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圆柱壳在热载荷作用下的非线性振动 总被引:5,自引:2,他引:3
采用伽辽金原理及改进的L-P法研究了圆柱壳在热载荷作用下的非线性振动,并讨论了分析了温度、长径比、厚径比对圆柱壳固有热振动频率的影响。 相似文献
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采用振型叠加法研究薄壁短圆柱壳受谐波激励的振动响应分析时模态截断数量的影响,且考虑简支-简支、固支-固支和固支-自由三种约束条件。首先基于Love壳体理论建立薄壁短圆柱壳的动力学模型。然后,给出采用振型叠加法进行薄壁短圆柱壳受径向谐波激励时的振动响应求解方法。在三种不同约束条件下,计算采用不同模态截断数量时的稳态响应的振动幅值,对比其一致性,并与实测结果进行比较。结果表明,在这三种约束条件下计算受谐波激励薄壁短圆柱壳的振动响应,需要截取前8阶模态函数用于表征位移模式;模态数据超过8阶对响应计算的精度没有明显改善,实测振动响应结果与解析结果基本吻合。 相似文献
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应用Donnell's简化壳理论,在考虑阻尼和几何非线性的情况下,基于Galerkin方法,对旋转的薄壁悬臂圆柱壳在法向激振力作用下的非线性行波振动进行了数值分析.在研究过程中,首先,考虑阻尼并引入几何非线性项,建立薄壁圆柱壳的非线性波动方程,然后,采用Galerkin方法对波动方程进行转换,选取不同的模态组合,得到相应模态坐标下的非线性微分方程,最后用Runge-Kutta法进行数值计算并对圆柱壳的非线性波动振动特性进行了分析.结果表明,几何非线性使圆柱壳呈现明显的硬特性,其硬特性随激振力幅值的增大而得到加强,共振区存在多值性,多模态分析表明,轴向二阶模态对主模态影响较大,计算时宜采用两个轴向模态. 相似文献
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为了提高旋转圆柱壳结构的使用性能和工作效率,减轻其质量已成为有效方式之一,针对这一需求,旋转圆柱壳结构有设计为厚度沿轴向变化即变厚度的趋势。基于此,利用Chebyshev-Ritz方法,对厚度沿轴向有3种线性变化形式的变厚度旋转圆柱壳的自由振动进行研究。考虑科氏力与离心力的影响,基于Sanders壳理论,将圆柱壳的位移场近似展开为Chebyshev多项式与边界函数乘积的形式,计算变厚度旋转圆柱壳的动能与势能,再根据Ritz方法获得变厚度旋转圆柱壳的频率方程。在此基础上,将所得结果与已有文献中的结果进行比较,验证了建模方法的准确性,并对计算结果进行了收敛性研究。最后比较了不同厚度变化形式下旋转圆柱壳的自由振动,并讨论了转速、厚度变化参数、圆柱壳长径比等参数对变厚度旋转圆柱壳自由振动的影响。 相似文献
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在7自由度线性系统的基础上考虑悬架弹簧、阻尼和轮胎的非线性,以高速路段的连续减速带作为整车激励,通过对力学模型进行分析并运用拉格朗日法建立系统微分方程。通过MATLAB仿真软件对整车7自由度非线性振动模型的微分方程进行仿真,得到阻尼非线性系数和激励频率的分岔图,发现在一定区域内系统出现复杂的非线性振动,并通过时间历程图、相位图、Poincare截面图和PSP峰值图深入研究系统的周期、拟周期和混沌运动,揭示出阻尼非线性系数和激励频率对系统振动的影响,最后通过拟合即时速度从变速的角度揭示减速车辆通过连续减速带时的振动情况。 相似文献
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Ali F. Farhat 《先进材料力学与结构力学》2015,22(11):885-896
This article considers a plane strain problem, which is known in conventional linear elasticity as cylindrical bending of simply supported plates and cross-ply laminates. By considering fibrous composites containing fibers resistant to bending, it formulates and solves corresponding polar elasticity equations governing the static and dynamic behavior of beam-like components made of a homogeneous or layered transversely isotropic material; each layer has embedded a single family of fibers. Fiber bending stiffness is accounted for through involvement of an extra elastic modulus, which, unlike its conventional elasticity counterparts that have dimensions of stress, has dimensions of force. Its involvement in the analysis implies existence of some intrinsic material area or length parameter, which may be associated, for instance, with fiber thickness of fiber spacing. A considerable amount of relevant numerical results are presented for thick beam components made of either homogeneous or two-layered transversely isotropic material. For the static bending problem, these include a detailed presentation of through-thickness distributions of displacements, stresses, as well as couple-stress. For the dynamic problem, attention is focused on the influence that fiber bending stiffness exerts on fundamental frequency parameters. 相似文献
