超空泡运动体圆柱薄壳的非线性动力屈曲分析

超空泡运动体的动力屈曲失稳具有隐蔽性、突发性和危险性, 因而必须研究清楚运动体的失稳区域边界及失稳振幅. 将超空泡运动体模拟成受轴向周期载荷作用的细长圆柱薄壳, 给出非线性几何方程、物理方程和平衡方程, 建立细长圆柱薄壳带有非线性项的动力屈曲微分方程组; 依据非线性项的形式, 给出合理的非线性位移表达式, 得到具有周期性系数的非线性横向振动微分方程; 采用伽辽金变分法和和鲍洛金方法, 获得带有周期性系数和非线性项的马奇耶方程; 求解非线性马奇耶方程, 得到第一、第二阶不稳定区域内的定态振动振幅的解析表达式; 绘制超空泡运动体的非线性参数共振曲线, 分析航行速度、载荷比例系数、轴向载荷频率和振型对参数共振曲线的影响. 以上研究为建立基于参数共振的圆柱薄壳动力失稳的可靠性分析及基于参数共振可靠性的结构动力优化设计的奠定了理论基础.      

复合材料层合扁球壳的非线性强迫振动

研究了考虑横向剪切的对称层合圆柱正交异性扁球壳的非线性强迫振动问题，得到了共振周期解和非共振周期解．最后，还分析了横向剪切对幅频特性曲线的影响     

宏纤维压电层合壳结构非线性屈曲分析

以纤维压电MFC （Micro-Fiber Composite）层合圆柱壳为例，研究了其在准静态屈曲下的非线性振动响应。基于Reissner-Mindlin一阶剪切变形假设，采用大转角几何全非线性理论，建立了带有纤维角度的MFC层合壳结构的非线性屈曲与振动分析模型。采用全拉格朗日方程（Total Lagrange Formulation）对非线性模型进行线性化处理，并结合Riks-Wempner弦长控制迭代法进行准静态求解，然后在每个解点进行自由振动分析。通过与文献数据对比验证了所建模型的准确性。并用该计算模型对MFC-d31层合圆柱壳进行屈曲及自由振动分析，研究了几何参数（曲率、厚度、纤维角度和不同外加电压）对频率的影响。结果表明，厚度、曲率和纤维增强角度对结构的临界载荷有显著的影响，且结构的临界载荷随着上述参数的增大而增大；电场强度可对不同纤维角度壳体的自振频率进行调节，能够提高结构的临界载荷；纤维角度越大，电压对结构自振频率调节的效果越明显。     

横观各向同性超弹性球壳的有限振动

应用有限变形动力学理论研究了一种横观各向同性不可压超弹性材料球壳在表面突加均布拉伸载荷作用下的有限振动问题．给出了球壳振动的振幅和外加载荷之间的关系,得到了,球壳振动的相同和近似的周期,讨论了球壳振动的振幅、相图及振动的周期和材料各向异性程度的关系．     

圆柱壳的非线性自由振动分析

本文分析了各向同性封闭圆柱壳的非线性自由振动。文中采用经典的非线性弹性力学方法推导了圆柱壳的大振幅运动方程,这些方程的静态形式与冯·卡门的板理论方程具有同样的精度。文中讨论了四种基本振动模态,并且还以数学公式的形式给出了一般的最终结果,一些例子以曲线给出结果,并进行了比较。结果还表明线性振动可以作为非线性振动的一种特例。     

超弹性材料中空穴的动态生成

本文在有限变形动力学的框架下研究了一种不可压超弹性材料圆柱体在表面突加均布拉伸载荷作用下空穴的动态生成问题,除一个相应于均匀变形状态的平凡解外,当外加载荷超过其临界值时,柱体内部还有空穴的突然生成,得到了空穴半径和表面载荷之间的一个精确的微分关系,证明了空穴随时间的演化是非线性的周期性振动,给出了空穴振动的相图、最大振幅、临界载荷及近似的周期。     

