用低阶模型参数检测平台损伤

检测海洋平台损伤是项极其重要的探索研究。本文对空间框架结构的平台计算了损伤前和五种损伤状态的前四十阶特征值和特征矢量,损伤前后的前9阶和后7阶振型均属局部振动,第10阶至第33阶是整体振动。损伤前后第1阶整体振动的固有频率变化很小,损伤后只减小1%左右,但是,第2阶的固有频率损伤后最大的减少达到35%,第6阶开始固有频率减少趋于变小。特征矢量 U_y 在损伤部位损伤前后只是第2阶有比较大的变化,其他各阶变化甚小,因此用第2阶的固有频率和特征矢量 U_y 可以检测损伤,文中用第1,2,3阶整体振动的振型经正规化后的特征参数检测损伤,第2阶的位移特征参数 U_y~*在五种损伤状态检测能力都明显提高。同时还用第1、2阶整体振动的模态柔度比法检测损伤,得到五种损伤状态下第2阶的模态柔度比大大高于第1阶的模态柔度比的检测能力。因此提出用第2阶模型参数检测损伤更为有效。     

利用模态柔度曲率差识别框架的损伤

采用结构模态参数进行损伤识别是研究较早，应用较多的无损探伤检测方法。提出了一种称为模态柔度曲率差的损伤检测指标。该指标利用模态柔度，不仅比频率和振型更敏感，而且对高阶模态的依赖大为减小。此外，曲率的采用也增加了其对损伤的敏感程度。对两个框架有限元模型进行了分析，详细比较了该指标和振型曲率改变率等其它一些指标在不同的损伤分布和损伤程度下的损伤识别效果，发现模态柔度曲率差识别效果最好，结果最稳定。     

框架结构损伤定位的比例柔度矩阵分解法试验研究

提出了基于比例柔度矩阵LU分解的结构损伤定位方法。该方法从结构振动响应入手,首先识别出结构前几阶模态振型和频率,构建结构比例柔度矩阵;然后对损伤前后的比例柔度矩阵差进行LU分解;最后基于U矩阵和曲率方法构建损伤指标对损伤进行定位。基于某20层框架结构进行了数值模拟损伤定位研究;并在实验室设计、建造一个6层集中质量剪切型框架模型,基于该模型分别进行了振动台试验和脉冲激励试验。模拟和试验下的单损伤和多损伤工况结果均表明:提出的方法能准确地对结构损伤进行定位。该方法只需要损伤前后测点的振动响应数据,不需要结构有限元模型,避免了复杂的结构有限元模型建模和模型修正工作;并且构建一个满足精确度的比例柔度矩阵只需要结构的前几阶低阶模态参数,而低阶参数的识别准确性相对较高,这些优点均为该方法的工程应用奠定了基础。     

基于秩分析的结构损伤识别研究

研究了结构损伤与系统矩阵秩变化之间的对应关系,以此为基础提出一种损伤识别方法。首先分析了结构损伤所引起的系统矩阵秩的变化,然后利用结构损伤前后的静力响应方程,推导了柔度扰动量的限定秩解计算公式,再结合柔度扰动新方法计算结构各单元损伤参数,据此确定损伤位置及损伤程度。研究表明,损伤前后结构静力位移差向量之间必然存在着线性相关性,因此,施加静力荷载的组数并非越多越好,而是只要大于柔度扰动矩阵的秩即可。由该方法所获得的柔度扰动量的限定秩解,是一种理论上的精确解,以它为基础可以获得很高精度的损伤识别结果。以桁架结构为例对所提方法进行了验证,结果表明了本文方法的可行性。     

