功能梯度三相复合材料圆柱壳固有振动特性分析

本文以一种石墨烯与碳纤维协同增强三相复合材料圆柱壳为研究对象,研究了在任意边界条件下该新型功能梯度三相复合材料圆柱壳的自由振动特性.首先,基于一阶剪切变形理论、Von Karman几何非线性关系和Hamilton原理,推导了三相复合材料圆柱壳结构运动控制方程.然后,应用Galerkin法离散求解三相复合材料圆柱壳的固有频率和模态振型.最后通过将本文方法与Abaqus仿真结果进行对比,验证了本文方法的准确性.此外,本文进一步分析了石墨烯质量分数、功能梯度形式和边界条件等不同因素对新型三相复合材料圆柱壳固有振动特性的影响.     

薄壁圆柱壳的高阶模态振动特性研究

采用解析法研究了不同边界条件下薄壁圆柱壳的高阶模态振动特性.首先基于Love壳体理论,在简支-简支、固支-固支和固支-自由三种边界条件下,通过伽辽金法建立了动力学模型,对模态特性进行求解,得到了高阶固有频率和三维模态振型,并通过文献和有限元法进行了比较.算例结果表明,两端简支边界条件下采用解析法得到的固有频率误差值不超过2%,当周向波数较小时固有频率先减小后增加,在高阶时的固有频率逐渐升高,当轴向半波数增加时固有频率明显增大,通过解析法、文献和有限元法得到的三维模态振型相吻合.     

功能梯度三相复合材料圆柱壳的非线性振动研究

论文研究了一种由环氧树脂、石墨烯纳米片、碳纤维制成的功能梯度三相复合材料圆柱壳的非线性振动响应.基于一阶剪切变形理论和von-Karman几何非线性关系,考虑到温湿效应、气动力和外激励的共同作用,利用Hamilton原理建立了两端固支圆柱壳的非线性偏微分运动方程.利用Galerkin法将非线性偏微分运动方程离散成一组相互耦合的二阶非线性常微分方程,利用伪弧长延拓法求解非线性常微分方程组,给出对应的幅频响应曲线.本论文中仅考虑湿度和外激励等参数的变化对新型三相复合材料圆柱壳结构非线性振动响应的影响,分析了湿度和外激励的变化对功能梯度三相复合材料圆柱壳共振响应的影响.     

基于有限差分法的端部约束同轴圆柱壳的流致失稳分析

本文基于经典壳体和理想势流理论建立圆柱壳流固耦合系统的运动方程,并引入有限差分法(FDM)对运动方程进行离散.为将壳体表面的扰动压力离散到差分网格节点,基于差分离散的原理,提出了以分段函数作为基函数的展开方法.本文对结构与压力控制方程均采用FDM方法进行求解,发展了一种基于FDM的同轴圆柱壳流固耦合求解策略.首先,利用本文方法计算了同轴圆柱壳在静态流体环境中的振动频率,并与有限元软件(ANSYS)的计算结果相比较,验证了本文方法的正确性；然后,探究了在静流体环境中同轴圆柱壳的结构参数变化对其振动频率的影响规律；最后,研究了同轴圆柱壳系统在运动流体环境中的流弹失稳问题.     

功能梯度材料圆板的非线性热振动及屈曲

采用弹性理论建立了功能梯度材料板的静力平衡方程,利用静力平衡方程确定了功能梯度材料板的中性面位置,在此基础上推导出了功能梯度材料板在均匀温度场中的非线性振动及屈曲微分方程组,求得了功能梯度材料圆板的非线性振动及屈曲的近似解,讨论分析了中性面位置、梯度指数、温度等因素对功能梯度材料圆板非线性振动及屈曲的影响.把该方法计算结果与有限元计算结果进行了比较,验证了该方法的计算结果是可靠的.算例分析表明,中性面位置对均匀温度场中功能梯度材料圆板的非线性振动及屈曲有一定影响.     

功能梯度材料椭圆板的非线性热振动及屈曲

采用弹性理论建立了功能梯度材料板的静力平衡方程,利用静力平衡方程确定了功能梯度材料板的中性面位置,在此基础上推导出了功能梯度材料板在均匀温度场中的非线性振动及屈曲微分方程组,求得了功能梯度材料椭圆板的非线性振动及屈曲的近似解,讨论分析了中性面位置、梯度指数、温度等因素对功能梯度材料椭圆板非线性振动及屈曲的影响.把该方法计算结果与有限元计算结果进行了比较,验证了该方法的计算结果是可靠的.算例分析表明,中性面位置对均匀温度场中功能梯度材料椭圆板的非线性振动及屈曲有一定影响.     

用Timoshenko修正理论研究有梯度界面层双材料梁的振动特性

采用Timoshenko梁修正理论研究了有梯度界面层双材料梁的振动问题,利用静力方程确定了有梯度界面层双材料梁的中性轴位置,在此基础上应用Timoshenko梁修正理论建立了有梯度界面层双材料梁的振动方程,求得其自振频率表达式及其在简谐荷载作用下强迫振动的解析解.讨论分析了梯度界面层高度等因素对有梯度界面层双材料梁的振动影响,并用有限元法验证了Timoshenko梁修正理论.通过实例计算,得到了梯度界面层高度等因素对有梯度界面层双材料梁振动特性有较大影响的结论.     