阶跃扭矩作用下弹性圆柱壳冲击屈曲

本文首先基于Koiter初始后屈曲理论和Thompson离散坐标方法,给出了受扭圆柱壳的缺陷敏感性分析及冲击扭转屈曲渐近分析,并指出它对应于对称失稳的情形。然后通过求解受扭圆柱壳的非线性动力学方程,指出在阶跃扭矩作用下的后屈曲阶段,壳体的振动幅值剧增,周期变大。     

正弦波纹扁球壳的非线性强迫振动

波纹壳是传感器弹性元件的一类重要形式,也是精密仪器仪表弹性元件中的一类重要形式。由于波纹壳形状复杂、参数众多、厚度薄,对其进行非线性分析非常重要同时也是十分困难的。本文考虑一种在传感器弹性元件中有重要应用价值的正弦波纹浅球壳体,将这种壳体视为结构上的圆柱正交异性扁球壳,根据Andryewa的思想,分别得到了正弦波纹壳径向、环向在拉伸、弯曲下的等价的四个各向异性参数;建立了正弦波纹扁球壳的非线性强迫振动微分方程;得到了正弦波纹扁球壳非线性强迫振动的共振周期解及幅频特性曲线。     

周期集中载荷作用下球形扁壳的非线性振动问题

本文用半解析法推导了周期集中载荷作用下,周边固定球形扁壳的非线性振动微分方程.然后用小参数法求出了非线性的非共振周期解和共振周期解.绘出了不同几何特征参数下的振幅——频率图.     

变厚度圆板的非线性强迫振动

本文研究了厚度呈幂指数规律变化的变厚度圆饭的非线性强迫振动问题。文中首先用半解析法求解了动态Von Ka＇rma＇n大变形方程,导出了周期均布荷载作用下轴对称变厚度薄圆板的非线性强迫振动微分方程。然后用小参数摄动法求解了振动方程,得到了非线性的非共振周期解和共振周期解。绘制了振幅——频率关系图。     

Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction

The dielectric elastomer (DE) is an important intelligent soft material widely used in soft actuators, and the dynamic response of the DE is highly nonlinear due to the material properties. In the DE, electrostriction denotes the deformation-dependent permittivity. In the present study, we formulate the nonlinear dynamic governing equations of the DE membrane considering the electrostriction effect. The free vibration and parametric excitation of the DE membrane with different geometric sizes are calculated. The free vibration bifurcations induced by the initial location and the voltage are both discussed according to an energy-based approach. The amplitude-frequency characteristics and bifurcation diagrams of parametric excitation are also given. The results show that electrostriction decreases the free vibration amplitude and increases the frequency, but it has less influence on the parametric excitation oscillation frequency and decreases the parametric excitation amplitude except when the membrane resonates. The initial location and the applied voltage can induce the snap-through instability of the free vibration. A large geometric size will lead to a much lower resonance frequency. The resonance amplitudes increase while the resonance frequencies decrease with the increase in the applied voltage. The critical voltage of snap-through instability for the parametric excitation is larger than that for the free vibration one.

     

轴向运动复合材料圆柱壳的非线性振动研究

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。     

Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields

The bending and free vibration of a rotating sandwich cylindrical shell are analyzed with the consideration of the nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields by use of the first-order shear deformation theory (FSDT) of shells. The governing equations of motion and the corresponding boundary conditions are established through the variational method and the Maxwell equation. The closed-form solutions of the rotating sandwich cylindrical shell are obtained. The effects of geometrical parameters, volume fractions of carbon nanotubes, applied voltages on the inner and outer piezoelectric layers, and magnetic and thermal fields on the natural frequency, critical angular velocity, and deflection of the sandwich cylindrical shell are investigated. The critical angular velocity of the nanocomposite sandwich cylindrical shell is obtained. The results show that the mechanical properties, e.g., Young’s modulus and thermal expansion coefficient, for the carbon nanotube and matrix are functions of temperature, and the magnitude of the critical angular velocity can be adjusted by changing the applied voltage.     

