共查询到14条相似文献,搜索用时 171 毫秒
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研究具有大范围运动和非线性变形的空间柔性梁的有限元动力学建模.首先在精确描述空间柔性梁的非线性变形的基础上,采用有限元方法对梁结构进行离散,导出其动能、势能及外力对应的广义力,然后利用Lagrange方程建立了空间柔性梁的精确动力学方程.该方程在原有一次耦合模型的基础上,增加了新的表征纵向、横向、侧向弯曲变形,以及扭转变形的耦合项,同时包含了变形运动与大范围运动之间的相互耦合项.本建模方法和所得结论可为以后空间柔性梁的动力学特性分析作以参考. 相似文献
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对固结于旋转刚环上内接柔性梁的刚柔耦合动力学特性进行了研究. 在精确描述柔性梁非线性变形基础上, 利用Hamilton变分原理和假设模态法, 在计入柔性梁由于横向变形而引起的轴向变形二阶耦合量的条件下, 推导出一次近似耦合模型. 忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量, 对简化模型做无量纲化处理. 首先分析在非惯性系下内接悬臂梁的动力学响应, 并与外接悬臂梁进行比较; 其次研究内接悬臂梁的稳定性;最后分析内接悬臂梁失稳临界转速的收敛性. 研究发现, 与外接悬臂梁存在动力刚化效应不同,内接悬臂梁存在着动力柔化效应; 给出了内接悬臂梁无条件稳定的临界径长比以及失稳的临界转速的计算方法; 若第一阶固有频率随转速增大而减小,则该内接悬臂梁处于有条件稳定; 随着模态截断数的增加,内接悬臂梁失稳的临界转速减小且有收敛值.
关键词:
内接悬臂梁
一次近似简化模型
动力柔化
临界转速 相似文献
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在旋转柔性梁变形场描述中,引入Bezier插值离散方法.首先构建旋转运动悬臂梁物理模型,接着采用第二类Lagrange动力学方程和Bezier插值离散方法,在计入柔性梁横向弯曲变形引起的纵向缩短的情况下,推导了旋转柔性梁的刚柔耦合动力学方程,并编制旋转柔性梁的动力学仿真软件,然后通过仿真算例对系统的动力学问题进行研究.最后将仿真结果与有限元法、假设模态法进行分析比较,验证了提出的Bezier插值离散方法的正确性,并得出Bezier插值离散法的计算效率较高;计算精度符合工程实际需要,高速时计算精度大于假设模态法;Bezier插值离散方法在处理大柔性问题时比假设模态法合理.因此在多体系统动力学领域具有优良性能和应用价值的Bezier插值离散方法将具有推广价值. 相似文献
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将基于多项式点插值的无网格方法用于旋转悬臂梁的动力学分析. 利用无网格点插值方法对柔性梁的变形场进行离散, 考虑梁的纵向拉伸变形和横向弯曲变形, 并计入横向弯曲变形引起的纵向缩短, 即非线性耦合项, 运用第二类Lagrange方程推导得到系统刚柔耦合动力学方程. 与有限元法相比, 该方法只需节点信息, 无需定义单元, 具有前处理简单的优势; 构造的形函数采用更多的节点插值, 具有高阶连续性. 将无网格点插值方法的仿真结果与有限元和假设模态法进行比较分析, 验证了该方法的正确性, 并表明其作为一种柔性体离散方法在刚柔耦合多体系统动力学的研究中具有可推广性. 相似文献
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对二维剪切梁单元进行研究,利用平面旋转场理论推导了精确曲率模型.采用几何精确梁理论构建了剪切梁单元弹性力矩阵.通过绝对节点坐标方法建立了系统的非线性动力学方程,提出基于旋转场曲率的二维剪切梁单元,并分别引入经典二维剪切梁单元和基于位移场曲率的二维剪切梁单元进行比较研究.首先,静力学分析证明了所提模型的正确性;其次,特征频率分析验证了模型可与理论解符合,收敛精度高,并且能准确地预测单元固有频率对应的振型;最后,在非线性动力学问题上,通过与ANSYS结果对比分析,证明了该模型可有效处理柔性大变形问题,并且与经典二维剪切梁单元相比具有缓解剪切闭锁的优势.因此,本文提出的基于旋转场曲率的二维剪切梁单元在处理几何非线性问题中具有较大的应用潜力. 相似文献
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从梁的弯曲振动方程出发,利用传递矩阵法,给出了无限周期结构的一维多振子声子晶体梁的弯曲振动能带结构,并利用有限元方法计算了有限周期结构梁的弯曲振动频率响应.建立了多振子声子晶体梁的简化模型,推导出带隙起始截止频率公式.结果表明:一维多振子声子晶体梁具有比单振子声子晶体梁更宽更丰富的振动带隙,可应用于呈倍频关系的减振降噪中;振动在带隙频率范围内频率响应具有明显的衰减;所建立的简化模型与理论模型结果符合较好.研究工作为梁类结构的减振提供一种新的思路. 相似文献
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In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation. 相似文献
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Most existing beam formulations assume that the cross section of the beam remains rigid regardless of the amplitude of the displacement. The absolute nodal coordinate formulation (ANCF); however, allows for the deformation of the cross section and leads to a more general beam models that capture the coupling between different modes of displacement. This paper examines the effect of the order of interpolation on the modes of deformation of the beam cross section using ANCF finite elements. To this end, a new two-dimensional shear deformable ANCF beam element is developed. The new finite element employs a higher order of interpolation, and allows for new cross section deformation modes that cannot be captured using previously developed shear deformable ANCF beam elements. The element developed in this study relaxes the assumption of planar cross section; thereby allowing for including the effect