基于模态参数进行连续梁损伤诊断的数值研究

以一矩形等截面二跨梁有限元模型为研究对象,通过数值模型,利用梁损伤前后一阶振型的改变率、前四阶振型曲率的绝对差值以及两个特征参数,分别实现了连续梁的损伤诊断。     

基于模态柔度曲率的损伤检测方法

由于模态柔度对结构损伤的高灵敏性,各种基于模态柔度的检测指标在结构无损探伤NDE(Nondestructive Damage Evaluation)中应用较多,如模态柔度差、模态柔度改变率和均匀荷载面曲率差等。这些指标经应用验证都具有一定的有效性。在此基础上,采用模态柔度曲率的改变构建一种新的指标,称为模态柔度曲率差(MFC)。尽管均匀荷载面曲率差也采用曲率,但不同的是它先将模态柔度矩阵按行加起来,再求损伤前后的曲率差。而提出的模态柔度曲率差则按列计算损伤前后模态柔度矩阵的曲率差,然后挑选每列里面最大的值作为指标。采用一个简支梁和一个四跨连续梁为算例,考虑各种损伤情况,将该指标与模态柔度差、模态柔度改变率和均匀荷载面曲率差、以及振型曲率改变率等指标进行了比较,证明了模态柔度曲率差检测损伤的有效性和优越性。     

应振型损伤特征量在混凝土结构损伤诊断中的应用

为检测混凝土构件损伤的出现、损伤位置及损伤程度，本利用位移振型特征量推导了相应的应变振型特征量，并利用Matlab软件编制了混凝土悬臂梁的有限元振动计算程序，对混凝土悬臂梁在发生损伤前后的位移和应变振型特征量进行了仿真计算。结果表明，位移和应变振型特征量均可确定混凝土悬臂梁上存在的损伤，并可确定损伤位置。应变振型特征量较位移振型特征量对损伤更敏感，可用于混凝土构件的损伤检测。     

基于模态柔度矩阵的结构损伤识别

基于模型修正技术的结构损伤识别方法,无需事先知晓结构的损伤位置,比仪器直接探测更具优势。模型修正大多以模态频率和振型为修正目标。然而,结构损伤对系统的模态频率和振型影响较小,采用模态频率和振型为目标的传统修正方法,难以识别出结构的损伤。为此,引入对结构损伤极为灵敏的模态柔度矩阵,研究以模态柔度矩阵为目标函数的损伤识别方法。选取某带孔的矩形长铁片为研究对象,沿其纵向等分为31块,计算模态柔度矩阵关于各等效模量相对量的灵敏度。结合灵敏度矩阵,利用实测和有限元模型间的柔度矩阵残差建立目标函数,并引入正则化方法求解目标函数的超定方程组。经过9次迭代目标函数收敛,损伤识别结果与实际值保持高度一致,从而验证该方法的正确性和实用性。     

基于柔度的钢桁架结构损伤识别方法

提出了一种用于结构损伤识别的新方法--柔度曲率幅值突变系数法.该方法在不需已知结构损伤前完好状态结构动力参数的情况下,仅对当前情况进行测试得到结构的前几阶频率和振型即可求出结构的柔度曲率幅值突变系数,根据这一参数即可找到结构损伤的位置并确定结构损伤的程度.本文通过利用DASP软件对一个平面钢桁架模型进行实测得到实验数据,对这一理论进行验证,得到了较好的效果.     

基于柔度差曲率矩阵的结构损伤识别方法

柔度是较频率和位移模态更敏感的结构损伤标示量。提出利用结构损伤前、后的柔度矩阵,先后对柔度矩阵差的列、行进行两次差分,求得柔度差曲率矩阵(δFlexibility Curvature Matrix),并以其对角元素作为检测结构损伤指标(δFCMD)的新方法。该方法仅需低阶模态参数即可进行损伤检测,不论对简支梁、悬臂梁、固支梁,或多跨连续梁,单一位置损伤、支撑处损伤、轻微损伤,还是多种损伤共存,均具有损伤定位的能力、并能定性反映损伤程度。通过与已有的柔度差、柔度变化率、均匀荷载面曲率差等柔度指标的数值模拟分析研究,显示了该指标检测损伤的有效性和优越性。     

Torsional vibrations of circular elastic plates with thickness steps

This paper presents a theoretical study of torsional vibrations in isotropic elastic plates. The exact solutions for torsional vibrations in circular and annular plates are first reviewed. Then, an approximate method is developed to analyze torsional vibrations of circular plates with thickness steps. The method is based on an approximate plate theory for torsional vibrations derived from the variational principle following Mindlin's series expansion method. Approximate solutions for the zeroth- and first-order torsional modes in the circular plate with one thickness step are presented. It is found that, within a narrow frequency range, the first-order torsional modes can be trapped in the inner region where the thickness exceeds that of the outer region. The mode shapes clearly show that both the displacement and the stress amplitudes decay exponentially away from the thickness step. The existence and the number of the trapped first-order torsional modes in a circular mesa on an infinite plate are determined as functions of the normalized geometric parameters, which may serve as a guide for designing distributed torsional-mode resonators for sensing applications. Comparisons between the theoretical predictions and experimental measurements show close agreements in the resonance frequencies of trapped torsional modes.     

