粘弹层合板的稳态振动和层间应力

应用混合分层理论和Ressiner混合变分原理，在板厚方向取二次位移插值函数和三次、四次横向应力插值函数推导出粘弹层合板的动力学方程，得出简支粘弹层合板稳态振动的解。不仅得出与三层弹性板精确的自振频率吻合良好的解，而且对于粘弹层合板，所计算的自振频率和结构损耗因子也与三维结果吻合较好。计算了自由阻尼层合板对应的低阶法向位移响应幅值和层问横向应力的幅值。结果表明，较高的层间横向正应力是低频稳态振动中引起粘弹层合板分层破坏的主要因素，采用适当模量和厚度的粘弹性材料将有效地降低粘弹层合板的层间横向正应力的幅值。     

On the finite displacement analysis of quadrangular plates

In this paper, a numerical method for the linear and geometrically non-linear static analysis of thin plates is presented. The method begins with the elasticity equations pertaining to strain components, stresses, displacement components, strain energy and work due to externally applied loads. The plate geometry is defined by a quadrangular boundary with four straight edges and the natural coordinates in conjunction with the Cartesian coordinates are used to map the geometry. The matrix equation of equilibrium is derived using the work-energy principle with the displacement fields expressed by algebraic polynomials, the coefficients of which are then manipulated to satisfy the kinematic boundary conditions. To validate the results from the present method, square plates having all sides fully fixed and all sides simply supported without in-plane movement are analysed. Comparison is made for the uniformly loaded square plate with the results obtained by Levy who solved the non-linear plate bending problem using the Th.von Ka’rma’n’s equations. Rhombic plates are examined and numerical results corresponding to these cases are presented in this paper. Very good comparison of the results regarding deflection and bending stresses with other sources available in the literature is found.     

一种提高薄板稳定分析精度的方法

在薄板稳定分析中，九参数三角形薄板单元因其形状简单，使用方便，在实际工程中得到了广泛应用。本文基于参数调正的几何刚度矩阵，对九参数三角形薄板单元的一致刚度矩阵进行了修正，为提高计算精度提供了一种有效方法。     

Wavelet-Based Analysis of Parametric Vibrations of Flexible Plates

Wavelet-based methods are reviewed, and their advantages in comparison to standard approaches are outlined. Then, a wavelet analysis is performed to investigate parametric vibrations of flexible plates under a sinusoidal load. In particular, a scenario leading from regular motion to chaos is analyzed     

Interfacial stresses in curved members bonded with a thin plate

The use of steel plates or externally bonded fibre-reinforced polymer laminates for flexural strengthening of concrete, masonry, timber or metallic structures is a technique that has become very popular. The effectiveness of this technique hinges heavily on the performance of the bond between the strengthening plate and the substrate, which has been the subject of many existing studies. In particular, the interfacial stresses between a beam and a soffit plate within the linear elastic range have been addressed by numerous analytical investigations. Surprisingly, none of these investigations has examined interfacial stresses in members with a curved soffit, despite that such members are often found in practice. This paper presents an analytical model for the interfacial stresses between a curved member of uniform section size and a thin plate bonded to its soffit. The governing differential equations for the interfacial shear and normal stresses are formulated and then solved with appropriate simplifying assumptions. Two numerical examples are presented to illustrate the effect of the curvature of the member on the interfacial stress distributions in a simply supported curved beam for the two cases of a point load and a uniformly distributed load. The analytical solution is verified by comparing its predictions with those from a finite element model.     

非惯性参考系中弹性薄板动力系统在纵横振动相互耦合时的全局分岔及混沌性质

讨论非惯性参考系中弹性薄板动力系统１∶１内共振时的全局分岔及其混沌性质．首先对系统的奇点进行了分析，进而得到了奇点附近同宿轨的参数方程，再用Ｍｅｌｎｉｋｏｖ方法研究了系统的同宿轨分岔及其混沌运动．研究表明，对各种不同共振情形，系统将由同宿轨分岔过渡到混沌运动．最后用数值仿真证实了理论分析的结果．     

有初内力的板的内共振

本文利用非线性时空有限方法和样条有限元技术对具有初内力的板的非线性频响特性进行了分析，计算了在不同初始内力下方板的大振幅自由振动、有阻尼强迫振动和矩形板的内共振。     

非均匀圆柱型正交各向异性圆板的弯曲

研究了非均匀圆柱型正交各向异性圆板在均布横向载荷作用下的弯曲问题，求得了折算刚度随半径按指数规律变化的非均匀圆柱型正交各向异性圆板弯曲问题的渐近解，给出了周边固支和简支条件下的渐近解．通过算例可以看出，这种非均匀性对圆板中心挠度的影响是显著的     

Characterization of short duration stress pulses generated by impacting laminated carbon-fiber/epoxy composites with magnetic flyer plates

Short duration stress pulses are of particular interest in determining the interfacial crack tip instability criteria for the dynamic fracture behavior of laminated carbon-fiber/epoxy composites. However, the heterogeneous architectures of laminated composites can alter the characteristics of a stress pulse as it propagates toward a crack tip. This makes it difficult to use standard dynamic testing techniques for characterizing these materials, since these techniques assume the characteristics of the stress pulse do not change as a result of propagation and can therefore be unambiguously determined from impact conditions. This paper presents a novel experimental technique that has been developed for characterizing short duration stress pulse propagation in laminated composite materials. In this technique, a dynamic moiré interferometer is used to capture fringe patterns corresponding to displacement fields associated with short duration stress pulses that were generated by impacting 0° and 90°/0°/90° carbon-fiber/epoxy composites with a magnetic flyer plate. Appropriate dynamic testing conditions for capturing high fidelity fringe patterns were determined using the recently developed dynamic moiré fringe contrast factor. The effects of the composite architecture on the propagation of short duration stress pulses observed with the dynamic moiré interferometer were confirmed by transient dynamic finite element analysis. From comparisons of experimental and numerical data, it was determined that the impact conditions for the magnetic flyer plate and laminated composite will not necessarily be planar, which has a significant effect on the intensity and duration of the propagating stress pulse.     

An alternative alpha finite element method with discrete shear gap technique for analysis of laminated composite plates

This paper presents an alternative alpha finite element method using triangular meshes (AαFEM) for static, free vibration and buckling analyses of laminated composite plates. In the AαFEM, an assumed strain field is carefully constructed by combining compatible strains and additional strains with an adjustable parameter α which can produce an effectively softer stiffness formulation compared to the linear triangular element. The stiffness matrices are obtained based on the strain smoothing technique over the smoothing domains and the constant strains on triangular sub-domains associated with the nodes of the elements. The discrete shear gap (DSG) method is incorporated into the AαFEM to eliminate transverse shear locking and an improved triangular element termed as AαDSG3 is proposed. Several numerical examples are then given to demonstrate the effectiveness of the AαDSG3.