密集模态挠性结构传感器/作动器的优化配置

在适当的假设条件下,推导出了压电作动器产生的弯矩与输入电压的关系式及压电传感器输出电压与输入弯矩的关系,进而得到H型密集模态挠性板模型的状态空间表达式,并由此模型出发,采用一种基于能量的传感器/作动器的优化配置策略,该准则可以很自然地研究整个动态模型的可控性和可观性,进而确定传感器/作动器的位置。针对H型密集模态挠性板振动主动控制的数值仿真表明了该准则的有效性。     

TORSIONAL VIBRATIONS OF RIGID CIRCULAR PLATE ON TRANSVERSELY ISOTROPIC SATURATED SOIL

An analytical method was presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil. By Hankel transform, the dynamic governing differential equations for transversely isotropic saturated poroelastic medium were solved. Considering the mixed boundary-value conditions, the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established. By appropriate transform, the dual integral equations were converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficient, the torsional angular amplitude of the foundation and the contact shear stress were expressed explicitly. Selected examples were presented to analyse the influence of saturated soil's anisotropy on the foundation's vibrations.     

A Comment on Governing Equations of Envelope Surface Created by a Two-Dimensional Directional Wavepacket Centered around a Propagation Direction on an Elastic Plate

Plates are common structural elements of most engineering structures, including aerospace, automotive, and civil engineering structures. The study of plates from theoretical perspective as well as experimental viewpoint is fundamental to understanding of the behavior of such structures. The dynamic characteristics of plates, such as natural vibrations, transient responses for the external forces and so on, are especially of importance in actual environments. In this paper, we consider natural vibrations of an elastic plate and the propagation of a wavepacket on it. We derive the two-dimensional equations that govern the spatial and temporal evolution of the amplitude of a wavepacket and discuss its features. We especially consider a directional wavepacket on an elastic plate, which propagation direction is centered around a main direction, but which wavenumber and frequency are fixed by a certain value. The fact that its envelope becomes time-invariant and is governed by the Schrödinger–Nohara type equation is shown.     

用局部Petrov-Galerkin法分析薄板自由振动

利用薄板振型方程的等效积分弱形式和对振型函数采用移动最小二乘近似函数进行插值，本文进一步研究了无网格局部Petrov-Galerkin方法在薄板自由振动问题中的应用。它不需要任何形式的网格划分，所有的积分都在规则形状的子域及其边界上进行。在插值近似时，采用虚拟-实际节点值变换方法直接引入本质边界条件。通过数值算例和与其他方法的结果进行比较，表明无网格局部Petrov-Galerkin法求解弹性薄板自由振动问题具有收敛性好、精度高等一系列优点。     

刚塑性圆板受水下爆炸载荷时的动力响应

分析了简支刚塑性圆板受水下爆炸载荷时的塑性动力响应。考虑到流固耦合作用，应用Taylor平板理论求水下爆炸压力，用刚塑性法分析了圆板的永久变形场，引入膜力因子考虑了圆板大变形时的膜力效应。计算结果同用ABAQUS程序的计算结果进行了比较，表明不考虑空泡时所得结果较精确。最后考察了流固耦合作用及空泡对结构响应的影响。     

Nonlinear analyses of wrinkles in a film bonded to a compliant substrate

Subject to a compressive membrane force, a film bonded to a compliant substrate often forms a pattern of wrinkles. This paper studies such wrinkles in a layered structure used in several recent experiments. The structure comprises a stiff film bonded to a compliant substrate, which in turn is bonded to a rigid support. Two types of analyses are performed. First, for sinusoidal wrinkles, by minimizing energy, we obtain the wavelength and the amplitude of the wrinkles for substrates of various moduli and thicknesses. Second, we develop a method to simultaneously evolve the two-dimensional pattern in the film and the three-dimensional elastic field in the substrate. The simulations show that the wrinkles can evolve into stripes, labyrinths, or herringbones, depending on the anisotropy of the membrane forces. Statistical averages of the amplitude and wavelength of wrinkles of various patterns correlate well with the analytical solution of the sinusoidal wrinkles.     

Asymmetric vibrations and stability of a rotating annular plate loaded by a torque

The paper investigates transverse vibration of a thin annular plate clamped at its inner edge to a rigid shaft, while its outer edge is clamped to a rigid cylinder. The shaft and the outer edge of the plate are loaded by torques of the same intensity, but of opposite directions. The whole structure rotates at a constant angular speed. The solution has been determined using Galerkin’s method. The obtained results illustrate the impact of the torque, angular speed and inner and outer radia ratio to transverse asymmetric vibration frequency of the plate. Stability of the plate has been examined and critical values of angular speed and torque leading to the loss of stability of the plate have been determined. Some mode shapes have been drawn and the influence of torque and angular speed on nodal lines has been shown.     

带剪切型压电激励器的板的高阶剪切变形理论

利用压电材料固有的正，逆压电效应可以对结构变形和振动进行控制。与外加电场与极化方向平行于板厚度的压电材料的拉伸作动机制相比，外加电场与极化方向垂直的压电材料的剪切作动机制可以在作动器内产生较小的应力，从而降低作动器边界产生分层破坏的危险。本文对于压电材料的剪切作动机制进行研究，应用三阶剪切变形理论建立带剪切型压电激励器的智能层合板模型。采用哈密顿原理导出带剪切型压电激励器的层合板的控制方程。采用空间法得到了各种边界条件组合条件下板的解析解。数值算例对一三层板采用高阶和一阶剪切变形理论进行计算，结果表明两种理论所得的变形曲线很相似。但对于厚度剪切型激励器而言，由于激励器是引起板的剪切变形，而高阶剪切变形理论比一阶剪切变形理论能更好地反映结构的剪切应变能，因此高阶剪切变形理论可以提供板变形的更为精确的解。因此，对于厚度剪切型激励器，剪切变形理论的选取对于板变形结果的好坏有重要的作用。     

一种高阶非线性钢筋混凝土平板单元

在文献［１］高阶钢筋混凝土膜元的基础上，提出了一种具有１４个节点的高阶钢筋混凝土平板单元．钢筋混凝土材料模型仍采用Ｖｅｃｃｈｉｏ的抹平旋转裂缝模型，几何非线性仍采用所谓总体Ｌａｇｒａｎｇｅ列式法，非线性方程采用割线刚度位移增量迭代法．数值算例表明本文的方法是可靠的，高阶平板单元虽然列式复杂，但与低阶元相比，其计算量要少且精度要高     

软铁磁薄板磁弹性耦合作用的变分原理

研究磁弹性耦合问题的关键是正确计算作用在铁磁弹性体上的磁力，该文以磁场系统的磁能与磁介质弹性板应变能之和作为软铁磁薄板位于外加磁场合作用系统的能量泛函，以磁标势函数和位移函数的变分为独立变量，给出软铁磁薄板在任意外磁场中磁弹性耦俣作用变分原理，由此不仅导出磁和结构变形的联立控制方程，而且获得作用在薄板上的磁力表达式，进而可以对两类不同性质的铁磁板耦合作用的实验现象进行理论模拟