大型水平轴风力机叶片气动弹性计算

给出了一种考虑几何非线性的大型风力机静、 动气动弹性一体化计算方法．采用涡尾迹方法进行风力机气动载荷计算．建立风力机风轮的三维壳模型．沿周向平均风力机叶片载荷并加载到结构模型进行非线性静气动弹性分析．基于动力学小扰动假设, 在静平衡构型下进行动力学线性化, 计算风轮固有振动特性．继而结合非定常涡尾迹方法计算风力机动气动弹性响应．计算了NH 1500叶片考虑几何非线性的静气动弹性位移和动气动弹性响应．结果表明,大型风力机叶片几何非线性较为明显地减小静气动弹性位移,同时降低动气动弹性的响应幅值．大型风力机气动弹性响应计算需要考虑几何非线性     

损伤粘弹性Timoshenko梁的拟静态力学行为分析

从考虑损伤的粘弹性材料——一种卷积型本构关系出发,应用Timoshenko梁的基本变形假设,建立损伤粘弹性Timoshenko梁的静、动力学行为研究的数学模型.分析了损伤粘弹性Timoshenko梁在阶跃载荷作用下的准静态力学行为,在Laplace域中得到了挠度和损伤的解析表达式．应用数值逆变换技术,考察了材料粘性参数对梁的挠度和损伤的影响,得到不同时刻损伤和挠度随时间的变化曲线．     

周期载荷下超弹性圆柱壳的动力响应

研究了不可压超弹性圆柱壳在内表面周期载荷及突加常值载荷作用下的运动与破坏等动力响应问题．通过对所得描述圆柱壳内表面运动的非线性常微分方程解的数值计算和动力学定性分析,发现存在一个临界载荷;当突加常值载荷或周期载荷的平均载荷值小于这一临界值时,圆柱壳的运动随时间的演化是周期性的或拟周期性的非线性振动,而当其大于这一临界值时,圆柱壳将被破坏．另外,准静态问题的解可作为突加常值载荷作用下系统动力响应解的不动点,且不动点的性质与动力响应解及圆柱壳运动的性质有关．讨论了圆柱壳的厚度和载荷等参数对临界载荷值和圆柱壳运动特性的影响．     

考虑大变形的刚-柔耦合旋转智能结构动力学分析

基于Hamilton原理对带端部质量的刚柔耦合旋转智能结构建立了耦合的非线性动力学模型．根据一阶近似耦合（FOAC）模型理论,通过有限元方法,得到了系统的有限维模型．模型中考虑了轴向、横向位移和转动角度的非线性几何效应,以及压电材料和结构的大变形及离心刚化效应．在有限元模型的基础上,建立了3种实际系统模型方程,分别是无压电层的结构,有压电层开环状态和闭环状态．最后基于简化模型的仿真结果显示出有端部质量和没有端部质量的差异,智能结构梁在闭环和开环的差异,高速旋转梁的离心作用及结构外加电载荷的动力响应．     

具有分数导数本构关系的粘弹性Timoshenko梁的静动力学行为分析

利用粘弹性材料的三维分数导数型本构关系,建立粘弹性Timoshenko梁的静、动力学行为研究的数学模型;分析Timoshenko梁在阶跃载荷作用下的准静态力学行为,得出了问题的解析解,考察了一些材料参数对梁的挠度的影响。基于模态函数讨论了粘弹性Timoshenko梁在横向简谐激励作用下的动力响应,并考察了剪切和转动惯性对梁振动响应的影响。     

具强迫项非线性梁方程解的渐近性

本文同时考虑纵横弯曲及粘性效应,建立了一类轴向载荷和横向载荷作用下的非线性粘弹性简支梁方程。利用Faedo-Galerkin法,证明了该方程解的存在唯一性,讨论了该方程解的渐近性,并给出了有界吸收集的存在性证明。     

聚合物材料损伤理论

本文研究了外界环境如载荷、温度、湿度、辐射、腐蚀介质、非相容介质等对聚合物材料变形的影响,给出了微分型和积分型损伤演化方程;讨论了非线性弹性体和非线性粘弹性损伤变形以及腐蚀损伤.给出了粘弹性损伤变分原理.     

