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Nonlinear free vibration of functionally graded (FG) plates with in-plane material inhomogeneity subjected to different boundary conditions is presented. The nonlinear equations of motion and the related boundary conditions are extracted based on the classical plate theory. Green's strain tensor together with von Kármán assumptions is employed to model the geometrical nonlinearity. The differential quadrature method as an efficient and accurate numerical tool is employed to discretize the governing equations in spatial domain. After validating the presented approach, parametric studies are performed to clarify the effects of different parameters on the nonlinear frequency parameters of the in-plane FG plates. 相似文献
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A computational method based on radial basis functions has been applied to the linear solution of thin plates. This meshless numerical method gives high flexibility in the analysis of irregular geometries, due to its insensivity to spatial dimension. The multiquadrics approach is used in this paper. The numerical solution is compared with Kirchhoff theory for plates.__________Translated from Problemy Prochnosti, No. 2, pp. 72 – 84, March – April, 2005. 相似文献
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Following previous work, a wavelet finite element method is developed for bending, free vibration and buckling analysis of functionally graded (FG) plates based on Mindlin plate theory. The functionally graded material (FGM) properties are assumed to vary smoothly and continuously throughout the thickness of plate according to power law distribution of volume fraction of constituents. This article adopts scaling functions of two-dimensional tensor product BSWI to form shape functions. Then two-dimensional FGM BSWI element is constructed based on Mindlin plate theory by means of two-dimensional tensor product BSWI. The proposed two-dimensional FGM BSWI element possesses the advantages of high convergence, high accuracy and reliability with fewer degrees of freedoms on account of the excellent approximation property of BSWI. Numerical examples concerning various length-to-thickness ratios, volume fraction indexes, aspect ratios and boundary conditions are carried out for bending, free vibration and buckling problems of FG plates. These comparison examples demonstrate the accuracy and reliability of the proposed WFEM method comparing with the exact and referential solutions available in literatures. 相似文献
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本文根据由热力学第一、第二定律推出的能量守恒方程,进而导出平板几何非线性热力动力耦合振动有限元方程组,提出一种计算量少,精度高的校正显式积分格式,求解耦合方程组的时间历程问题。研究了热力动力耦合平板横向振动振幅频率的影响及热弹阻尼现象。 相似文献
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有面内张力和剪力作用的简支各向异性平行四边形板自由振动、屈曲和弯曲的精确解 总被引:2,自引:1,他引:2
对简支各向异性平行四边形板在而内张力和剪力作用下自由振动、屈曲和弯曲问题作了全面的研究。利用叠加法和本问题所固有的对称性优点得到了重富立叶级数解。与现有结果的比较验证了此法的精确性。文后给出了多种几何条件下的自由振动、屈曲和弯曲的数值结果。 相似文献
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研究非线性弹性地基上小挠度矩形薄板的非线性振动,应用弹性力学理论建立非线性弹性地基上小挠度矩形薄板受简谐激励作用的动力学方程,利用Galerkin方法将其转化为非线性振动方程。根据非线性振动的多尺度法求得系统主参数共振-主共振情况的一次近似解,并进行数值计算。分析了阻尼系数、地基系数、激励参数等对系统主参数共振-主共振的影响。系统主参数共振-主共振曲线均具有跳跃现象。随着阻尼、地基系数的改变,系统响应曲线具有“类软刚度特征”。随着参数激励幅值的改变,系统响应曲线具有“类硬刚度特征”。应用奇异性理论得到系统主参数共振-主共振稳态响应的转迁集和分岔图。 相似文献
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The main advantage of triangular differential quadrature method in numerical simulations of problems in triangular domain is that it needs very few grid points compared to those of low order methods. In the current work, the method is implemented to analyze the bending behavior of relatively thick triangular composite plates based on the concept of first-order shear deformation theory. A set of triangular symmetric laminated plates with various lay-ups, length to thickness ratios, and boundary conditions is considered. The results are discussed in detail and compared with those obtained from finite element method of analysis using ANSYS package. 相似文献
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利用分数阶Kevin粘弹性模型,建立矩形薄板的动力学方程,并利用拉普拉斯变换及其逆变换给出四边简支粘弹性薄板的解析解,并着重分析在常值荷载作用下,分数阶Kevin粘弹性模型的分数阶参数、粘性参数和模量参数对挠度的影响。结果表明,随着粘性参数和分数阶参数的增大,粘弹性板的挠度变小;随着模量参数增大,粘弹性板的挠度变大。 相似文献
