加显著;多荷载耦合作用下,采用传统线性叠加法相较于考虑加载历史更为保守且温度荷载起主要贡献;考虑加载历史时钢轨在往复荷载作用下会产生不可忽视的残余内力,且在循环荷载作用下将会产生收敛于第1次往复荷载下的残余内力,这是扣件纵向阻力的弹塑性滞回特性决定的;线性叠加法误差与曲线半径具有相关性,相较于挠曲、制动工况,伸缩工况下对其更为敏感。研究结果可为考虑加载历史下曲线桥梁结构设计提供参考。

富水砂卵石地层盆形冻结止水技术研究

为解决全断面砂卵石地层地下工程的地下水控制问题,提出盆形冻结止水技术。首先,采用三轴力学试验研究冻结砂卵石的压缩力学特性和蠕变力学特性;然后,采用大尺度物理模型试验和数值模拟方法研究盆形冻结的温度场扩展规律,并根据研究结果进一步提出盆形冻结积极冻结期的群孔布置技术和维护冻结期的精细化控制技术。结果表明:1)低围压(小于3 MPa)条件下,三轴抗压强度与围压呈正线性相关,然后围压继续增大时,强度基本不变;基于损伤理论建立冻结砂卵石全过程蠕变模型。2)荷载对冻胀率及融沉系数影响最大,细粒土质量分数次之,原状饱和砂卵石是不冻胀材料,并由此建立饱和砂卵石冻胀率及融沉系数三维预测模型。3)基于大型物理模型试验及数值模拟结果,盆形冻结可以在地下水渗流条件下形成完整的盆形结构,起到有效止水的效果。4)盆底冻结管在冻结过程中表现出与单管冻结迥异的“群孔效应”,根据试验结果提出包含冻结管间距、土体导热系数、渗流速度3因素的积极冻结期冻结管合理间距的确定与布置技术。5)为节约维护冻结期的能源,提出隔排切割冻结管、仅保留盆壁冻结管2种维护形式以对冻结区域进行精细化控制,经过分析,2种方式均可以有效满足盆形结构维护期的冷量供给,保持完整的盆形形态。

大型空泡水洞试验设施结构有限元分析

大型空泡水洞试验设施是目前中国规模最大的水洞系统,为评估其整体结构强度和抗震设计安全性,对空泡水洞结构进行三维有限元数值分析,考虑正常工作工况和地震载荷作用极限工况下的结构刚强度,基于振型分解反应谱法计算了地震惯性加速度载荷,并对结构地震位移响应进行校核。结果表明:空泡水洞的结构变形在正常工作工况主要表现为水洞内壁的膨胀变形,在极限工况下主要表现为由地震载荷引起的水洞顶部水平位移;空泡水洞高应力区域主要位于结构角隅处的筒壁和加强筋。这对中国自主研发大型空泡水洞具有重要的借鉴意义。

盐渍土环境下考虑耐久性损伤的输电塔风振时程分析

长期服役于盐渍土环境下的输电塔耐久性损伤较为严重,当其材料力学性能退化到一定程度时,在强风作用下,输电塔可能会发生破坏,危害线路的安全运行。基于±800kV天中线特高压直流输电工程直线塔,考虑基础钢筋锈蚀、基础混凝土侵蚀、输电塔杆塔钢材锈蚀以及基础箍筋的约束效应,在ABAQUS有限元软件中建立塔-线-基础耦合模型,研究不同风攻角和材料耐久性损伤对塔身动力响应的影响。结果表明:90°风攻角下塔身顺风向位移最大,为最不利风向基本工况;90°风攻角下输电塔塔顶顺风向位移响应贡献主要以背景分量为主,但共振分量也有一定贡献,主要以输电塔1阶振型频率为主,且随着服役时间的增加,振型频率逐渐降低,相应响应的贡献程度逐渐提高;相同风荷载作用下,随着服役时间的增加,塔身位移逐渐增大,相同服役时间下,随着塔身高度的增加,塔身位移响应峰值增长速度变快,结构振动更加明显,材料耐久性损伤对输电塔的位移响应影响较大。

不同道路服务水平下连续梁桥动力响应研究

为了解不同道路服务水平与桥梁动力响应间的内在关系,以(50+100+50)m三跨连续梁桥为工程实例,采用交通流理论,引入平均车头间距与车流密度的相互关系,获取道路服务水平为一级至四级所对应的车辆间距分布规律,基于模态综合法和结构动力学原理,通过轮-桥之间的几何位移和力学耦合关系,组建多车车桥耦合时变动力分析模型,提出多车车桥耦合振动系统数值分析方法,研究不同车辆数量和不同道路服务水平下桥梁关键截面动力响应的变化规律。结果表明:随着车辆数量逐渐增加,桥梁关键截面处的挠度响应时程曲线呈先增大后减小的趋势变化,其中当桥面上的车辆数量为4辆时,桥梁关键截面的挠度响应幅值达到最大;当桥面上的车辆数量继续增加到8辆时,桥梁挠度响应幅值达到基本稳定。在此基础上,计算得出不同车辆间距变化,即随着道路服务水平由一级变化到四级时,桥梁关键截面挠度响应幅值呈增大趋势,其动力响应均大于单车作用下桥梁挠度响应幅值;而桥梁冲击系数则呈现先增大后减小的变化趋势,也均大于单车规范取值;在不同道路服务水平中均存在有利车队布置形式,使得桥梁振动响应影响较小。

黄河流域生态敏感性评价研究

以黄河流域为研究对象,依据地形条件、自然环境和人类活动3个方面,选取了7个指标,构建了生态敏感性评价体系,采用AHP层次分析法确定各指标权重,运用GIS加权叠加法对黄河流域生态敏感性进行综合评价。结果表明:黄河流域生态敏感性的空间分布存在显著差异,呈现出中上游高、下游低的分布格局,整体上中敏感区占主导地位,面积达33.59万km^(2),占流域总面积的42.25%,高敏感区和极高敏感区面积17.37万km^(2),占流域总面积的21.85%。

考虑高阶振型效应的大跨度钢桁拱桥瑞利阻尼参数取值研究

为了解高阶振型效应对大跨度钢桁拱桥地震反应的影响机制,以及在采用直接积分法时构建合适的瑞利阻尼矩阵,以某490 m跨径钢桁拱桥为背景,采用SAP 2000软件建立全桥弹性动力计算模型。针对主拱圈上(下)弦杆轴力、弯矩,研究振型参与质量最大的7阶(第1、4、8、11、13、23、49阶)振型反应与总反应的占比关系,并对构建瑞利阻尼矩阵的特征频率选取方法展开研究。结果表明:主拱圈上、下弦杆拱脚区域的轴力主要由1阶振型(第1阶)控制,由拱脚向拱顶过渡,逐渐转变为由2~4阶振型控制,高阶振型效应显著;同一阶振型对主拱圈上、下弦杆轴力贡献率及分布规律的影响不同;对于复杂钢桁拱桥,采用振动方向上振型参与质量较大的2阶振型特征频率构建瑞利阻尼矩阵可能因高估了高阶振型阻尼比,导致除拱脚区域以外的拱圈弦杆杆件轴力计算结果偏小,结构偏于不安全;采用直接积分法对复杂钢桁拱桥进行地震反应分析时,建议选取多阶控制振型构建相应的瑞利阻尼工况,并对其计算结果取包络用于抗震设计。