Study of vibration characteristics for orthotropic circular cylindrical shells using wave propagation approach and multivariate analysis

A study of free vibration of orthotropic circular cylindrical shells is presented. The vibration control equations of shells are based on Flügge classical thin shell theory. Wave approach is used in the analysis, in which the boundary conditions of shells can be simplified according to the associated beam. The free vibration frequencies of shells can be obtained from a frequency polynomial equation of order 6. The parametric analysis of the free vibration of orthotropic cylindrical shells is investigated using a statistical method. The effects of geometrical parameters and material characteristics upon frequencies are investigated here. Multivariate analysis (MVA) can be a useful tool for this parametric study. Some statistical characteristics, including correlation analysis and ANOVA are applied. ANOVA has been conducted to predict the statistical significance of the various factors. Calculations are performed in the Minitab statistical software. The results show that the L/R, h/R and m have larger effects on the lowest frequency. The importance of input parameters is ranked according to their contributions to the total variance. A knowledge and data visualization approach, Self-organizing mapping (SOM) is also adopted here for mining some intrinsic characteristics of shells.     

基于平均法的旋转薄壁圆柱壳非线性行波振动研究

应用Donnell's简化壳理论,在考虑阻尼和几何非线性的情况下,基于平均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研究.在分析过程中,首先,引入考虑阻尼及几何非线性的薄壁圆柱壳非线性波动方程,进行降阶处理后,得到模态坐标下的振动方程;其次,对模态方程进行平均化处理,确定转换矩阵,进行变量的幅值相角化,从而得到自治的标准化方程组;最后,由系统谐波共振周期解对应平均方程稳态解的原理,得到幅频特性方程.根据上述所得结果,进行了系统参数振动及稳定性研究,并进一步将结果与谐波平衡法及数值解作了比较.     

Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements

This paper presents a formulation of an approximate spectral element for uniform and tapered rotating Euler–Bernoulli beams. The formulation takes into account the varying centrifugal force, mass and bending stiffness. The dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain, where two different interpolating functions for the transverse displacement are used for the element formulation. Both free vibration and wave propagation analysis is performed using the formulated elements. The studies show that the formulated element predicts results, that compare well with the solution available in the literature, at a fraction of the computational effort. In addition, for wave propagation analysis, the element shows superior convergence.     

Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach

The vibration characteristics of a functionally graded material circular cylindrical shell filled with fluid are examined with a wave propagation approach. The shell is filled with an incompressible non-viscous fluid. Axial modal dependence is approximated by exponential functions. A theoretical study of shell vibration frequencies is analyzed for simply supported-simply supported, clamped-simply supported, and clamped-clamped boundary conditions with the fluid effect. The validity and the accuracy of the present method are confirmed by comparing the present results with those available in the literature. Good agreement is observed between the two sets of results.     

单层偏心圆柱薄壳的自由振动特性分析研究

论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.论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.     

Free vibration of layered cylindrical shells filled with fluid

The vibration of the layered cylindrical shells filled with a quiescent, incompressible, and inviscid fluid is analyzed. The governing equations of the cylindrical shells are derived by Love’s approximation. The solutions of the displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms of the displacement functions. The displacement functions are approximated by Bickley-type splines. A generalized eigenvalue problem is obtained and solved numerically for the frequency parameter and an associated eigenvector of the spline coefficients. Two layered shells with three different types of materials under clamped-clamped (C-C) and simply supported (S-S) boundary conditions are considered. The variations of the frequency parameter with respect to the relative layer thickness, the length-to-radius ratio, the length-to-thickness ratio, and the circumferential node number are analyzed.     

Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer

An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric (FGP) layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton’s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different parameters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.     

Free vibration analysis of open thin deep shells with variable radii of curvature

In the present paper, free vibration of a thin open curved shell with parabolic curvature was studied. This shell has a curvature with variable radius in one direction. The equations of motion of this shell were inferred by first order shell theory. According to perpendicular nature of loading on shell of marine structures, the assumptions of Donnell–Mushtari–Vlasov can be used with an acceptable level of accuracy and the in-plane displacement along shell straight direction “x” can be neglected as compared to the displacement in two other directions. The natural frequencies and mode shapes related to the first five vibrational modes were extracted using semi-analytical methods including power series method, Galerkin method and beam function method. The results of the semi-analytical methods were validated against those obtained by using the finite element method. Out of the studied semi-analytical methods, Galerkin method was found to have an appropriate convergence in both natural frequency and mode shape. Adopting eight terms of the response series, Galerkin method has an appropriate convergence compared with the results of finite element.     

