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1.
求解不连续中厚板自由振动的微分容积单元法 总被引:2,自引:0,他引:2
基于区域叠加原理和微分容积法,发展了一种新型的数值方法——微分容积单元法,用以分析具有不连续几何特征的中厚板的自由振动。根据板的不连续情况将其划分为若干单元,在每个单元内用微分容积法将控制微分方程离散成为一组线性代数方程.在相邻的单元连接处应用位移连续条件和平衡条件,引入边界约束条件后得到一套关于各配点位移的齐次线性代数方程,由此可导出求解系统固有频率的特征方程。本文用子空间迭代法求解特征方程,并以开孔板、混合边界条件板和突变厚度板为例研究了方法的收敛性和计算精度。 相似文献
2.
Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method 总被引:1,自引:0,他引:1
D. Zhou Y. K. Cheung F. T. K. Au S. H. Lo 《International Journal of Solids and Structures》2002,39(26):6339-6353
This paper describes a method for free vibration analysis of rectangular plates with any thicknesses, which range from thin, moderately thick to very thick plates. It utilises admissible functions comprising the Chebyshev polynomials multiplied by a boundary function. The analysis is based on a linear, small-strain, three-dimensional elasticity theory. The proposed technique yields very accurate natural frequencies and mode shapes of rectangular plates with arbitrary boundary conditions. A very simple and general programme has been compiled for the purpose. For a plate with geometric symmetry, the vibration modes can be classified into symmetric and antisymmetric ones in that direction. In such a case, the computational cost can be greatly reduced while maintaining the same level of accuracy. Convergence studies and comparison have been carried out taking square plates with four simply-supported edges as examples. It is shown that the present method enables rapid convergence, stable numerical operation and very high computational accuracy. Parametric investigations on the vibration behaviour of rectangular plates with four clamped edges have also been performed in detail, with respect to different thickness-side ratios, aspect ratios and Poisson’s ratios. These results may serve as benchmark solutions for validating approximate two-dimensional theories and new computational techniques in future. 相似文献
3.
A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to (1) uniform and non-uniform
tent-like temperature loading; and (2) combined axial compression and uniform temperature loading. The initial geometrical
imperfection of plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the
effects of rotary inertia and transverse shear deformation. The analysis uses a deflection-type perturbation technique to
determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the
performances of perfect and imperfect, moderately thick rectangular plates and are compared with the results predicted by
the thin plate theory. 相似文献
4.
I.IntroductionTheproblelllsofthefol.cedvibrationofelasticthickrectallgularplatestobesolvedareofgreattheoreticalsignificanceandpractical\7altle.Asthevibratinggoverningequationofthethickplateismorecomplicatedthallthatofthinplate.itisdil'ficulttoso]\'einmathematics.Manyscholarshat,eresearchedintotheseproblemsalldadvancedvariousspecialapproximations.Suchassuperpositionmethod.initialfLinctiollnletllod.thecombinedseriesot'theeigenftlnctionsofdeepbeamabouttilecorrespondillgboulldarycollditions.eller… 相似文献
5.
XIAO Yong-gang 《应用数学和力学(英文版)》2005,26(8):963-972
IntroductionThe moderate thickness plates on elastic foundation are a kind of important structure instructural engineering. The mechanic characters of the plates on elastic foundation withdifferent boundary conditions have been received considerable atten… 相似文献
6.
I.Introduction'TheclassicalplatetheoryofvibrationisbasedontheKirchhoffhypotllcsis.andtheeffectoftransversesheardeformationandrotatoryinertiaareneglected.111[lltllcfreevibratiollfrequenciesofthinplates,allkindsofboundaryconditionshavebeensolved.Fortheanalysisofthevibrationalproblemsofthickplate,thetheoryofReissuer,MindlinandHenkyisused.Accordingtothedegreesoftheeffectsoftransverseshearstress,transversenormalstressandrotatoryinertia,somedynamicproblemsinEngineeringhavebeensolvedl:l.Regardless… 相似文献
7.
非均质中厚板的无网格LRPIM动力学分析 总被引:1,自引:1,他引:0
用局部加权残值法建立了非均质中厚板的局部径向点插值离散系统方程,采用无网格局部径向点插值法分析了非均质中厚板的自由振动和强迫振动问题。用径向基函数耦合多项式基函数来近似试函数,用四次样条函数做为加权残值法中的权函数。所构造的形函数具有Kronecker delta性质,可以很方便地施加本质边界条件。该方法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。在计算过程中,取积分中的高斯点的材料参数来模拟问题域材料特性的变化。计算结果表明,利用该方法计算非均质中厚板的自由振动和强迫振动问题可以得到具有较高精度的解。 相似文献
8.
According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed. 相似文献
9.
RECIPROCALTHEOREMMETHODFORSOLVINGTHEPROBLEMSOFBENDINGOFTHICKRECTANGULARPLATESFuBao-lian(付宝连)Tanwen-feng(谭文锋)(YanshanUnirersit... 相似文献
10.
