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电活性聚合物圆柱壳静态与动态电压下的响应及稳定性 总被引:1,自引:1,他引:0
摘要:在电活性聚合物圆柱壳内外表面施加电压,圆柱壳会变薄并且伸长,因此相同的电压会在圆柱壳内产生更大的电场。这个正反馈可能使圆柱壳厚度不断变薄,最终导致其失稳破坏。本文研究了电活性聚合物圆柱壳在静态和周期电压作用下的响应及稳定性问题。采用neo-Hookean材料模型得到描述圆柱壳表面运动的非线性常微分方程。给出了圆柱壳在不同厚度和边界条件下外加电压随圆柱壳变形的变化曲线,结果表明存在一个临界电压,当外加电压大于这一临界值时,圆柱壳将被破坏。同时,也讨论了厚度和边界条件对临界电压的影响。圆柱壳在正弦周期电压作用下,其运动随时间的变化是周期性的或拟周期性的非线性振动。给出了圆柱壳振动固有频率的计算结果,采用打靶法得到圆柱壳振动的周期解,并且用数值法研究了周期解的稳定性。采用数值仿真得到圆柱壳振动振幅随外加动态电压激励频率的变化曲线,结果表明圆柱壳会发生多频共振,共振时圆柱壳振幅发生跳跃,导致圆柱壳失稳破坏。最后给出共振点临近点的振动曲线和相图,并对其振动特性进行讨论。 相似文献
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采用Runge–Kutta法和多尺度法对轴向运动分层复合材料薄壁圆柱壳的非线性振动特性进行了研究。首先根据层合壳理论建立轴向运动分层复合材料薄壁圆柱壳的波动方程,利用Galerkin法对方程进行离散,得到相互耦合模态方程组。然后应用Runge –Kutta法分析了不同参数条件下的幅频特性曲线,得到了系统由于固有频率接近所导致的内共振现象,以及系统呈现软特性等非线性特性。最后采用多尺度法进行了系统1:1内共振时的近似解析分析,对系统在不同参数下的振动研究表明,激振力幅值、阻尼、速度等参数对位移响应幅值、共振区间、模态间的耦合度及系统软特性程度均有影响,其结论与数值计算结果一致,并同时对解的稳定性进行了研究。 相似文献
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依据经典Flügge壳体理论,利用功能梯度材料(FGM)和均匀材料物理性质和力学行为相似性的均匀化转换计算方法,研究了静水压力下FGM圆柱壳临界压力的预测方法。针对水下FGM圆柱壳耦合系统的振动问题,考虑流体影响,采用波动法推导出相应的振动方程,使用了牛顿迭代法,以确定在静水压力下FGM圆柱壳的固有频率。根据临界载荷与固有频率为零的载荷水平线性相关性,运用拟合曲线法和均匀化转换后的公式法对静水压力下FGM圆柱壳临界压力进行了预测分析,并讨论了FGM圆柱壳各项参数对静水压力下FGM圆柱壳临界压力的影响。结果表明,FGM圆柱壳的材料弹性模量E合值、几何尺寸h/R和L/R,以及不同边界条件改变对临界压力影响较大。通过对多组算例的对比分析,证明了本研究方法的正确性和有效性。使用该方法进行预测的精度高,计算量小,能够为非均匀结构力学行为的分析提供新的研究途径。 相似文献
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本文从偏心圆柱壳截面的几何特性出发,将偏心圆柱壳问题转化为一个周向变厚度圆柱壳问题,随后利用其状态向量之间的传递矩阵将壳体的振动控制方程转化为矩阵微分方程形式,通过Magnus级数法求解传递矩阵得到频率方程。采用Lagrange插值法得到偏心圆柱壳体自由振动状态下的固有频率,并且与圆柱壳的固有频率进行了比较。对影响结构固有频率的主要参数进行了分析,得到了这些参数和固有频率之间的关系。本文不仅提出了一种有效求解偏心圆柱壳固有频率的新方法,同时亦可为检测偏心圆柱壳的偏心距提供一种新的思路和方法。 相似文献
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本文采用半解析法分析了弹性介质中有限长双层圆柱壳的动力响应。与有限元法比较,此法具有精度高、计算工作量小的优点,不但可以用来求解具有任意经典端部条件的双层圆柱壳在非对称平面冲击波作用下的动力响应问题,而且还可以方便地推广应用于各种由圆柱壳和薄板相连接而成的组合结构动力响应分析。 相似文献
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主动约束层阻尼部分覆盖圆柱壳耦合振动控制 总被引:14,自引:0,他引:14
采用分布参数建模,从Ham ilton变分原理出发推导了主动约束层阻尼(ACLD)覆盖圆柱壳耦合振动的运动微分方程和边界条件,并扩展适合一维连续结构分析的基于解析解的谱传递矩阵法(STMM)用于ACLD部分覆盖圆柱壳。通过数值计算,研究了ACLD的长度和位置对固有频率和模态耗散因子的影响。STMM能有效克服有限元法单元数目多、动力学方程阶数高及ACLD长度和位置变化时须重复建模的缺点,以最少的单元数目建立低阶控制方程。典型算例显示了STMM的有效性和精确性。 相似文献
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Buckling behavior of compression-loaded composite cylindrical shells with reinforced cutouts 总被引:1,自引:0,他引:1
Results from a numerical study of the response of thin-walled compression-loaded quasi-isotropic laminated composite cylindrical shells with unreinforced and reinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the non-linear response of the shells are described. A high-fidelity non-linear analysis procedure has been used to predict the non-linear response of the shells. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate the complex non-linear response of a compression-loaded shell with an unreinforced cutout. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex non-linear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell. However, results are presented that show how certain reinforcement configurations can cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved buckling response characteristics. 相似文献
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R. Heuer 《Nonlinear dynamics》1994,5(1):25-38
A dynamic nonlinear theory for layered shallow shells is derived by means of the von Karman-Tsien theory, modified by the generalized Berger-approximation. Moderately thick shells with polygonal planform composed of multiple perfectly bonded layers are considered. The shell edges are assumed to be prevented from in-plane motions and are simply supported. A distributed lateral force loading is applied to the structure, and additionally, the influence of a static thermal prestress, corresponding to a spatial distribution of cross-sectional mean temperature, is taken into account. In the special case of laminated shells made of transversely isotropic layers with physical properties symmetrically distributed about the middle surface, a correspondence to moderately thick homogeneous shells is found. Application of a multi-mode expansion in the Galerkin procedure