主动约束层阻尼圆柱壳体的振动特性研究

基于弹性、粘弹性和压电材料本构方程,应用能量法建立了主动约束层阻尼（ACLD）圆柱壳体的有限元动力学方程。通过对压电传感层自感电压的比例、微分反馈控制,对主动约束层阻尼（ACLD）圆柱壳体进行了主被动一体化振动控制,研究了复合圆柱壳体的动力学响应特性。讨论了主动约束层阻尼（ACLD）片体的位置、覆盖率、粘弹性层厚度及控制增益等关键参数对圆柱壳体振动特性的影响。研究表明：主动约束层阻尼（ACLD）片体的粘贴位置与模态有关,针对不同模态,应采用不同的粘贴位置;覆盖率、粘弹性层厚度及控制增益等直接影响到振幅衰减程度,通过对片体位置、覆盖率、粘弹性层厚度及控制增益等关键参数的优化,能有效降低主动约束层阻尼圆柱壳体的振动,具有十分重要的工程应用价值。     

Geometrically nonlinear vibration of laminated composite cylindrical thin shells with non-continuous elastic boundary conditions

The geometrically nonlinear forced vibration response of non-continuous elastic-supported laminated composite thin cylindrical shells is investigated in this paper. Two kinds of non-continuous elastic supports are simulated by using artificial springs, which are point and arc constraints, respectively. By using a set of Chebyshev polynomials as the admissible displacement function, the nonlinear differential equation of motion of the shell subjected to periodic radial point loading is obtained through the Lagrange equations, in which the geometric nonlinearity is considered by using Donnell’s nonlinear shell theory. Then, these equations are solved by using the numerical method to obtain nonlinear amplitude–frequency response curves. The numerical results illustrate the effects of spring stiffness and constraint range on the nonlinear forced vibration of points-supported and arcs-supported laminated composite cylindrical shells. The results reveal that the geometric nonlinearity of the shell can be changed by adjusting the values of support stiffness and distribution areas of support, and the values of circumferential and radial stiffness have a more significant influence on amplitude–frequency response than the axial and torsional stiffness.

     

Torsional vibration and stability of functionally graded orthotropic cylindrical shells on elastic foundations

In this study, the torsional vibration and stability problems of functionally graded (FG) orthotropic cylindrical shells in the elastic medium, using the Galerkin method was investigated. Pasternak model is used to describe the reaction of the elastic medium on the cylindrical shell. Mixed boundary conditions are considered. The material properties and density of the orthotropic cylindrical shell are assumed to vary exponentially in the thickness direction. The basic equations of the FG orthotropic cylindrical shell under the torsional load resting on the Pasternak-type elastic foundation are derived. The expressions for the critical torsional load and dimensionless torsional frequency parameter of the FG orthotropic cylindrical shell resting on elastic foundations are obtained. The effects of variations of shell parameters, the exponential factor characterizing the degree of material gradient, orthotropy, foundation stiffness and shear subgrade modulus of the foundation on the critical torsional load and dimensionless torsional frequency parameter are examined.     

Dynamical response of hyper-elastic cylindrical shells under periodic load

Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of the nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing motion of the inner surface of the shell. Motion of the shell is nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. Solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of the dynamical solution and motion of the shell. The effects of thickness and load parameters on the critical value and oscillation of the shell are discussed.     

Dynamic stability of a thin cylindrical shell with top mass subjected to harmonic base-acceleration

This paper considers the dynamic stability of a harmonically base-excited cylindrical shell carrying a top mass. Based on Donnell’s nonlinear shell theory, a semi-analytical model is derived which exactly satisfies the (in-plane) boundary conditions. This model is numerically validated through a comparison with static and modal analysis results obtained using finite element modelling. The steady-state nonlinear dynamics of the base-excited cylindrical shell with top mass are examined using both numerical continuation of periodic solutions and standard numerical time integration. In these dynamic analyses the cylindrical shell is preloaded by the weight of the top mass. This preloading results in a single unbuckled stable static equilibrium state. A critical value for the amplitude of the harmonic base-excitation is determined. Above this critical value, the shell may exhibit a non-stationary beating type of response with severe out-of-plane deformations. However, depending on the considered imperfection and circumferential wave number, also other types of post-critical behaviour are observed. Similar as for the static buckling case, the critical value highly depends on the initial imperfections present in the shell.