基于区域分解的薄壁回转壳自由振动分析

提出了一种区域分解法来分析不同组合边界条件的薄壁回转壳的自由振动.首先沿壳体母线方向将壳体分解为一些自由壳段,并采用广义变分和最小二乘加权残值法将壳体分区界面上的位移协调方程引入到壳体的势能泛函中;然后将壳段位移变量以Fourier级数和Chebyshev多项式展开,对总的势能泛函变分后得到回转壳的离散动力学方程.采用区域分解法分析了不同边界条件的圆柱壳、圆锥壳、抛物壳的自由振动,并将计算结果与其它文献值及 ANSYS 结果对比,结果表明:随着回转壳分区数目的增大,区域分解法计算出的壳体频率很快收敛;本文结果与其它方法计算结果非常吻合(相对误差不超过0.4%).采用该方法可高效计算不同组合边界条件回转壳体的低阶和高阶振动频率.     

On the cell-dependent vibrations and wave propagation in uniperiodic cylindrical shells

Continuum Mechanics and Thermodynamics - The objects of consideration are thin linearly elastic Kirchhoff–Love-type circular cylindrical shells having a periodically micro-heterogeneous...     

Nonlinear vibration of a rotating laminated composite circular cylindrical shell: traveling wave vibration

In this paper, the large-amplitude (geometrically nonlinear) vibrations of rotating, laminated composite circular cylindrical shells subjected to radial harmonic excitation in the neighborhood of the lowest resonances are investigated. Nonlinearities due to large-amplitude shell motion are considered using the Donnell’s nonlinear shallow-shell theory, with account taken of the effect of viscous structure damping. The dynamic Young’s modulus which varies with vibrational frequency of the laminated composite shell is considered. An improved nonlinear model, which needs not to introduce the Airy stress function, is employed to study the nonlinear forced vibrations of the present shells. The system is discretized by Galerkin’s method while a model involving two degrees of freedom, allowing for the traveling wave response of the shell, is adopted. The method of harmonic balance is applied to study the forced vibration responses of the two-degrees-of-freedom system. The stability of analytical steady-state solutions is analyzed. Results obtained with analytical method are compared with numerical simulation. The agreement between them bespeaks the validity of the method developed in this paper. The effects of rotating speed and some other parameters on the nonlinear dynamic response of the system are also investigated.     

Stability analysis of stationary and rotating circular cylindrical shells conveying flowing and rotating fluid

The paper deals with numerical analysis of the stability of stationary and rotating cylindrical shells interacting witha fluid flowing and rotating inside them. It is shown that in the case of the fluid combined flow, the type of the loss of stability depends on the type of the boundary conditions. It is also shown that for different cases of boundary conditions and different geometric dimensions, the fluid rotation can result in an increase or a decrease in the critical velocity of the fluid axial flow.     

Free vibration and stability of an axially moving thin circular cylindrical shell using multiple scales method

This paper investigates the linear free vibration of axially moving simply supported thin circular cylindrical shells with constant and time-dependent velocity considering the effect of viscous structure damping. Classical shell theory is employed to express strain-displacement relation. Linear elasticity theory is used to write stress–strain relation considering Hook’s Law. Governing equations in cylindrical coordinates are derived using the Hamilton principle. Equilibrium equations are rewritten with the help of Donnell–Mushtari shell theory simplification assumptions. Motion equations for displacements in axial and circumferential directions are solved analytically concerning to displacement in the radial direction.As the displacement in the radial direction is the combination of driven and companion modes, the third motion equation is discretized using the Galerkin method. The set of ordinary differential equation obtained from the Galerkin method is solved using the steady-state method, which in practice leads to the prediction of the exact frequencies of vibration. By employing multiple scale method the critical speed values of a circular cylindrical shell and several types of instabilities are discussed. The numerical results show that by increasing the mean velocity, the system always loses stability by the divergence instability in different modes, and the critical speed values of lower modes are higher than those of higher modes. As well as the unstable regions for the resonances between velocity function fluctuation frequencies and the linear combination of natural frequencies is gained from the solvability condition of second order multiple scale method. The accuracy of the method is checked against the available data.

     

Free flapewise vibration analysis of rotating double-tapered Timoshenko beams

Free vibration analysis of a rotating double-tapered Timoshenko beam undergoing flapwise transverse vibration is presented. Using an assumed mode method, the governing equations of motion are derived from the kinetic and potential energy expressions which are derived from a set of hybrid deformation variables. These equations of motion are then transformed into dimensionless forms using a set of dimensionless parameters, such as the hub radius ratio, the dimensionless angular speed ratio, the slenderness ratio, and the height and width taper ratios, etc. The natural frequencies and mode shapes are then determined from these dimensionless equations of motion. The effects of the dimensionless parameters on the natural frequencies and modal characteristics of a rotating double-tapered Timoshenko beam are numerically studied through numerical examples. The tuned angular speed of the rotating double-tapered Timoshenko beam is then investigated.