高轴压比、低剪跨比双钢板-混凝土组合剪力墙拟静力试验研究

双钢板-混凝土组合剪力墙可减小墙体厚度、提高承载力和延性,为研究双钢板-混凝土组合剪力墙高轴压比下的抗震性能,完成了5个剪跨比为1.0的双钢板-混凝土组合剪力墙试件的拟静力试验,研究了剪力墙在低周往复荷载作用下的受力性能和破坏模式等,分析了轴压比、距厚比等因素对抗震性能的影响。试验结果表明:低剪跨比试件发生弯剪破坏;墙体钢板在平均位移角1/83时发生局部屈曲,初始屈曲形态受距厚比影响显著;试件峰值荷载、位移延性系数、刚度等受轴压比、距厚比的影响较小;试件平均极限位移角达1/72、平均有效破坏位移角达1/52,具有良好的变形能力;距厚比增大,试件滞回性能稳定性降低;试件耗能随变形增大而迅速增长,抗震性能良好。建议低剪跨比双钢板-混凝土组合剪力墙轴压比限值取0.7。     

Generalized thermoelastic waves in spherical curved plates without energy dissipation

In this article, the propagation of thermoelastic waves in orthotropic spherical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green–Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The theoretical formulation is based on the linear GN thermoelastic theory. The coupled wave equation and heat conduction equation expressed by the displacement and temperature are obtained. By the Legendre orthogonal polynomial series expansion approach, the coupled controlling equations are solved. The convergence of the method is demonstrated through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding purely elastic spherical plate are also shown to analyze the influence of thermoelasticity on elastic modes. The displacement, temperature and stress distributions of both elastic modes and thermal modes are calculated to show their differences. A thermoelastic spherical plate with a different ratio of radius to thickness is considered to show the influence of the ratio on the characteristics of thermoelastic waves.     

三维编织复合材料与金属胶接结构的力学性能及优化

通过试验和理论研究了三维编织纤维增强树脂基复合材料（FRP）与钢板的单搭粘结性能。建立了三维编织复合材料和钢板的单搭粘结有限元模型,并基于内聚区模型和Hashin破坏准则来模拟胶接层及三维编织复合材料的破坏,分别从极限载荷、破坏位移和破坏模式三方面将计算结果与试验结果进行对比,验证了有限元模型的有效性。在此模型基础上,研究了胶层厚度、粘结长度对单搭粘结极限载荷和破坏位移的影响,并提出针对不同工况下的优化方案选择的建议。最后建立了一种新型连接结构,相比较于原有单搭接连接方式,其拉伸强度和弯曲强度均有了较大提升。     

非规则梁桥的振型重要性指标研究

针对非规则梁桥的振型重要性指标进行研究。首先,通过理论分析,确定在判断振型重要性方面,传统的振型质量参与系数存在缺点,并定义了振型位移贡献、振型位移贡献系数、振型位移贡献比例等新指标。然后,针对一座典型的非规则梁桥,通过振型质量参与系数分析和振型位移贡献系数分析的对比研究,确定采用振型位移贡献比例判断振型重要性,更加合理。最后,通过多座桥梁的参数分析,验证了振型位移贡献比例比质量参与系数更加优越。研究结果表明:振型质量参与系数仅能反映振型对于结构总体动力反应的重要性,而不能明确反映振型对于结构局部动力反应的重要性;振型位移贡献比例能弥补这一缺陷,可以作为振型重要性的指标;当前n阶振型位移贡献比例之和超过80%时,以前n阶振型为基础得到的结构位移可以满足非规则梁桥计算精度的需要。     

Exact three-dimensional free vibration analysis of thick homogeneous plates coated by a functionally graded layer