带裂纹石墨烯增强金属泡沫梁的振动特性研究

分析了带裂纹功能梯度石墨烯增强金属泡沫梁的自由振动.采用Timoshenko梁理论进行建模,裂纹由无质量扭转弹簧模拟,利用Halpin Tsai微观力学模型预测材料的有效性能.通过哈密顿原理,得到了带裂纹功能梯度石墨烯增强金属泡沫(FG GPLRMF)梁的运动方程及其边界条件.采用微分变换法分析带裂纹FG GPLRMF梁的自由振动.结果表明,带裂纹FG GPLRMF梁的振动特性受到石墨烯几何尺寸、孔隙类型和石墨烯分布的影响显著.     

圆柱壳弹性波超材料分级排列的带隙拓宽方法研究

圆柱壳弹性波超材料的弯曲波带隙拓宽问题限制其满足实际工程中的宽频隔振要求,针对该问题,本文首先研究了基于局域共振机理的圆柱壳弹性波超材料弯曲波带隙特点,研究局域谐振器质量和弹簧劲度系数的关系,然后将周期分级排列的组合方式应用于圆柱壳类弹性波超材料的带隙拓宽中,并利用有限元法进行能带结构和振动传输特性计算.研究结果显示：该方法可实现弯曲波带隙的拓宽;利用组合法构建的轴向周期分级排列圆柱壳弹性波超材料可实现705-1226Hz频率范围内弯曲波的高效衰减,带隙拓宽至分别为单一谐振器的2.55倍,这表明该方法在宽频减振方面具有明显优势,应用前景广阔.     

航空发动机叶片非线性动力学分析

论文研究了航空发动机叶片的非线性振动问题,将叶片简化为功能梯度材料薄壁悬臂梁,考虑几何大变形的影响,基于一阶活塞气动力理论,利用Hamilton原理建立了叶片的非线性偏微分运动方程.综合运用Galerkin方法、多尺度方法和数值方法对叶片模型进行了非线性动力学分析,通过相图、波形图和频谱图分析了不同气流流速情况下旋转叶片的动态响应.结果表明:随着气流流速的增加,系统呈现倍周期运动和混沌运动等多种复杂动力学行为.     

Effect of boundary conditions on natural frequencies for rotating composite cylindrical shells with orthogonal stiffeners

The effect of the boundary conditions on the natural frequencies for rotating composite cylindrical shells with the orthogonal stiffeners is investigated using Love’s shell theory and the discrete stiffener theory. The frequency equation is derived using the Rayleigh–Ritz procedure based on the energy method. The considered boundary conditions are four sets, namely: (1) clamped–clamped; (2) clamped–simply supported; (3) clamped–sliding; and (4) clamped–free. The beam modal function is used for the axial vibration mode and the trigonometric functions are used for the circumferential vibration mode. The composite shells are stiffened with uniform intervals and the stiffeners have the same material. By comparison with the previously published analytical results for the rotating composite shell without stiffeners and the orthogonally stiffened isotropic cylindrical shells, it is shown that natural frequencies can be determined with adequate precision.     

Jacobi–Ritz method for free vibration analysis of uniform and stepped circular cylindrical shells with arbitrary boundary conditions: A unified formulation

A semi analytical approach is employed to analyze free vibration characteristics of uniform and stepped circular cylindrical shells subject to arbitrary boundary conditions. The analytical model is established on the basis of multi-segment partitioning strategy and Flügge thin shell theory. The admissible displacement functions are handled by unified Jacobi polynomials and Fourier series. In order to obtain continuous conditions and satisfy arbitrary boundary conditions, the penalty method about the spring technique is adopted. The solutions about free vibration behavior of circular cylindrical shells were obtained by approach of Rayleigh–Ritz. To confirm the reliability and accuracy of this method, convergence study and numerical verifications for circular cylindrical shells subject to different boundary conditions, Jacobi parameters, spring parameters and maximum degree of permissible displacement function are carried out. Through comparative analyses, it is obvious that the present method has a good stable and rapid convergence property and the results of this paper agree closely with the published literature. In addition, some interesting results about the geometric dimensions are investigated.     

恒定磁场中简支圆柱壳的磁弹性振动分析

依据电磁场方程及相应的电磁本构关系,给出了作用于圆柱壳体上的电磁力及力矩表达式.在此基础上,分别推得了纵向和横向磁场中圆柱壳体的磁弹性轴对称振动方程.针对两端简支约束条件,通过位移函数的设定,得到了相应的有阻尼振动微分方程.通过算例,给出了系统衰减振动的响应曲线图和相图,分析了磁感应强度和壳体厚度对系统振幅衰减速度的影响.结果表明,通过改变磁感应强度可以达到控制系统振动的目的.     