不同边界条件对路基结构动力学响应的影响

分别采用静力人工边界、无限元边界、粘弹性动力人工边界和远置静力人工边界对承受交通载荷的典型路基结构进行有限元分析。以远置静力人工边界计算获得的路面竖向位移和面层底部拉应力时程曲线为参考解,揭示边界条件对路基结构动力学响应的影响。分析结果表明:边界条件对拉应力的影响很小,它们与参考解的最大误差为0.82%;静力人工边界下的位移时程曲线一直在参考解附近震荡,无限元边界下的位移解高于参考解,粘弹性动力人工边界下的路面位移与参考解最为接近。综合考虑位移和应力的精确度与CPU的计算时间,粘弹性动力人工边界为最佳的路基结构动力学分析边界条件。     

考虑损伤效应的正交各向异性板的弹塑性后屈曲分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程和损伤演化方程．基于经典非线性板理论,得到了考虑损伤效应的正交各向异性板的增量型非线性平衡方程,且采用有限差分法和迭代法进行求解．数值算例中,讨论了损伤演化、初始缺陷对正交各向异性板弹塑性后屈曲行为的影响．数值结果显示了弹塑性后屈曲与弹性后屈曲的不同,并且损伤和损伤演化对板的弹塑性后屈曲的影响不可忽略．     

饱和粘弹性土层中端承桩纵向振动的轴对称解析解

基于弹性和饱和多孔介质理论,将桩和饱和土层分别视为单相弹性介质和饱和粘弹性介质,利用Helmholtz分解和变量分离法,在频率域研究了饱和粘弹性土层中端承桩纵向振动的动力特性,给出了饱和粘弹性土层中桩纵向振动时动力响应的轴对称解析解及桩头复刚度的解析表达式．通过数值计算,给出了桩头动刚度因子和等效阻尼随激励频率的响应,考察了饱和土物性参数、桩土模量比、桩长径比、桩Poisson比等参数对桩头刚度因子和阻尼的影响．研究表明:由于考虑了桩的径向变形效应以及饱和粘弹性土层对桩的径向力作用,轴对称精确解的桩头动刚度因子和阻尼分别与经典Euler-Bernoulli杆模型桩的桩头动刚度因子和阻尼有较大的区别,特别是在若干激励频率处．因此,经典Euler-Bernoulli杆模型桩的适用性具有一定的局限,更加精确的分析应采用三维精确模型．     

具损伤压电智能层合板的非线性主动控制和损伤监测

基于Hamilton原理、高阶剪切变形板理论、von Krmn型几何非线性应变-位移关系以及应变能等效原理,考虑压电层的质量和刚度及复合材料层内的损伤效应,建立了具损伤压电智能层合板的非线性运动方程．采用耦合正、逆压电效应的负速度反馈控制原理,形成闭环控制回路,实现了对压电智能层合板的主动控制和损伤监测．数值计算中,以四边简支面内不可动的层合矩形板为例,讨论了压电层位置对振动控制的影响,以及损伤程度和损伤位置对传感层输出电压的影响,提出一种损伤监测的方法．     

Quasi-three-dimensional theory for solution of dynamic thermoelastic problem of laminated composite plates

An uncoupled dynamic thermoelastic problem for laminated composite plates has been considered. The hypotheses used take into account the nonlinear distribution of temperature and displacements over the thickness of a laminated plate. On the basis of these hypotheses a quasi-three-dimensional (layerwise) theory is constructed that makes it possible to investigate the internal thermal and stress-strain states, as well as the edge effects of the boundary layer type for laminated plates. Systems of the heat conduction and motion equations are derived using the variational method. The order of the equations depends on the number of layers and terms in expansions of temperature and displacements of each layer. An analytical solution of the dynamic thermoelastic problem is presented for a cross-ply laminated rectangular plate with simply supported edges. The reliability of the results is confirmed by a comparison with the known exact solutions. The results based on the proposed theory can be used for verifying various two-dimensional plate theories when solving the dynamic thermoelastic problems for laminated composite plates.     

考虑地基耦合效应含裂纹中厚矩形板的非线性振动分析

基于Reissner板理论和Hamilton变分原理,建立了双参数地基上具有表面横向贯穿裂纹的中厚矩形板的非线性运动控制方程.在周边自由的条件下,提出了一组满足问题全部边界条件和裂纹处连续条件的试函数.且利用Galerkin法和谐波平衡法对方程进行求解,分析了考虑地基耦合效应的中厚矩形裂纹板的非线性振动特性.数值计算中,讨论了不同裂纹位置、裂纹深度、板的结构参数和地基物理参数对弹性地基上具裂纹的四边自由中厚矩形板的非线性幅频响应的影响.     