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运用非线性振动的模态方法对非线性动力吸振器进行了动力学分析,研究了该类吸振器的反共振工作点、工作点的稳定性以及阻尼对反共振工作点的影响. 相似文献
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This paper extends the numerical method, originally developed by Onate and his colleagues for the static analysis of plates,
to enable modal (vibration) and bifurcative (buckling) analyses of plates to be undertaken. The procedure uses a rotation-free
triangular element, and is based on combining the finite element method and the finite volume method so as to produce a triangular
element with only three displacement degrees of freedom. Elastic stiffness, stability (geometric stiffness) and mass matrices
are developed using the mixed formulation, and these are implemented in routine computer coding in order to demonstrate the
validity and efficacy of the solution technique when compared with results reported by independent investigators. Natural
frequencies and local buckling coefficients are given for plates with interior line supports, and these are used to illustrate
the prowess of the numerical technique for the analysis of a wide class of plate buckling and vibration problems, whose analysis
by non-discretisation techniques has found favour recently in deference to general finite element modelling which tends to
introduce some inaccuracies. The element developed in this paper, however, is both accurate and has the attractive meshing
characteristics of the finite element method for analysing more arbitrary geometric structural topologies. 相似文献
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This paper investigates the nonlinear free vibration of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory and von Kármán geometric nonlinearity. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction and estimated though the rule of mixture. The Ritz method is employed to derive the governing eigenvalue equation which is then solved by a direct iterative method to obtain the nonlinear vibration frequencies of FG-CNTRC beams with different end supports. A detailed parametric study is conducted to study the influences of nanotube volume fraction, vibration amplitude, slenderness ratio and end supports on the nonlinear free vibration characteristics of FG-CNTRC beams. The results for uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) beams are also provided for comparison. Numerical results are presented in both tabular and graphical forms to investigate the effects of nanotube volume fraction, vibration amplitude, slenderness ratio, end supports and CNT distribution on the nonlinear free vibration characteristics of FG-CNTRC beams. 相似文献
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M. S. Hussein D. Lesnic & M. Ivanchov 《East Asian journal on applied mathematics.》2013,3(4):295-310
Free boundary problems with nonlinear diffusion occur in various applications,
such as solidification over a mould with dissimilar nonlinear thermal properties
and saturated or unsaturated absorption in the soil beneath a pond. In this article,
we consider a novel inverse problem where a free boundary is determined from the
mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem,
and a stability estimate is established. The problem is recast as a nonlinear least-squares
minimisation problem, which is solved numerically using the lsqnonlin routine
from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For
noisy data, instability is manifest in the derivative of the moving free surface, but not in
the free surface itself nor in the concentration or temperature. 相似文献
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提出了一种分析滑移边界各向同性和正交各向异性矩形板振动特性的数值方法一双向样条离散法。该方法适用于各种可能组合边界矩形板的自由振动分析;边界包括自由、简支、固定和滑移边界。在x和y方向,板被离散成N和M个等分区间。为适应任意边界,修改N+3和M+3维硝样条函数向量的最前和最后三个函数,得到x方向N+1个点、y方向M+1个点和x-y方向两个附加点的修正的邱样条函数向量,并以此作为板的位移试函数。在给定边界下,修正的B3样条函数向量对位移、位移的一阶导数和二阶导数都仅保留一个未知系数。基于矩形板的势能泛函导出其特征方程。与有限元法和样条有限条法相比,本文方法具有自由度少、计算效率高和输入数据少等优点。数值计算结果表明,本方法具有高的计算精度。 相似文献
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矩形板的非线性热弹耦合振动 总被引:11,自引:0,他引:11
本文从完整的弹性力学方程出发,导出了板的非线性热弹耦合振动基本方程,分析了力和温度场的边界条件,并对夹支边界和混合边界情况作了具体的分析和数字计算,得到了热弹耦合效应对热弹耦合振动的振幅和频率的作用机理.所得结果对板动力学的理论研究和实际应用有较大参考价值. 相似文献
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复合材料层合矩形板非线性湿热振动 总被引:1,自引:1,他引:0
在考虑湿热影响的基础上,研究了复合材料层合矩形板的非线性湿热振动,并讨论分析了湿度、温度、长宽比对复合材料层合矩形板非经性固有振动周期的影响。 相似文献