A study on the free vibration of the joined cylindrical–spherical shell structures

The free vibration characteristics of the joined spherical–cylindrical shell with various boundary conditions are investigated. The boundary conditions considered herein are free–free, simply supported–free and clamped–free for the joined cylindrical–spherical shell structures. The Flügge shell theory and Rayleigh’s energy method are applied in order to analyze the free vibration characteristics of the joined shell structure and individual shell components. In the modal test, the I-DEAS test module is used to calculate mode shapes and natural frequencies of the joined shell structure. The natural frequencies and mode shapes are calculated numerically and they are compared with those of the FEM and modal test to confirm the reliability of the analytical solution. The effects of the shallowness of the spherical shell and length of the cylindrical shell to the free vibrational behavior of joined shell structure are investigated.     

Nonlinear primary resonance of imperfect spiral stiffened functionally graded cylindrical shells surrounded by damping and nonlinear elastic foundation

In this paper, an analytical method is used to study the nonlinear primary resonance of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal stiffeners. The SSFG cylindrical shell is surrounded by linear and nonlinear elastic foundation and the effect of structural damping on the system response is also considered. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. Three-parameter nonlinear elastic foundation model is consists of two-parameter linear elastic foundation (Winkler and Pasternak) and one hardening/softening cubic nonlinearity parameter. Based on the von Kármán nonlinear equations and the classical plate theory of shells, the strain–displacement relations are derived. The smeared stiffener technique is used to the model of the internal stiffeners. Using the Galerkin method, the partial differential equations of motion are discretized. The nonlinear primary resonance is analyzed by means of the multiple scales method. The effects of various geometrical characteristics, material parameters and elastic foundation coefficients are investigated on the nonlinear primary resonance.

     

Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution

Based on the First-order Shear Deformation Theory (FSDT) this paper focuses on the dynamic behavior of moderately thick functionally graded conical, cylindrical shells and annular plates. The last two structures are obtained as special cases of the conical shell formulation. The treatment is developed within the theory of linear elasticity, when materials are assumed to be isotropic and inhomogeneous through the thickness direction. The two-constituent functionally graded shell consists of ceramic and metal. These constituents are graded through the thickness, from one surface of the shell to the other. A generalization of the power-law distribution presented in literature is proposed. Two different four-parameter power-law distributions are considered for the ceramic volume fraction. Some material profiles through the functionally graded shell thickness are illustrated by varying the four parameters of power-law distributions. For the first power-law distribution, the bottom surface of the structure is ceramic rich, whereas the top surface can be metal rich, ceramic rich or made of a mixture of the two constituents and on the contrary for the second one. Symmetric and asymmetric volume fraction profiles are presented in this paper. The homogeneous isotropic material can be inferred as a special case of functionally graded materials (FGM). The governing equations of motion are expressed as functions of five kinematic parameters, by using the constitutive and kinematic relationships. The solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell. The discretization of the system equations by means of the Generalized Differential Quadrature (GDQ) method leads to a standard linear eigenvalue problem, where two independent variables are involved without using the Fourier modal expansion methodology. Numerical results concerning six types of shell structures illustrate the influence of the power-law exponent, of the power-law distribution and of the choice of the four parameters on the mechanical behaviour of shell structures considered.     

Free flexural vibration behavior of laminated angle-ply elliptical cylindrical shells

This paper deals with the free flexural vibration characteristics of anisotropic laminated angle-ply elliptical cylindrical shells using finite element approach. The formulation is based on first-order shear deformation theory. The present model accounts for in-plane and rotary inertia effects. A detailed study is carried out to highlight the effects of shell geometry, cross-sectional properties, lap-up and ply-angle on the natural frequencies pertaining to different types of modes of vibrations of non-circular shell structures.     

Influence of edge conditions on the modal characteristics of cross-ply laminated shells

The dynamic and static behavior of cross-ply laminated shells are investigated using the third-order shear deformation shell theory of Reddy. The theory is a modification of the Sanders shell theory and accounts for parabolic distribution of the transverse shear strains through the thickness of the shell and does not require shear correction coefficients. The Lévy-type exact solutions for bending, buckling and natural vibration are presented for doubly curved, cylindrical and spherical shells under various boundary conditions.     

An exact solution for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends

In this paper, a new exact solution based on the classical shell theory (CST) for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends is proposed. The present exact solution can be summed up in the following steps: Firstly, the displacement functions are constructed by the governing differential equations with the exact closed form solutions; Then, the artificial spring technology is introduced to simulate the general boundary conditions of the two end edges of shell; Thirdly, the equation for natural frequencies is obtained by means of the method of reverberation-ray matrix (MRRM); Lastly, the vibration results are presented by the modified golden section search (MGSS) algorithm. By comparing the present method with published papers, the accuracy of present method is verified. On the basis of that, some new exact nature frequencies and mode shapes of the cross-ply laminated composite cylindrical shells with various classical boundary conditions and elastic restraints are performed and they can be served as the benchmark data for the future.