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复合材料叠层圆柱曲板振动分析的半解析解 总被引:4,自引:1,他引:3
用三维弹性理论求解复合材料叠层圆柱曲板问题。在圆柱坐标系中,将三维弹性理论表述成哈密顿形式体系,得到一个变分原理,然后有限元法,给出一种半解析解,克服了过去完全的解析解及基于二维近似理论的数值解的不足。数值算例表明本文的方法是有效的。 相似文献
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本文在介绍圆柱厚壳应力与位移理论分析发展的前提下,建立了有限长圆柱厚壳在非轴对称移动载荷作用下的三维力学模型,假设沿厚度方向径向剪切应变二次分布、径向正应变线性分布,且建立了为满足边界条件待定的位移表达式,采用Heaviside函数和Dirac函数表达移动和作用变化着的移动载荷的基础上,用最小势能原理建立了该圆柱厚壳的动力学微分方程组,应用Galerkin法和修正的Runge–Kutta–Fehlberg法,求得了非轴对称移动载荷作用下的圆柱厚壳的动力响应。通过具体算例,对有限长圆柱厚壳的位移响应和应力状态进行了分析,并将动态响应的理论解与ANSYS数值解进行了对比,从而相互印证了解的可靠性。 相似文献
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环加肋圆柱壳振动分析的复合有限条法 总被引:2,自引:0,他引:2
提出一种分析环加肋圆柱壳自由振动问题的高效半解析方法──复合有限条法。该方法可在一个有限条元内计入若干个横向加肋的影响,包含横向加肋的有限条元称为复合有限条元,环加肋圆柱天采用一系列复合有限条元进行离散。复合有限条法可按加强肋骨的实际分布情况进行计算,而不必采用将加肋的影响平均到整个壳体的方法,且可考虑肋骨偏心的影响,它是一种子结构求解技术。算例表明,复合有限条法具有良好的求解精度和很高的求解效率,与常规有限元法相比,复合有限条法大大减少了系统自由度和计算工作量,且易于程序实现,是一种分析加肋板壳结构振动问题的较理想方法。 相似文献
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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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In this article, an inhomogeneous model is proposed to predict the material properties of porous GPL-reinforced composite (GPLRC) and to predict the mechanical responses of a sandwich plate which consists of top and bottom metal face sheets and a porous GPLRC core. The GPLRC core is assumed to be multilayers, and each layer may have different values of porosity coefficient to achieve a piece-wise functionally graded pattern. Young's moduli along with shear modulus of porous GPLRC core are predicted by a generic Halpin-Tsai model in which the porosity is included. Thermo-mechanical properties of both metal face sheets and porous GPLRC core are assumed to be temperature-dependent. The governing equations of motion for porous sandwich plates are solved by applying a two-step perturbation approach to obtain the analytical solutions for the two cases of nonlinear vibration and nonlinear bending of porous sandwich plates. Numerical studies are performed to compare the results obtained from the present model and the equivalent isotropic model (EIM). The results reveal that, for most cases, the difference of natural frequencies between two models is over 30%, and the vibration frequency–amplitude curves and the bending load–deflection curves are underestimated by using the EIM. 相似文献