共查询到19条相似文献,搜索用时 140 毫秒
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研究了弹性地基上带传力杆的间断中厚矩形板结构的非线性振动特性。荷载在传力杆中的传递由竖向弹簧模拟,其弹簧刚度取决于传力杆的特性以及杆与板间的相互作用。根据能量变分原理,考虑地基耦合效应,建立了双参数地基上带传力杆的间断矩形中厚板的非线性运动控制方程。应用伽辽金法和谐波平衡法对该组非线性方程进行了求解。在算例中,讨论了传力杆参数、板的结构参数以及地基参数对中厚矩形板的非线性自由振动特性的影响。 相似文献
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饱和弹性半空间地基与中厚圆板的动力相互作用 总被引:1,自引:0,他引:1
利用Fourier-Bessel级数,对横观各向同性饱和弹性半空间地基与中厚圆板的动力相互作用问题进行了系统地分析。板的位移函数、荷载、地基反力及板下地基表面的沉降均被展开为二重Fourier-Bessel级数,这些级数中的待定系数由板的边界条件、板的控制方程及板-地基的相容条件加以确定,从而将饱和弹性半空间地基与中厚圆板的动力相互作用问题转化为数值积分和代数方程组的求解问题。数值计算表明,该级数解答具有较快的收敛速度。可以将该方法推广到弹性半空间与梁、矩形板相互作用问题的分析。 相似文献
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考虑板的横向剪切变形和转动惯量的影响,采用改进Fourier级数的方法对任意弹性边界条件下的中厚矩形板进行振动功率流分析。将板的横向振动位移和转角表示为标准的二维Fourier余弦级数和辅助级数的线性组合。通过辅助级数的引入,解决了位移函数和转角函数的导数在边界不连续的问题,从而使此法适用于任意的弹性边界条件。结合Hamilton原理和Mindlin理论建立求解方程,得到中厚矩形板振动方程的矩阵表达式。最后进行了数值仿真,得到了正弦点力作用下中厚板的功率流场图。 相似文献
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针对四边自由矩形板横向振动目前没有精确解的问题,构造出四边自由矩形板横向振动振型函数的一种近似解。由于矩形板发生横向振动时会形成驻波,按不同的驻波类型,我们采用不同的组合级数对驻波所反映的矩形板振型函数精确解进行逼近,进而得到了四边自由矩形板振型函数的近似解。为了验证近似解的有效性,搭建了四边自由矩形薄板横向振动的实验平台。通过简谐激励得到了薄板在0~2 000 Hz频带内的一系列二维驻波图形(克拉尼斑图)。将实验结果(克拉尼斑图)与近似解得到的驻波图形相比,发现两者从定性、定量两方面均吻合得较好,从而验证了近似解的正确性。 相似文献
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本文运用文所建立的方法,研究Winkler弹性地基上正交各向异性自由矩形板弯曲问题的精确解。以受集中载荷作用的板为例,给出不同弹性系数地基上板的位移和弯矩的数字计算结果。 相似文献
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In this paper, nonlinear dynamic response of rectangular laminated composite plate resting on nonlinear Pasternak type elastic foundations is investigated. First-order shear deformation theory (FSDT) is used for modeling of moderately thick plates. The plate formulation is based on the von Karman nonlinear equation. The resulting nonlinear governing equations for transient analysis of laminated plates on elastic foundation are integrated using the discrete singular convolution-differential quadrature coupled approaches. The nonlinear governing equations of motion of plate are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the foundation parameters, boundary conditions and geometric parameters of plates on nonlinear dynamic response of laminated thick plates are investigated. 相似文献
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In this article, an exact analytical solution for stability analysis of vertical moderately thick laminated rectangular plates subjected to selfweight and top load on the basis of the first-order shear deformation plate theory is presented. It is assumed that the symmetric laminated rectangular plate is composed of transversely isotropic layers. Employing an analytical approach, the coupled governing stability equations of the laminated plate are converted into two uncoupled partial differential equations in terms of transverse displacement and an auxiliary function. It is considered that the vertical sides of the laminated plate are simply supported. Using Levy-type solution, the decoupled equations are reduced to two ordinary differential equations. One of these equations has variable coefficients, for which an exact analytical solution is obtained in the form of power series method of Frobenius. After appropriate convergence study, the present analysis is validated by comparing the results with the existing data reported in the literature. Furthermore, the effects of aspect ratio, plate thickness, boundary conditions, weight of plate and top load on the stability of laminated rectangular plates are investigated and discussed in details. The presented formulations and results can be used as benchmark for future research studies. 相似文献
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点支撑预应力中厚矩形板的横向振动 总被引:1,自引:0,他引:1
基于Reissner-Mindlin一阶剪切变形板理论,讨论在预加面内机械荷载或温度场作用下,点支撑中厚矩形板的横向振动。温度场假定沿板表面为均布,沿板厚方向为线性分布的。利用考虑剪切变形影响的Timoshenko梁函数,采用Rayleigh-Ritz法给出不同边界条件下点支撑中厚板的自振频率。结果表明,温度升高与预加面内压力将使板的自振频率下降,支撑点位置的变化、边界约束条件和横向剪切变形效应都对板的自振频率有显著影响。 相似文献
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In this paper, the nonlinear behavior of symmetric and antisymmetric cross ply, thin to moderately thick, elastic rectangular laminated plates resting on nonlinear elastic foundations are studied using differential quadrature method (DQM). The first-order shear deformation theory (FSDT) in conjunction with the Green’s strain and von Karman hypothesis are assumed for modeling the nonlinear behavior. Elastic foundation is modeled as shear deformable with cubic nonlinearity. The differential quadrature (DQ) discretized form of the governing equations with the various types of boundary conditions are derived. The Newton–Raphson iterative scheme is employed to solve the resulting system of nonlinear algebraic equations. Comparisons are made and the convergence studies are performed to show the accuracy of the results even with a few number of grid points. The effects of thickness-to-length ratio, aspect ratio, number of plies, fiber orientation and staking sequence on the nonlinear behavior of cross ply laminated plates with different boundary conditions resting on elastic foundations are studied. 相似文献
