集成结构振动主动控制和抑制

采用一种新的压电板单元,建立了含有分布压电传感元件和执行元件的集成结构的有限元动力模型。研究了这种集成结构在常增益负速度反馈控制规律作用下,振动的主动控制与抑制的问题,并提出了集成结构振动主动控制和抑制的一般方法。最后,提供了数值示例,说明本文提出方法的有效性。     

A wavelet-based stochastic finite element method of thin plate bending

A wavelet-based stochastic finite element method is presented for the bending analysis of thin plates. The wavelet scaling functions of spline wavelets are selected to construct the displacement interpolation functions of a rectangular thin plate element and the displacement shape functions are expressed by the spline wavelets. A new wavelet-based finite element formulation of thin plate bending is developed by using the virtual work principle. A wavelet-based stochastic finite element method that combines the proposed wavelet-based finite element method with Monte Carlo method is further formulated. With the aid of the wavelet-based stochastic finite element method, the present paper can deal with the problem of thin plate response variability resulting from the spatial variability of the material properties when it is subjected to static loads of uncertain nature. Numerical examples of thin plate bending have demonstrated that the proposed wavelet-based stochastic finite element method can achieve a high numerical accuracy and converges fast.     

Nonlinear finite element analysis of functionally graded plates integrated with patches of piezoelectric fiber reinforced composite

In this paper, a nonlinear static finite element analysis of simply supported smart functionally graded (FG) plates in the presence/absence of the thermal environment has been presented. The substrate FG plate is integrated with the patches of piezoelectric fiber reinforced composite (PFRC) material which act as the distributed actuators of the plate. The material properties of the FG substrate plate are assumed to be temperature dependent and graded along the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The derivation of this nonlinear thermo-electro-mechanical coupled finite element model is based on the first order shear deformation theory and the Von Karman type geometric nonlinearity. The numerical solutions of the nonlinear equations of the finite element model are obtained by employing the direct iteration method. The numerical illustrations suggest the potential use of the distributed actuator made of the PFRC material for active control of nonlinear deformations of smart FG structures. The effects of volume fraction index of the FG material of the substrate plates and the locations of the PFRC patches on the control authority of the patches are investigated. Emphasis has also been placed on investigating the effect of variation of piezoelectric fiber orientation angle in the PFRC patches on their actuation capability for counteracting the large deflections of FG plates.     

Static and dynamic analysis of smart cylindrical shell

Shell type components and structures are very common in many mechanical and structural systems. In smart structural applications, piezolaminated plates and shells are commonly used. In this paper a finite element formulation is presented to model the static and dynamic response of laminated composite shells containing integrated piezoelectric sensors and actuators subjected to electrical, mechanical and thermal loadings. The formulation is based on the first order shear deformation theory and Hamilton's principle. In this formulation, the mass and stiffness of the piezo-layers have been taken into account. A nine-noded degenerated shell element is implemented for the analysis. The model is validated by comparing with existing results documented in the literature. A simple negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of an integrated structure through a closed control loop. The influence of the stacking sequence and position of sensors/actuators on the response of the laminated cylindrical shell is evaluated. Numerical results show that piezoelectric sensors/actuators can be used to control the shape and vibration of laminated composite cylindrical shell.     

Elasticity Solutions for Cylindrical Bending of Functionally Graded Piezoelectric Material Plates北大核心CSCD

功能梯度压电材料（FGPM）同时兼具功能梯度材料和压电材料特性,可为多功能或智能化轻质结构设计提供支撑,在诸多领域有着广泛的应用前景.将Mian和Spencer功能梯度板理论由功能梯度弹性材料推广到功能梯度压电材料,解析研究了FGPM板的柱面弯曲问题,其中,材料弹性常数、压电和介电参数沿板厚方向可以任意连续变化.最终,给出了FGPM板受横向均布荷载作用下柱面弯曲问题的弹性力学解.通过算例分析,重点讨论了压电效应对FGPM板静力响应的影响.     

在集中荷载作用下角支矩形板的弯曲

本文引用广义简支边的概念并应用迭加法,解有一集中力作用在角支矩形板的中线上任一点的弯曲问题,给出数值例子.     