of warping as well as for different stretch values at different points on the element cross section. The displacement field of the new element is assumed to be cubic in the axial direction and quadratic in the transverse direction. Using this displacement field, more expressions for the element extension, shear and the cross section stretch can be systematically defined. The change in the cross section area is measured using Nanson’s formula. Measures of the shear angle, extension, and cross section stretch can also be systematically defined using coordinate systems defined at the element material points. Using these local coordinate systems, expressions for a nominal shear angle are obtained. The differences between the cross section deformation modes obtained using the new higher order element and those obtained using the previously developed lower order elements are highlighted. Numerical examples are presented in order to compare the results obtained using the new finite element and the results obtained using previously developed ANCF finite elements. 相似文献
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《Journal of sound and vibration》1987,119(3):487-508
Transient dynamic analysis of flexible structures undergoing large motions is considered. For rotating structures, it is explicitly shown that appropriate account of the influence of centrifugal force on the bending stiffness requires the use of a geometrically non-linear (at least second-order) beam theory. Use of a first-order (linearized) linear beam theory results in a spurious loss of bending stiffness. For a rotating plane beam, a set of linear partial differential equations of motion—that includes all inertia effects (Coriolis, centrifugal, acceleration of revolution) and coupling between extensional and flexural deformations—is derived from the fully non-linear beam theory by consistent linearization. The analysis is subsequently extended to the more general case of a plate, accomodating shear deformation, and undergoing a general three-dimensional rotating motion. The discretization process of the resulting linear equations of motion for the beam and the plate is also discussed. 相似文献
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Development of dynamic models of flexible linkages, with flexible motion caused by rigid body motion and electromechanical coupling of transduction devices and the host linkage, is very important for the design of active vibration control laws for flexible-link mechanisms. In the first part of this paper, the Lagrange finite element (FE) formulation is used to derive such a dynamic model for a flexible planar linkage with two translational and one rotational degrees of freedom. Linear electromechanical coupling of surface-bonded lead zirconate titanate (PZT) patches with the host linkage is incorporated into the model. In the second part of this paper, this dynamic model is applied to a flexible-link planar parallel manipulator. Based on standard kineto-elastodynamic assumptions, the linkage dynamic model is simplified and simulation of strain rate feedback control using PZT sensors and actuators is performed. Numerical results show that PZT actuators effectively damp vibration of the flexible linkages. 相似文献