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Vibration analysis of a functionally graded rectangular plate resting on two parameter elastic foundation is presented here. The displacement filed based on the third order shear deformation plate theory is used. By considering the in-plane displacement components of an arbitrary material point on the mid-plane of the plate and using Hamilton’s principle, the governing equations of motion are obtained which are five highly coupled partial differential equations. An analytical approach is employed to decouple these partial differential equations. The decoupled equations of functionally graded rectangular plate resting on elastic foundation are solved analytically for levy type of boundary conditions. The numerical results are presented and discussed for a wide range of plate and foundation parameters. The results show that the Pasternak (shear) elastic foundation drastically changes the natural frequency. It is also observed that in some boundary conditions, the in-plane displacements have significant effects on natural frequency of thick functionally graded plates and they cannot be ignored. 相似文献
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D. J. Henwood J. R. Whiteman A. L. Yettram 《International journal for numerical methods in engineering》1982,18(12):1801-1820
A Fourier series solution is presented for a system of first-order partial differential equations which describe the linear elastic behaviour of a thick rectangular plate resting on an elastic foundation and carrying an arbitrary transverse load. The lateral edges of the plate are unstressed. A central step in the method for solving the system of equations is to combine a complementary function with a particular solution of the system in order to satisfy the boundary conditions. The complementary function is the sum of two series. The terms of the first series are products of a Fourier term in one space variable with the solution of an eigenvalue problem in the other space variable. The second series is similar and comes from reversing the roles of the space variables. 相似文献
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Hui-Shen Shen 《Journal of Engineering Mathematics》1998,33(3):259-270
A thermal postbuckling analysis is presented for a simply supported, moderately thick rectangular plate subjected to uniform or nonuniform tent-like temperature loading and resting on a softening nonlinear elastic foundation. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first-order shear-deformation effect, and including plate-foundation interaction and thermal effects. 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 plates resting on softening nonlinear elastic foundations. The effects played by foundation stiffness, transverse shear deformation, plate aspect ratio, thermal load ratio and initial geometrical imperfections are studied. Typical results are presented in dimensionless graphical form and exhibit interesting imperfection sensitivity. 相似文献
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In this paper exact closed-form solutions of 3-D elasticity theory are presented to study both in-plane and out-of-plane free vibrations for thick functionally graded simply supported rectangular plates. The solution procedure of the transverse vibration utilizes Levinson’s representation form to describe the displacement; in this way, the 3-D elasto-dynamic equations are written in terms of some suitable independent functions satisfying ordinary differential equations. A similar procedure is presented for in-plane vibration by introducing an appropriate displacement field. In each case, the obtained ordinary differential equations are analytically solved and boundary conditions are satisfied. The proposed solutions are validated by comparing some of the present results with corresponding results known in the literature as well as with 3-D Finite Element Method. Finally, the influence of inhomogeneity on the natural frequencies for a thick functionally graded rectangular plate is discussed. 相似文献
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Maxwell模型粘弹性矩形厚板固有横向振动 总被引:5,自引:2,他引:3
由于各向同性粘弹性体剪应力-角应变的本构关系与应力-应变的本构关系相似,据此可得到Maxwell模型粘弹性矩形厚板固有横振微分方程。并讨论了Maxwell粘弹性矩形厚板的振动特性。 相似文献