矩形夹层板稳定性分析

本文在Reissner 理论基础上,应用功的互等定理推导了夹层矩形板稳定问题的基本解,在已推导出的夹层板基本解的基础上,利用功的互等法求解了两对边固定一边简支一边自由、两邻边简支另两邻边自由且角点支承、两邻边简支另两邻边自由且角点悬空三种不同边界条件下夹层板的稳定问题,给出了挠曲面方程及其对应的执行方程;进行了数值计算,并与有限元结果进行对照分析．结果表明：本文方法求解过程更简单,提供了一种求解夹层板稳定问题的新方法,计算结果对解决工程实际问题具有一定的参考价值．     

Transverse vibration of rectangular plates elastically supported at points on edges

This paper studies transverse vibration of rectangular plates with two opposite edges simply supported, other two edges arbitrarily supported and free edges elastically supported at points. A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular plates elastically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourier series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given. Inherent frequencies and mode shape with any accuracy can be gained.     

Airy stress function for describing the non-linear effect of simply supported plates with movable edges

The general form of the solution of the Airy function for the stress distributions that describe the non-linear effect developed from the large deflection of simply supported plates with movable edges are found by superposition of the Airy functions, which satisfy the large deflection condition and the boundary conditions of the edges. Each term of the Airy function consists of a particular solution and a homogeneous one. The particular solution satisfying the large deflection condition is classified into six cases, depending on the combinations of the modal numbers of the comparison functions. The corresponding homogeneous solution is found to make each Airy function satisfy the boundary condition by using the Fourier series method. The solution is applied to the non-linear analysis of the deflection of the simply supported plates with movable edges under transverse loading, and is verified by comparison with other investigation.     

弹性地基上Euler-Bernoulli梁的热屈曲模态跃迁特性

采用解析方法研究了置于线性弹性地基上的Euler-Bernoulli梁在均匀升温载荷作用下的临界屈曲模态跃迁特性;分别在两端不可移简支和夹紧边界条件下,给出了弹性梁屈曲模态跃迁点的地基刚度值以及屈曲载荷值的精确表达式,并分析了模态跃迁特点.结果表明:随着地基刚度参数值的增大临界屈曲模态通过跃迁点从低阶次向高阶次跃迁;两端简支梁的模态跃迁具有突变特性,而两端夹紧梁的模态跃迁则是一个缓慢变化过程,它是通过端截面的弯矩或曲率的正负号改变实现的.     

Analytical solution of a simply supported piezoelectric beam subjected to a uniformly distributed loading

IntroductionIntelligentstructureisakindofnewstructuremodelsandhasbeenreceivedmuchattentioninrecentyears.Usedaspiezoelectricsensorsandactuators,thiskindofintelligentstructureshasmanyadvantagessuchasthepromptnessofresponseandtheconvenienceforthesignalcontrol.Soitisfollowedwithinterestbothinthetheoreticalstudyandintheengineeringapplications[1].Forexample ,theresearchoffundamentalsolution[2 ,3]andellipsoidalinclusion[4 ]forthree_dimensionalpiezoelectricmaterialbyuseofFouriertransformation ;thestu…     

Multi-mode parametric excitation of a simply supported plate under time-varying and non-uniform edge loading

In this study, multi-mode parametric excitation of a simply supported plate under time-varying and non-uniform edge loading is modeled and the solution is found. Equations for multi-mode parametric excitation of a simply supported plate are derived using stress distributions within the plate as well as on the edges, considering both the effects of non-uniform edge loading and the non-linearity caused by the large deflection. The multi-mode equations are coupled by first-order linear terms, even in the case of simply supported boundary conditions, due to the non-uniform edge loading. The perturbation solutions of two-mode parametric excitation are examined by the method of multiple scales. For the edge loading, which consists of a uniform term as well as a non-uniform one, equations could be coupled or de-coupled by parametric excitation terms, and the numbers and values of the resonance frequencies of the parametric excitations could also differ, depending on whether the non-uniform term of the edge loading is time-varying or not. In addition to the resonant frequencies of the case when only the uniform term of the edge loading is time-varying, there are additional combination resonances at the vicinity of the sum of two natural frequencies of each mode when the non-uniform term of the non-uniform edge loading is time-varying.     