Free vibration analysis of piezoelectric coupled annular plates with variable thickness

This paper presents the free vibration analysis of piezoelectric coupled annular plates with variable thickness on the basis of the Mindlin plate theory. No work has yet been done on piezoelectric laminated plates while the thickness is variable. Two piezoelectric layers are embedded on the upper and lower surfaces of the host plate. The host plate thickness is linearly increased in the radial direction while the piezoelectric layers thicknesses remain constant along the radial direction. Different combinations of three types of boundary conditions i.e. clamped, simply supported, and free end conditions are considered at the inner and outer edges of plate. The Maxwell static electricity equation in piezoelectric layers is satisfied using a quadratic distribution of electric potential along the thickness. The natural frequencies are obtained utilizing a Rayleigh–Ritz energy approach and are validated by comparing with those obtained by finite element analysis. A good compliance is observed between numerical solution and finite element analysis. Convergence study is performed in order to verify the numerical stability of the present method. The effects of different geometrical parameters such as the thickness of piezoelectric layers and the angle of host plate on the natural frequencies of the assembly are investigated.     

解任意四边形板弯曲问题的样条有限元法

关于用样条函数解板的弯曲问题,[1]在1979年讨论了矩形板和菱形板的弯曲;[2]在1981年对简支边界条件的矩形板,用振动梁函数和B样条函数组合作为插值函数,得到了效率更高的算式;[3]在1984年对[2]作了补充,采用拉格朗日乘子法,得到了在各种边界条件下平板弯曲的近似解,但所讨论的仍然是矩形板.     

A symplectic analytical wave propagation model for damping and steady state forced vibration of orthotropic composite plate structure

An analytical wave propagation model is proposed in this paper for damping and steady state forced vibration of orthotropic composite plate structure by using the symplectic method. By solving an eigen-problem derived in the symplectic dual system of free bending vibration of orthotropic rectangular thin plates, the wave shape of plate is obtained in symplectic analytical form for any combination of simple boundary conditions along the plate edges. And then the specific damping capacity of wave mode is obtained symplectic analytically by using the strain energy theory. The steady state forced vibration of built-up plates structure is calculated by combining the wave propagation model and the finite element method. The vibration of the uniform plate domain of the built-up plates structure is described using symplectic analytical waves and the connector with discontinuous geometry or material is modeled using finite elements. In the numerical examples, the specific damping capacity of orthotropic rectangular thin plate with three different combinations of boundary condition is first calculated and analyzed. Comparisons of the present method results with respect to the results from the finite element method and from the Rayleigh–Ritz method validate the effectiveness of the present method. The relationship between the specific damping capacity of wave mode and that of modal mode is expounded. At last, the damped steady state forced vibration of a two plates system with a connector is calculated using the hybrid solution technique. The availability of the symplectic analytical wave propagation model is further validated by comparing the forced response from the present method with the results obtained using the finite element method.     

样条有限元

本文用三次B样条变分方法解规则区域上板梁组合弹性结构的平衡问题.推导出了适用于各种边界条件的统一计算格式,便于在计算机上实现.与通常有限元相比,具有计算量少、精确度高等显著特点.文中对自然边界条件作为约束条件的影响给予了考虑,并以板的弯曲问题为例说明影响极微.给出了几个数值的例子.     

Hamilton等参元与智能叠层板的半解析法

根据压电材料修正后的Hellinger-Reissner(H-R)变分原理,建立了各向异性压电材料4节点Hamilton等参元的一般形式．为智能叠层板自由振动问题和带有压电块的叠层悬臂梁的瞬态响应等问题提出了一种新的半解析法．数学模型的基本步骤:将压电层和主体层看成独立的三维体,在平面内离散各层,分别建立各层的方程;根据主体层和压电层在连接界面上广义应力和广义位移的连续条件,联立主体层和压电层的方程得到全结构的控制方程．等参元不限制智能板侧面的几何边界形状、板的厚度和层数,有广泛的应用领域．     

周期性正弦凸起凹凸板等效刚度的研究

针对构造正交各向异性周期性正弦凸起结构凹凸板的等效刚度问题，根据经典弹性薄板理论，基于对单胞结构力学特性分析和单胞结构在板宏观结构上周期性均匀化分布的特点，推导了正弦凸起凹凸板的等效刚度解析公式.以四边简支周期性正弦凸起结构凹凸板为例，将该文计算结果与有限元模拟结果进行对比，验证了该文等效刚度的合理性和精确性.最后，分析了正弦凸起凹凸板几何参数对等效刚度特性的影响，给出了结构几何参数与等效刚度之间的关系.结果表明:应用该文方法可以有效计算周期性正弦凸起凹凸板的等效刚度；由于凹凸板在构造上的几何结构变化，与基础平板相比其弯曲刚度和抗扭刚度都有明显的提升.该研究结果对凹凸板静力学和动力学的进一步研究以及实际工程应用具有指导意义.     