运用边界积分法研究了四边简支、两对边固定另两对边简支、四边固定三种复杂边界条件下厚矩形板的受迫振动问题,求解过程清晰,从而给出了受迫振动控制方程和挠曲面方程。通过在Matlab平台上进行数值计算,得出了图表形式的计算结果,并与有限元模拟值进行对照。研究表明,边界积分法用于求解厚矩形板的受迫振动问题的准确性,本文推导的控制方程和挠曲面方程的正确性,进而对工程实际中的各种相关问题具有一定的现实意义,也为求解此类问题提供了一种新途径,可以直接运用到工程实际中。 相似文献
11.
本文建立了分析含随机材料参数并具厚度不均匀性的中厚板问题的随机边界元法,基于Taylor级数展开技术,分析和到广义位移的均值和一阶偏差的积分方程,其中将材料参数的随机性和厚度的不均匀性作为等效荷载处理,从而得到广义边界位移或面力的均值和协方差,并进一步求出部点广义位移和内力的均值和协方差,最后用本文方法计算了两个数例,并对所得结果进行了分析,探讨。 相似文献
12.
In this paper, applying the method of the reciprocal theorem, we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic load acting at any point of the plates, the figures and tables of number value of bending moment and the deflection amplitudes as well. 相似文献
13.
SOLVINGVIBRATIONPROBLEMOFTHINPLATESUSINGINTEGRALEQUATIONMETHOD¥(许明田,程德林)XuMingtian;ChengDelin(Department.ofMathematicsandPhysi... 相似文献
14.
I.IntroductionGenerally,asathree-dimensionaI(3-D)solid-theplateshouldbeanalysedwiththethickplatetheory.Thethickplatetheoryismultifarious:Acust0marythick[heoryoriginatesfromvariousmodificationsofthethinplatetheory,whichisbasedonKirchhoffLovehypothesis'with… 相似文献
15.
基于一阶剪切变形理论,提出了复合材料层合板自由振动分析的无网格自然邻接点Petrov-Galerkin法。计算时在复合材料层合板中面上仅需要布置一系列的离散节点,并利用这些节点构建插值函数。在板中面上的局部多边形子域上,采用加权余量法建立复合材料层合板自由振动分析的离散化控制方程,并且这些子域可由Delaunay三角形方便创建。自然邻接点插值形函数具有Kronecker delta函数性质,因而无需经过特别处理就能准确地施加本质边界条件。对不同边界条件、不同跨厚比、不同材料参数和不同铺设角度的复合材料层合板,由本文提出的无网格自然邻接点Petrov-Galerkin法进行自由振动分析时均可得到满意的结果。数值算例结果表明,本文方法求解复合材料层合板的自由振动问题是行之有效的。 相似文献
16.
Huang Yuying 《Acta Mechanica Sinica》1988,4(3):275-283
Based on Reissner's plate theory, a localized variational principle for the coupled vibrations of moderately thick floating
plates seated on the sea floor with variable water depth is presented in this paper. It will be a powerful tool to formulate
various approximate methods of moderately thick floating plates. By means of this variational principle a formula for calculating
the natural frequencies of moderately thick floating plates is also obtained. A numerical example shows that high accuracy
and computational time saving may be achieved in calculation. 相似文献
17.
In the present study, the static and dynamic analyses of elliptical functionally graded sandwich(FGS) plates are investigated. The constituent materials of the sandwich plates are ceramic and metal so that the core is made of pure metal, while the face sheets consist of a combination of metal and ceramic according to a four-parameter power-law distribution. Different material profiles such as classic, symmetric, and asymmetric can be obtained using the applied generalized power-law distribution ... 相似文献
18.
利用基于局部移动Kriging插值无网格法对层合板自由振动进行了数值分析,基于一阶剪切层合理论导出了层合板振动的控制方程和边界条件,进一步得到了自由振动的离散化特征方程。由于Kriging插值函数具有Kronecker delta函数性质,可以直接施加本质边界条件。通过本文给出的方法,对不同边界条件、不同跨厚比、不同材料参数和铺设角度的层合板的振动频率进行了计算,均得到满意结果。最后用该方法对层合板的铺设角度进行优化设计,得到了与已有文献完全一致的优化结果。数值结果充分表明了无网格Kriging方法分析层合板自由振动问题的有效性和高精确度。 相似文献
19.
20.
The almost sure stability of homogeneous viscoelastic plates subjected to a random wide-band stationary in-plane load is investigated.
The viscoelastic behavior of the plate is described in terms of the Boltzmann superposition principle, the relaxation kemels
of which are represented by the sums of exponents. On the assumption that the in-plane load is random wide-band stationary
process, sufficient conditions for almost sure stability of viscoelastic plates are obtained by the applications of Lyapunov's
direct method.
Project supported by the National Natural Science Foundation of China (No. 59635140) and the National Postdoctoral Foundation. 相似文献