Bending of uniformly loaded rectangular plates with two adjacent edges clamped, one edge simply supported and the other edge free

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Modeling of dynamic deformation of rigid-plastic doubly connected plates with arbitrary fixed curvilinear contours on a viscoelastic foundation

A general solution is obtained for the problem of dynamic bending of an ideal rigid-plastic doubly connected plate with arbitrary simply supported or clamped curvilinear contours subjected to short-time high-intensity explosive dynamic loading uniformly distributed over the surface. The plate rests on a viscoelastic foundation. It is demonstrated that there are several mechanisms of plate deformation. Equations of dynamic deformation are derived for each mechanism, and implementation conditions are analyzed. Numerical examples are given.     

面内功能梯度矩形板的近似理论与解答

提出了面内功能梯度矩形板在竖向载荷作用下的近似 理论与解析解. 假设材料常数在面内x轴方向按指数规 律变化.引入了板理论的Reissner-Mindlin假设, 并考虑了板中面上的剪切变形的影响.推导了板在平行于y轴的两边简支, 平行于x轴方向的两边简支或固支情况下中性层法线转角和挠度用Fourier级数表示的解.讨论了退化为Kirchhoff假设下经典薄板理论的解的情况.提供了经典薄板理论在和Reissner-Mindlin假设下的算例并与三维有限元的计算结果进行了比较, 说明了该方法在厚板情况下也是相当精确的.     

A three-dimensional displacement analysis from an image-plane hologram

The three-dimensional displacement components can be determined from a double-exposure image-plane hologram by the method presented in this paper. An overdetermined set of equations is developed at each point of interest and is combined by a least-squares solution to provide the displacements. The validity of the method is demonstrated by analyzing a simply supported beam, a cantilever beam and a propeller blade, and comparing the results with theoretical values and results of other optical methods. The displacements at the tip of a crack are provided as an example of the usefulness of the method.     

An analytical solution of rectangular laminated plates by higher-order theory

I.IntroductionSincecompositematerialshavesuperiormechanicalproperties,theyarewidelyconcernedbytechnicians.Fromtheclassicallaminatetheorytothefirst-ordersheardeformationtheoryandfromthehigher-ordertheorytotheelasticitytheory,thetheoriesoflaminatedplatesofcompositemeterialsgetfastdevelopment.TheNaviersolutionofsimplysupportedrectangularplateswasdevelopedbyWhitneyandLeissalllforclassicallaminatetheory.TheNaviersolutionwasdevelopedbyWhitneyandPaganol'1forthefirst-ordersheardeformationtheory.Th…     

Natural frequencies of thin,rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass

The approximate solution for the title problem is obtained in the case of simply supported and clamped rectangular plates made of isotropic or orthotropic materials. A variational approach (the well known Rayleigh–Ritz method) is used, where the displacement amplitude is expressed in terms of beam functions. This means that each coordinate function satisfies identically all the boundary conditions at the outer edge of the plate. Free vibration analysis has been performed on various different cases; solid isotropic and orthotropic plates, orthotropic plates with a hole and isotropic plates with an orthotropic inclusion or “patch”, carrying an elastically mounted concentrated mass. It is important to point out that the case of an orthotropic patch is interesting from a technological viewpoint since it constitutes a model of a repair implemented on the virgin structural element when it has suffered damage. This approach has been implemented by the aeronautical industry in some instances. The obtained results are in very good agreement with those of particular cases of simply supported plates available in the literature.     

Buckling of stochastically heterogeneous beams,using a functional perturbation method

The buckling load and its probabilistic nature (average and variance) of Bernoulli beams with stochastic material (bending stiffness) properties is derived analytically by a new functional perturbation method (FPM). A buckling shape function is assumed, based on the homogeneous solution and additional terms to account for the morphology effects. The buckling load in the transcendental equation is treated as a functional of the bending modulus (stiffness or compliance) field. Applying a functional perturbation to the above equation, the buckling load is found analytically to any desired degree of accuracy, as a function of material morphology. The FPM is executed using both stiffness and compliance statistical data. The impact of each of the two data sources on the solution accuracy is examined, showing that compliance based solutions are accurate for small correlation lengths. Statically indeterminate problems can be treated with no additional effort. An example of a simply supported beam is solved in detail. Comparison with previous studies, where stochastic finite element and Monte Carlo simulation were used, showed the relative accuracy and insight capabilities of the method. The clamped-free case is also studied to demonstrate that symmetry conditions, used for homogeneous beams to find the buckling load on the basis of a simply supported case, are not valid for heterogeneous beams.     