Optimization of the static and dynamic characteristics of plates with isogrid stiffeners

In this paper, the orientation angles of stiffeners arranged in the form of isogrid configuration over a flat plate are selected to optimize the static and dynamic characteristics of these plates/stiffeners assemblies. The static characteristics are optimized by maximizing the critical buckling loads of the isogrid plate, while the dynamic characteristics are optimized by maximizing multiple natural frequencies of the stiffened plate.

A finite element model is developed to describe the statics and dynamics of Mindlin plates which are stiffened with arbitrarily oriented stiffeners. The model is used as a basis for optimizing separately or simultaneously the critical buckling loads and natural frequencies of the plates per unit volume of the plates/stiffeners assemblies.

Numerical examples are presented to demonstrate the utility of the developed model and optimization procedures. The presented approach can be invaluable in the design of plates with isogrid stiffeners for various vibration and noise control applications.     

Finite Element Modelling of Cracks Based on the Partition of Unity Method

In this paper a finite element model for the analysis of brittle materials in the post cracking regime is presented. The model allows the representation of failure zones several times smaller than the structure itself using relatively coarse finite element meshes. The formulation is based on the partition of unity method. Discontinuous shape functions are used to enrich the continuous approximation of the displacement field where a crack has opened [2]. The magnitude of the displacement jump is determined by extra degrees of freedom at existing nodes. The crack path is completely independent of the structure of the mesh and is continuous across element boundaries. To model inelastic deformations around the crack tip a cohesive crack model is used. A representative numerical example illustrates the performance of the proposed model.     

Modelling and control of a shell structure based on a finite dimensional variational formulation

A mathematical model of a controlled shell structure based on Hamilton’s principle and the generalized Ritz–Galerkin method is proposed in this paper. The problem of minimizing the stress energy is solved explicitly for a static version of this model. For the dynamical system under consideration, a procedure for estimating external disturbances and the state vector is derived. We also propose an observer design scheme and solve the stabilization problem for an arbitrary dimension of the linearized model. This approach allows us to perform control design for double-curved shells of complex geometry by combining analytical computation of the controller parameters with numerical data that represent the reference configuration and modal displacements of the shell. As an example, the parameters of our model are validated by results of a finite element analysis for the Stuttgart SmartShell structure.     

A simple four-node quadrilateral finite element for plates

A simple and accurate four-node quadrilateral finite element based on the Mindlin plate theory and Kirchhoff constraints is presented for general thin plate bending applications. The derivation of the element stiffness properties is straightforward, starting with a specified eight-node interpolation; usual discrete Kirchhoff (DK) constraints are employed to constrain out the four midside nodes of the element. The present resulting DK element passes patch tests with elements of arbitrary and even highly distorted mesh types. Numerical studies of the element convergence behaviours are undertaken for various plate bending problems so far investigated. It is indicated from comparative examples that fairly good convergence characteristics have been achieved.     

Extension of the scaled boundary finite element method to plate bending problems

The scaled boundary finite element method (SBFEM) is extended to the static analysis of thin plates in the framework of Kirchhoff's plate theory. The governing equations are transformed into scaled boundary coordinates. Applying a discrete form of the Kantorovich reduction method results in a set of ordinary differential equations, which can be solved in a closed-form analytical manner. The element stiffness matrices for bounded and unbounded media can be computed, using appropriate subsets of the analytical solution. Examples show the efficiency of the method, applied to plate bending problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

复合材料层合板的弯曲与振动

本文应用应力杂交有限元方法分析了复合材料层合板的弯曲与振动.在本文中,首先根据修正的余能变分原理,构造了一个适合于复合材料层合板特点的矩形应力杂交板弯曲单元.在单元内,分层假设应力参数,在单元的边界上,根据YNS理论的假设确定边界位移场.这样使得构造出来的单元不仅能够考虑横向剪切变形的影响和局部扭曲效应,而且具有较少的自由度数.其次,用此单元求解了层合板的弯曲与振动问题,并将计算结果与精确解进行了比较,比较表明二者非常接近.这说明了在计算方面本文单元具有较高的精确度.     

非均匀薄板弯曲的精确元法

本文在阶梯折算法的基础上,提出构造有限元的新方法——精确元法.它不用一般变分原理,可适用于任意变系数正定和非正定偏微分方程.利用该方法,得到薄板弯曲一个非协调三角形单元,它具有6个自由度.文中给出证明,位移和内力均收敛于精确解,并有很好的精度.文末给出算例.算例表明利用本文的方法,内力和位移均可获得满意的结果.     

自由边界问题的样条有限元法

本文讨论薄板弯曲自由边界问题的样条有限元法,对障碍问题和“弹塑性”弯曲问题,采用三次B样条元及二次多结点Hermite元,比较其优劣,证明离散解的收敛性.