共查询到18条相似文献,搜索用时 406 毫秒
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轴向运动结构的工程振动问题一直是动力学领域中的重要课题之一。为了更全面地分析工程中的振动,针对磁场作用下轴向运动功能梯度Timoshenko 梁的振动特性展开论述。基于梁的动力学方程组和相应的简支边界条件,应用复模态方法,得到不同参数时固有频率和衰减系数与轴向运动速度的对应关系。采用微分求积法分析磁场作用下前四阶固有频率和衰减系数随轴向运动速度的变化,并与复模态方法的结果进行对比验证。数据结果表明复模态方法得到的结果是精确解析解。衰减系数呈现不对称性,耦合固有频率呈现分离性。随着轴速、磁场强度和功能梯度指数的增大,梁的固有频率减小;随着支撑刚度参数的增大,梁的固有频率增大。 相似文献
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研究带有扭转弹簧两端铰支轴向运动梁的横向振动。利用边界条件得到系统的频率方程,通过数值方法解出系统的前两阶固有频率随轴向速度变化的情况,并导出了系统的前两阶复模态函数。讨论了固有频率与模态函数、轴向速度及弹簧弹性系数的关系。 相似文献
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根据分离变量法得到了Winkler弹性地基上矩形薄板自由振动问题的精确解, 分析了地基模量对频率的影响, 其中边界条件为CCCC、SCCC和SSCC情况的精确解过去被认为是难以得到的。在分离变量方法中, 不需要事先人为的选取满足某一组对边边界条件的挠度函数, 而是直接利用控制方程本征根给出振型函数通解的一般解析形式, 再利用边界条件得到振型函数系数和频率方程的精确形式。数值结果与有限元结果及文献结果吻合较好, 验证了该文方法和结果的的正确性。 相似文献
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基于考虑有限深度土体运动的Winkler地基梁理论,建立移动荷载作用下弹性地基上有限长梁的横向运动方程。利用模态叠加法求得移动荷载作用下有限长梁动力响应的解析解,进而以移动荷载离开时梁的响应为初值,采用分离变量法求得有限长梁自由振动的一阶近似解;通过数值计算和参数分析,揭示了移动荷载作用下有限深度Winkler地基上简支边界梁的动力学特性,分析地基深度、地基黏滞阻尼系数和荷载移动速度等对有限长梁受迫振动阶段和自由振动阶段动力响应的影响,全面揭示有限深度土体运动对临界速度的作用效应。结果表明:地基深度显著降低了临界速度,且弹性地基黏滞阻尼明显延长了自由振动衰减时间;荷载移动速度加剧了有限深度弹性地基与其支承梁的相互作用效应,系统振动的幅值和响应周期均发生显著变化。 相似文献
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In this paper, the generalized differential quadrature (GDQ) method is presented for solving the nonlinear, fully intrinsic equations of geometrically exact rotating and nonrotating beams. The fully intrinsic equations of beams involve only moments, forces, velocity and angular velocity, and in these equations, the displacements and rotations will not appear explicitly. This paper presents the generalized differential quadrature method for solution of these equations. To show the accuracy, validity and applicability of the proposed generalized differential quadrature method for solving the fully intrinsic beam equations, different cases are considered. It is found that the GDQ method gives very accurate results with very few numbers of discrete points and also has very low computational cost as compared to some other conventional numerical methods and therefore this method is very efficient, accurate and fast for solving the fully intrinsic equations. 相似文献
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复杂变截面梁的轴向自由振动分析的近似方法 总被引:3,自引:1,他引:2
介绍了带有附加影响的变截面梁轴向自由振动问题的求解方法-模态摄动法,这一方法在由等截面均匀梁低阶主模态函数组成的模态子空间中,将复杂梁的变系数微分方程的求解化为线性代数方程组的求解,从而简化了计算过程,通过与其它方法的比较,说明了本文方法的优越性。 相似文献
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用微分求积法求解梁的弹塑性问题 总被引:7,自引:0,他引:7
根据梁塑性弯曲的工程理论,采用微分求积法进行了梁的弹塑性平面弯曲分析。微分求积法是一种直接求解微分方程(组)的数值方法,不依赖于变分原理,且能以较少的网格点求得微分方程的高精度数值解。与有限元分析结果的比较,表明了微分求积法求解梁的弹塑性问题的计算效率和精度。微分求积法的计算结果不受荷载步长的限制,也不需要迭代求解,特别对于承受非线性分布荷载作用的梁的弹塑性分析具有很大的优越性。通过选用不同的网格点数目,分析了微分求积法的稳定性和收敛性。 相似文献
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An accurate and efficient solution procedure based on the three-dimensional elasticity theory for the free vibration analysis of thick laminated annular sector plates is presented. Plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. In order to accurately model the variation of material properties across the thickness, the layerwise theory is used to approximate the displacement components in this direction. Then, employing the Hamilton’s principle together with the modal analysis, through-the-thickness and circumferential discretized form of the equations of motion and the related boundary conditions are obtained. Finally, the differential quadrature method (DQM) as an efficient and accurate numerical method is applied to discretize the resulting variable coefficients differential equations in the radial direction. The fast rate of convergence of the method is demonstrated and to show its high accuracy, comparison studies with the available results in the literature are made. Finally, some new results are prepared, which can be used as benchmark solutions for future works. 相似文献
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研究非线性轴向运动黏弹性Rayleigh梁因速度周期变化产生的亚谐波共振。轴向运动速度在平均速度附近做简谐周期性脉动。通过取物质导数的Kelvin本构关系描述Rayleigh梁的黏弹性。运用多尺度近似解析方法,构建轴向运动Rayleigh梁的非线性偏微分方程的可解性条件,分析参数振动稳态响应的振幅与扰动速度频率关系。并运用微分求积方法直接离散非线性Rayleigh梁的控制方程,以验证近似解析方法分析。通过数值算例,分析了系统参数对稳态响应曲线的影响。 相似文献
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该文导出了面内热载荷作用下, 梁在其过屈曲构形附近微幅振动的解析解。首先基于经典梁理论, 推导了控制轴向和横向变形的基本方程。然后, 将2 个非线性方程化为一个关于横向挠度的四阶非线性积分-微分方程。假设梁的振幅以及由此引起的附加应变为无限小, 另设其响应为谐振, 则该非线性积分-微分方程将化为两组耦合的微分方程:一组控制非线性静态响应;另一组就是叠加于梁屈曲构形之上的线性振动方程。直接求解这些问题, 可以得到梁热过屈曲构形以及固有频率的解析解, 这些解是外加热载荷的函数。该文得到的精确解可以用于验证或改进各类近似理论和数值方法。 相似文献
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S. Soleimani KutanaeiNaeem Roshan A. VosoughiS. Saghafi A. Barari Soheil Soleimani 《Engineering Analysis with Boundary Elements》2012,36(5):633-638
This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation of derivatives and function approximation of Radial Basis Function. As a result, the method can be used to directly approximate the derivatives of dependent variables on a scattered set of knots. In this study knots were distributed irregularly in the solution domain using the Halton sequences. The method is applied on a two-dimensional geometry. The obtained results from the numerical simulations are compared with those gained by previous works. Outcomes prove that the current technique is in very good agreement with previous investigations and this fact that RBF-DQ method is an accurate and flexible method in solution of partial differential equations (PDEs). 相似文献