压电材料椭圆夹杂界面开裂问题的电弹性耦合解

本文研究了在反平面剪切和面内电场的共同作用下，压电材料椭圆夹杂的界面开裂问题，假定夹杂是刚性的导体，采用复变函数保角变换和级数展开方法，可确定压电材料基体的复势表达式，进而求得夹杂界面开裂的电弹性耦合的能量释放率。     

Localized solutions to the nonlinear wave equation for flexural motions of an elastic beam traveling in an air-filled tube

Steady-progressive-wave solutions are sought to the nonlinear wave equation derived previously [J. Fluids Struct. 16 (2002) 597] for flexural motions of an elastic beam traveling in an air-filled tube along its center axis at a subsonic speed. Fluid-structure interactions are taken into account through aerodynamic loading on the lateral surface of the beam subjected to small but finite deflection but end effects and viscous effects are neglected. Linear dispersion characteristics are first examined by exploiting the small ratio of the induced mass to the mass of the beam per unit length. Centered around the traveling speed of the beam, there exists such a narrow range of propagation velocity that the linear steady propagation is prohibited. In this range, it is revealed that some interesting nonlinear solutions exist. The periodic wavetrain is found to exist as the exact solution. Asymptotic analysis is then made by applying the method of multiple scales and the stationary nonlinear Schrödinger equation is derived for a complex amplitude. A monochromatic solution to this equation corresponds to the exact periodic solution. Imposing undisturbed boundary conditions at infinity, it is revealed that the localized solution exists as a result of balance between the linear instability and the nonlinearity. This solution is checked by solving the nonlinear equation numerically. It is further revealed that the amplitude-modulated wavetrain exists not only in the range of the velocity mentioned above but also outside of it.     

Principal parametric and three-to-one internal resonances of flexible beams undergoing a large linear motion

A set of nonlinear differential equations is established by using Kane‘s method for the planar oscillation of flexible beams undergoing a large linear motion. In the case of a simply supported slender beam under certain average acceleration of base, the second natural frequency of the beam may approximate the tripled first one so that the condition of 3 : 1 internal resonance of the beam holds true. The method of multiple scales is used to solve directly the nonlinear differential equations and to derive a set of nonlinear modulation equations for the principal parametric resonance of the first mode combined with 3 : 1 internal resonance between the first two modes. Then, the modulation equations are numerically solved to obtain the steady-state response and the stability condition of the beam. The abundant nonlinear dynamic behaviors, such as various types of local bifurcations and chaos that do not appear for linear models, can be observed in the case studies. For a Hopf bifurcation,the 4-dimensional modulation equations are reduced onto the central manifold and the type of Hopf bifurcation is determined. As usual, a limit cycle may undergo a series of period-doubling bifurcations and become a chaotic oscillation at last.     

Nonlinear Equations of Motion of an Extensible Underground Pipeline: Derivation and Numerical Modeling

Slow motion of a pipeline modeled by a bent rod in a viscous medium is studied. It is assumed that the displacements of the axial line of the rod are finite and its strains are small. The mutual influence of the tensile axial force and transverse deflections is taken into account. Equations of motion are derived and some numerical examples are considered. An approximate estimate of stresses in the pipeline wall is given.     

INVESTIGATION OF THE DYNAMIC BEHAVIOR OF TWO COLLINEAR ANTI-PLANE SHEAR CRACKS IN A PIEZOELECTRIC LAYER BONDED TO TWO HALF SPACES BY A NEW METOHD

IntroductionItiswell_knownthatpiezoelectricmaterialsproduceanelectricfieldwhendeformedandundergodeformationwhensubjectedtoanelectricfield .Thecouplingnatureofpiezoelectricmaterialshasattractedwideapplicationsinelectro_mechanicalandelectricdevices,suchaselectro_mechanicalactuators,sensorsandstructures.Whensubjectedtomechanicalandelectricalloadsinservice,thesepiezoelectricmaterialscanfailprematurelyduetodefects,e .g .,cracks,holds,etc.arisingduringtheirmanufactureprocess.Therefore,itisofgreatimp…     

一个改进的平面梁单元

根据有限单元法基本原理 ,提出了一个变截面平面梁单元 ,推导了其单元钢度矩阵。这一改进的梁单元用于分析梁高呈线性变化及二次抛物线变化的矩形截面梁 ,将得到准确解。文中给出了一个变截面悬臂梁算例 ,计算表明 ,这一改进的梁单元使变截面梁的分析大大简化     

Effects of static electric field on the fracture behavior of piezoelectric ceramics

The paper gives an overview on experimental observations of the failure behavior of electrically insulating and conducting cracks in piezoelectric ceramics. The experiments include the indentation fracture test, the bending test on smooth samples, and the fracture test on pre-notched (or pre-cracked) compact tension samples. For electrically insulating cracks, the experimental results show a complicated fracture behavior under electrical and mechanical loading. Fracture data are much scattered when a static electric field is applied. A statistically based fracture criterion is required. For electrically conducting cracks, the experimental results demonstrate that static electric fields can fracture poled and depoled lead zirconate titanate ceramics and that the concepts of fracture mechanics can be used to measure the electrical fracture toughness. Furthermore, the electrical fracture toughness is much higher than the mechanical fracture toughness. The highly electrical fracture toughness arises from the greater energy dissipation around the conductive crack tip under purely electric loading, which is impossible under mechanical loading in the brittle ceramics. The project supported by an RGC grant from the Research Grant Council of the Hong Kong Special Administrative Region, China     

ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

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自由梁受集中质量两点撞击的刚塑性动力响应

对矩形截面自由梁在两端同时受到完全相同的集中质量横向撞击问题进行了理论上的研究 ,通过采用刚塑性的材料模型得到了其动力响应完全解。结合数值方法给出了梁的瞬态变形 ,并讨论了输入能量、质量比等参数对梁的最终变形、能量耗散的影响。针对典型算例将完全解的结果与MSC/Dytran的计算结果进行了比较 ,两者具有合理的近似 ,但理论预测的结果略高估计了梁的最终变形。     

具有分支电路的可控压电阻尼减振技术

对近10年来国内外关于具有分支电路的可控压电阻尼减振技术研究的进展进行了较为详细的评述和讨论.文中首先说明了具有分支电路的压电阻尼减振技术的基本原理和基本形式,然后较为全面的评述不同形式基本分支电路压电阻尼系统的基本特点和研究进展,在讨论了以基本分支电路压电阻尼系统为基础的各种具有可控特性的分支电路压电阻尼系统(包括半主动的和主动-被动杂交的分支电路压电阻尼系统)的研究与发展之后,说明了这种技术在实际工程中的应用,最后建议了今后应深入研究的问题.