轴向运动粘弹性板的横向振动特性

研究了轴向运动粘弹性矩形薄板的动力特性和稳定性问题．从二维粘弹性微分型本构关系出发,建立了轴向运动粘弹性板的运动微分方程．采用微分求积法,对四边简支、一对边简支一对边固支两种边界条件下粘弹性板的无量纲复频率进行了数值计算．分析了薄板的长宽比、无量纲运动速度及材料的无量纲延滞时间对其横向振动及稳定性的影响．     

Damping sources interactions in impact of viscoelastic composite plates with damping treated SMA wires,using a hyperbolic plate theory

In the present paper, a comprehensive study is made on effects of the viscoelastic and the phase-transformation-based dissipations and their interactions on impact responses of viscoelastic composite plates with damping treated (structural hierarchy) shape memory alloy (SMA) wires, for the first time. In contrast to almost all of the available researches, a high-order hyperbolic plate theory that includes not only odd but also even functions of the transverse coordinate, is proposed and employed here. While a hierarchical viscoelastic constitutive law is employed for both the orthotropic and SMA materials, Brinson's constitutive law is refined to include the loading fluctuations and structural hierarchy of the SMA wire, simultaneously. The traditional Hertz and Yang-Sun contact laws are modified accordingly. The resulting highly nonlinear piecewise-defined integro-differential finite element governing equations are solved by an iterative algorithm within each time step. The presented discussions show that in contrast to the common belief, the zero-shear traction condition on the top and bottom surfaces of the viscoelastic orthotropic plate cannot be satisfied by the available plate theories, even for the symmetric lamination schemes. Results show that the viscoelasticity and phase-transformation effects on the resulting dynamic responses are more pronounced for the low and high energy impacts, respectively.     

面内平动黏弹性板非线性振动的内-外联合共振

研究了同时存在受迫共振和1∶3内共振时的面内平动黏弹性板的横向非线性振动问题．板的黏弹性材料用Kelvin本构关系描述．基于系统的运动方程和四边简支的边界条件,对偏微分方程应用直接多尺度法建立了联合共振时的可解性条件．应用Routh-Hurvitz判据对系统幅频响应的稳定性进行了判别．给出了黏弹性系数、面内平动速度和激励幅值3个参数对幅频响应的影响．最后,应用微分求积数值方法验证了近似解析方法的结论.     

Analysis of the effects of a pulsed electromagnetic field on the dynamic response of electrically conductive composites

The effects of pulsed electromagnetic fields on the dynamic mechanical response of electrically conductive anisotropic plates are studied. The analysis is based on the simultaneous solving of the system of nonlinear partial differential equations that include equations of motion and Maxwell’s equations. Physics-based hypotheses for electro-magneto-mechanical coupling in anisotropic composite plates and dimension reduction solution procedures for the nonlinear system of the governing equations are presented. A numerical solution procedure for the resulting two-dimensional nonlinear system of the governing equations has been developed and consists of the sequential application of time and spatial integration and quasilinearization. The developed methodology is applied to the problem of the dynamic response of a long current-carrying unidirectional carbon fiber polymer matrix composite plate subjected to transverse impact load and in-plane pulsed electromagnetic load. The interacting effects of the pulsed electric current, external magnetic field, and mechanical load are studied.     

The postbuckling analysis of laminated circular plate with elliptic delamination

Based on the Von Karman plate theory, considering the effect of transverse shear deformation, and using the method of the dissociated three regions, the postbuckling governing equations for the axisymmetric laminated circular plates with elliptical delamination are derived. By using the orthogonal point collocation method, the governing equations, boundary conditions and continuity conditions are transformed into a group of nonlinear algebraically equation and the equations are solved with the alternative method. In the numerical examples, the effects of various elliptical in shape, delamination depth and different material properties on buckling and postbuckling of the laminated circular plates are discussed and the numerical results are compared with available data.     

Local radial basis function collocation method for bending analyses of quasicrystal plates

The local radial basis function collocation method (LRBFCM) is proposed for plate bending analysis in orthorhombic quasicrystals (QCs) under static and transient dynamic loads. Three common types of the plate bending problems are considered: (1) QC plates resting on Winkler foundation (2) QC plates with variable thickness and (3) QC plates under a transient dynamic load. According to the Reissner–Mindlin plate bending theory, there is allowed to simulate the behavior of the two excitations in QC plates, phonon and phason, by 2D strong formulations for the system of governing equations. The governing equations, which describe the phason displacements, are based on Agiasofitou and Lazar elastodynamic model. Numerical results demonstrate the effect of the elastic foundation, as well as plate thickness on the phonon and phason characteristics in this paper. For the transient dynamic analysis, the influence of the phason friction coefficients on the responses of QC plate to transient dynamic loads is also studied.