Exact closed-form solutions are carried out for both in-plane and out-of-plane free vibration of thick homogeneous simply supported rectangular plates coated by a functionally graded (FG) layer, based on three-dimensional elasticity theory. The elasticity modulus and mass density of the FG coating are assumed to vary exponentially through the thickness of the coating layer, whereas Poisson’s ratio is remaining constant. The equations of motion are solved using two proposed displacement fields for the in-plane and out-of-plane vibration modes. By inserting the displacement fields in the 3-D elasto-dynamic equations, some independent ordinary equations are obtained and solved analytically. Natural frequencies are extracted by satisfying boundary conditions of interface and surfaces of the structure. The solution procedure is validated by comparing the obtained results with corresponding results of a 3-D finite element analysis. Finally, the influence of the FG coating layer on the natural frequencies of the structure is investigated and discussed. Clearly, the present closed-form solutions can exactly predict both in-plane and out-of-plane vibration modes of thick FG coated plates.     

复合材料层合板的声辐射模态幅值分析

低频时, 控制振动结构第一阶声辐射模态伴随系数可有效控制总声功率。通过分层有限元模型可以求解层合板的位移模式。对层合板的固有频率和动态响应进行了理论推导。结合声辐射模态理论, 研究了层合板铺设角度、 弹性模量比、 跨厚比以及阻尼比等结构参数对层合板结构第一阶声辐射模态伴随系数的影响。计算结果表明, 分层理论结合有限元方法可以较准确地计算层合板固有频率, 而且铺设角度和跨厚比对层合板结构声辐射模态影响较大。     

超声导波混频表征和定位早期局部损伤的研究进展

超声导波具有远距离传输的特性，能够快速、有效地大范围检出薄板中的损伤或缺陷。非线性超声导波相较于传统超声导波，主要研究基波与材料中微观组织演化相互作用而产生的高阶谐波，对尺寸远小于基波波长的损伤或缺陷比较敏感。其中，超声导波的二次谐波相对容易激发，已被用于定量评估早期损伤。但是，超声导波的二次谐波容易受到测量系统非线性的干扰，并且无法定位材料中的局部损伤。超声导波混频在频率、模式、传播方向的选择上具有一定的灵活性，克服了二次谐波的缺点。目前，超声导波混频在理论、模拟和实验上取得了一定的进展，已被用于表征和定位金属材料中处于早期阶段的疲劳、热老化、微裂纹、冲击损伤和局部塑性变形等。高频段超声导波混频、兰姆波相向混频和非共线混频中差频谐波或和频谐波的传播性，以及更多类型损伤的定位和表征仍有待进一步研究。     

An extended layerwise/solid-element method of stiffened composite plates with delaminations and transverse crack

The stiffened composite plates with the transverse crack and delamination were studied in this paper, and an extended layerwise/solid-element (XLW/SE) method was developed. In the proposed method, the governing equations of composite plates and stiffeners were established based on the extended layerwise method and 3D solid elements, respectively. The final governing equation of stiffened composite plates is assembled by using the compatibility conditions and internal force equilibrium conditions at the joint interface between the plates and stiffeners. For the stiffened composite plates with damages, the XLW/SE method can obtain the local stress and displacement fields accurately and simulate the in-plane transverse cracks and delaminations simultaneously, considering complicated stiffeners without any assumptions. In the numerical examples, the results obtained by the proposed method are compared with those obtained by the 3D elastic models developed in the general finite element code, and the good agreements were achieved for the stiffened composite plates with/without delaminations and/or transverse crack.     

Thermal postbuckling analysis of fiber–metal laminated plates including interfacial damage

Considering the effects of interfacial damage, geometric nonlinearity and transverse shear deformation, thermal postbuckling of fiber–metal laminated plates including interfacial damage is analyzed in detail. Firstly, the Heaviside step function and higher order shear deformation functions are introduced into displacement field so that the damage degree can be characterized. Then, the shape functions can be determined by using the stress continuity conditions between interfaces and the stress boundaries on surfaces. By using the generalized variational principle, the thermal postbuckling equilibrium equations of fiber–metal laminated plates including interfacial damage are established. Finally, the thermal postbuckling problem is solved by adopting finite difference method and iteration method. In numerical examples, the effects of interfacial damage, width-to-thickness ratio and thermal load on the thermal postbuckling of fiber–metal laminated plates including interfacial damage are investigated.