to the governing differential equation, where the eigenfunctions of the corresponding linear plate problem are used as space variables, renders a coupled set of ordinary time differential equations for the generalized coordinates with cubic as well as quadratic nonlinearities. The nonlinear steady-state response of shallow shells subjected to a time-harmonic lateral excitation is investigated and the phenomenon of primary resonance is studied by means of the perturbation method of multiple scales. A unifying non-dimensional representation of the nonlinear frequency response function is presented that is independent of the special shell planform. 相似文献
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圆锥壳自由振动传递函数解 总被引:2,自引:1,他引:2
本文在线性弹性理论基础上,给出了一种求解圆锥薄壳自由振动的渐进传递函数解法,壳体的三个位移分量,外力和边界条件首先沿环向展开的Fourier级数,然后关于时间变量进行Laplace变换,这样就将壳体的控制方程化为一系列含复参数s的变系数常微分方程组,通过定义状态变量。得到了壳体动力学问题的状态空间控制微分方程,引入一小参数,并利用摄动技术就可以得到微分方程的渐进传递函数解,将各于锥段的解进行综合, 相似文献
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基于欧拉方程推导出了含万向铰偏斜旋转轴的横向振动模型,利用多尺度方法对该模型进行求解,得出了该偏斜系统可能出现的多种共振模式,进而对含万向铰偏斜轴系横向振动和型组合共振、差型组合共振进行稳定性分析,并对该类偏斜系统横向振动和型组合共振响应进行数值计算与仿真,检验所得稳定性理论分析结果。研究表明:对于和型组合共振而言,其稳定性边界与输入扭矩T0、支撑轴承安装位置l、轴承刚度Kx2和Ky2等因素有关;当轴承安装位置距万向铰中心较近或者轴承弹簧刚度系数较小时,系统在频率(ω10+ω20)/2附近产生和型组合共振的区域减小,即能够抑制系统和型组合共振的产生。该研究可为偏斜轴系振动与噪声抑制提供理论支持。 相似文献
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Internal resonance in nonlinear vibration of functionally graded (FG) circular cylin- drical shells in thermal environment is studied using the Hamiltonian dynamics formulation. The material properties are considered to be temperature-dependent. Based on the Karman-Donnell's nonlinear shell theory, the kinetic and potential energy of FG cylindrical thin shells are formu- lated. The primary target is to investigate the two-mode internal resonance, which is triggered by geometric and material parameters of shells. Following a secular perturbation procedure, the underlying dynamic characteristics of the two-mode interactions in both exact and near resonance cases are fully discussed. It is revealed that the system will undergo a bifurcation in near resonance case, which induces the dynamic response at high energy level being distinct from the motion at low energy level. The effects of temperature and volume fractions of composition on the exact resonance condition and bifurcation characteristics of FG cylindrical shells are also investigated. 相似文献
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V. Tvergaard 《Journal of the mechanics and physics of solids》1976,24(5):291-304
The behaviour of elastic-plastic spherical shells under internal pressure is investigated numerically for thickness-to-radius ratios ranging from cases of thin shells to very thick shells. The shells under consideration are made of strain-hardening elastic-plastic material with a smooth yield-surface. Attention is restricted to axisymmetric deformations, and results are presented for initial thickness inhomogeneities in various axisymmetric shapes. For smooth thickness-variations in the shape of the critical bifurcation mode, the reduction in maximum pressure is studied together with the distribution of deformations in the final collapse mode. Also, the possibility of flow localization due to more localized, initially thin regions on a spherical shell is investigated. 相似文献
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Two new approaches are proposed for the numerical and analytical stability analyses of imperfect shells. One approach is based on the generalized mesh method, whereas the other employs a modified reduced-stiffness method. Both approaches apply to shells with initial geometrical imperfections. Numerical results are compared with experimental data for shells with a single dent. Analytical results are also presented and compared 相似文献
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旋转壳的数值传递函数方法 总被引:1,自引:0,他引:1
应用数值传递函数方法建立一种用于分析旋转壳静力、动力响应的截锥壳单元,在本方法中,单元的位移在环向展开为Fourier级数的形式,应用薄壳理论可以得到解耦的微分方程,通过Laplace变换可以将方程转化为频域内的常微分方程,将其表示为状态空间形式后,可以应用数值传递函数方法求解,对复杂的系统可以应用与有限元类似的方法,划分多个单元组合求解,文中给出了几种旋转壳的动力、静力问题的数值算例,并与其它方法进行了比较,表明本文方法具有精度高,计算方便等特点。 相似文献