Predicting buckling loads from vibration data

There are analytical methods for predicting the buckling loads of columns with the boundaries ideally fixed, i.e., simply supported or built-in, or partially fixed. Vibration-test results may furnish a practical method of measuring the fixity. In this investigation a beam, that may or may not be loaded as a column, is assumed to have a torsional spring at each end such that a zero torsional stiffness corresponds to a simply supported end and an infinite torsional stiffness corresponds to a built-in end. From a Rayleigh-Ritz analysis, the buckling load and the fundamental frequency of the beam are each computed as a function of the torsional stiffness. This procedure leads to a one-to-one nondimensional relationship between the buckling load and the natural frequency. From these calculations, it is seen that regardless of the degree of clamping of one end relative to the other end, all that is needed to predict the buckling load within a 15-percent range is a knowledge of the theoretical buckling load of the simply supported column; the theoretical fundamental frequency of the simply supported beam; and the experimental fundamental frequency. Experimental results are presented to support the theory.     

Solution of sector plate by Fourier-Bessel series

In this paper a solution of deflection in the form of Fourier-Bessel double series with supplementary terms is proposed to analyse bending and vibration problems of thin elastic sector plate with various edge conditions. This solution is suitable to a wider range, convenient for calculation and it is in an analytical form. As computational examples, the distribution curves of deflection and bending moment of plates with various sector angles, simply supported or clamped along the radial edges under uniform or concentrated load are obtained and the result are compared with the numerical results of related references. Thus the range of application of the Fourier series method with supplementary terms is extended. Frequencies and nodal lines in free vibration of plates with various sector angles simply supported along the radial edges are also given in this paper.Communicated by Hsueh Dai-wei.     

Non-linear bending of beams with uniformly distributed loads

The non-linear bending of both cantilever and simply supported beams subjected to a uniformly distributed load has been studied. The exact solutions for the slopes have been obtained and the solution for the maximum deflection and the horizontal projection of the beam length for the cantilever case are compared with a known approximate solution.     

Exact solutions for the stability of viscoelastic rectangular plate subjected to tangential follower force

An exact solution procedure is formulated for the stability analysis of viscoelastic rectangular plate with two opposite edges simply supported and other two edges clamped as well as the viscoelastic rectangular plate with one edge clamped and other three edges simply supported under the action of tangential follower force. Firstly, by assuming the transverse displacement (W) as independent functions which automatically satisfies the simply supported boundary conditions, the governing partial differential equation is reduced to an ordinary differential equation with variable coefficients. Then, by the normalized power series method and applying the boundary conditions yield the eigenvalue problem of finding the roots of a fourth-order characteristic determinant. The results show that the aspect ratio λ and the dimensionless delay time H have great effects on the types of instability and the critical loads of the viscoelastic plates.     

Mode jumping in the buckling of struts and plates: a comparative study

A detailed investigation of the phenomenon of mode jumping in compressed struts on stiffening foundations and elastic plates of varying lengths is performed, with emphasis on the effects of altering boundary conditions. The variety of possible modal interactions is presented in a concise form using the parameter space of Arnol'd tongues, borrowed from non-linear dynamical systems theory. For the strut system, a full range of end conditions from simply supported to clamped is examined. For the plate, simply supported and clamped flexural conditions along both long (unloaded) and short (loaded) edges are considered, together with in-plane conditions ranging from free to pull in, to fully restrained. For each system, simply supported end conditions are found to provide protection against early mode jumping in a so-called “safety envelope”, but this is eroded as the end conditions are systematically altered from simply supported to clamped. For the plate system, mode jumping is induced at an earlier stage in the loading process by restricting the long (unloaded) edges against in-plane movement, but is delayed by clamping the same edges against rotation.     

功能梯度热释电材料矩形板的三维精确分析

对四边简支、接地、等温的功能梯度热释电材料矩形板进行精确三维分析．根据正交各向异性热释电材料基本方程，导出了功能梯度热释电材料的状态方程．假定材料的机械、电学和热学性质沿板厚方向按统一的指数函数形式梯度分布，获得了四边简支、接地和等温的矩形板，在上下表面作用任意的机械荷载、电荷载和热荷载情况下的三维精确解．通过算例，分析了在机械荷载、电荷载和热荷载分别作用下，材料性质的不同梯度变化对平板结构响应的影响．所获得的精确结果可作为评价其他近似方法的标准解答或者作为建立简化的功能梯度热释电材料平板理论的基础。     

Navier solution for the elastic equilibrium problems of anisotropic skew thin plate wite variable thickness in nonlinear theories

This paper discusses the elastic equilibrium problems of anisotropic skew thin plate ofvariable thickness simply supported on all four sides in nonlinear theories,and uses theNavier method to seek an approach to the problem,and to illustrate the solution with theexamples.In conclusion,the mention is made of the scope of application and theconvergency of the solution.