波传播法求解低频激励下水中加端板圆柱壳的振动

采用波传播法研究了低频下水中壳体的振动与响应。水中壳体由有限长加流体载荷的圆柱壳和两端的圆形端板组成,其中外部流体载荷用无限长模型进行近似处理。为了模拟推动系统的激励及船体上某一点激励,分别考虑了不同位置的轴向载荷和径向载荷,讨论了单个周向模态下的位移在总位移中的比重。主要研究了4种载荷,即作用在端板中心的轴对称载荷、作用在端板与圆柱连接处的轴向载荷、作用在连接处的径向载荷和作用在壳体中间的径向载荷,比较得出了轴对称和非轴对称、同一点不同方向载荷、同一方向不同位置载荷的响应位移的不同。此外,还研究了两端端板对不同载荷下水中壳体响应的影响,得出了端板主要抑制了壳体的较高阶模态下径向位移的结论。解析法结果与有限元法结果进行了比较,验证了该方法的正确性。     

水下冲击载荷用下复合材料圆柱壳的弹性响应

研究了平面阶跃冲击波作用下沉浸无限长复合材料圆柱壳的瞬态响应。首先推导了基于Flugge薄壳理论的复合材料圆柱壳的控制运动方程,然后采用反射尾流虚源法建立流体-结构的相互作用,最后采用有限差分法来求解平面冲击波作用下无限长复合材料圆柱壳的控制运动微分方程。详细考察了复合材料纤维方向和壳的半径对复合材料圆柱壳的无因次中面应变、第0阶模态径向位移和第1阶模态径向速度的影响。     

水下冲击载荷作用下复合材料圆柱壳的弹性响应

研究了平面阶跃冲击波作用下沉浸无限长复合材料圆柱壳的瞬态响应。首先推导基于Flugge薄壳理论的复合材料圆柱壳的控制运动方程,然后采用反射尾流虚源法建立流体-结构的相互作用,最后采用有限差分法来求解平面冲击波作用下无限长复合材料圆柱壳的控制运动微分方程。详细考察了复合材料纤维方向和壳的半径对复合材料圆柱壳的无因次中面应变、第0阶模态径向位移和第1阶模态径向速度的影响。     

冲击载荷作用下金属圆柱壳能量吸收研究

对Singace叠缩模型进行了修正,选用Johnson-Cook本构方程,研究冲击载荷的应变强化效应、应变率强化效应和温度效应下圆柱壳的吸能情况,利用分步叠缩的方法计算得到金属圆柱壳在冲击载荷作用下所吸收的能量值、温度的增加值和瞬时载荷-位移曲线,分析了圆柱壳的半径和厚度以及叠缩速度和能量吸收之间的关系     

阶梯圆柱壳在轴向冲击载荷作用下的屈曲计算分析

建立并求解了阶梯圆柱壳径向位移控制方程,考虑边界条件及相容条件,得到应力波发生反射后阶梯圆柱壳的动态屈曲分叉条件。通过数值计算,分别给出了不同时间段屈曲临界载荷与应力波波阵面到达阶梯圆柱壳的位置、阶梯圆柱壳厚径比的关系。数值计算结果表明,阶梯圆柱壳发生轴对称屈曲相对非轴对称屈曲更容易;应力波传播经固定端反射,通过分界面后比通过分界面之前固定端部更难发生屈曲,而冲击端部较易发生屈曲。随着厚径比及厚度比的增大临界载荷也随之增大。质量相同的阶梯圆柱壳与等厚度圆柱壳,应力波经固定端反射通过分界面之前阶梯圆柱壳更易发生屈曲,而通过分界面之后阶梯圆柱壳更难发生屈曲。     

一般边界条件下受轴向冲击圆柱壳的动力特性计算分析

在受轴向冲击圆柱壳的非冲击端引入轴向、周向、径向和径向旋转4个方向边界弹簧模拟一般边界条件。根据Love薄壳理论得到圆柱壳变形过程中的应力应变,并采用一种改进的Fourier级数方法表示圆柱壳沿坐标轴方向的位移。将应力应变以及位移代入圆柱壳的能量表达式,采用基于Hamilton方程的一阶变分法对能量表达式进行推导和变换,得到一般边界条件下受轴向冲击圆柱壳的自然频率以及动力屈曲临界载荷的判别式。计算分析了一般边界条件对受轴向冲击圆柱壳的自然频率和屈曲临界载荷的影响,以及不同边界条件圆柱壳屈曲模态的类型特点。结果表明：一般边界条件下自然频率随着冲击载荷增大而降低;随着轴向波数的增加圆柱壳自然频率及屈曲临界载荷增大,随着周向波数的增加屈曲临界载荷也增大;轴向、周向、径向和径向旋转各个方向边界刚度对圆柱壳自然频率和屈曲临界载荷的影响都是刚度系数越小,自然频率越低而临界载荷越大;圆柱壳受轴向冲击,边界条件的改变会影响屈曲模态。     

方口径电磁轨道发射装置导轨及壁板的动力响应

本文将方口径电磁发射装置的导轨及壁板简化为双层弹性基础梁,分别采用Heaviside函数和Dirac函数表示随电枢移动所产生的均布电磁力和电枢作用在导轨上的集中载荷,建立了导轨及壁板的动态响应方程。应用模态正交性及正则化原理,求得了导轨及壁板的位移和应力的解析解。通过算例,分析了给定运动及结构参数的情况下,导轨及壁板的动力响应,并将解析解与采用ANSYS数值分析结果进行了比较,佐证了解析解的可靠性。本文的研究结果可为方口径电磁轨道发射装置的动态特性分析奠定了基础。     

压电层合纤维在动载荷作用下的应力和电势的瞬态响应

利用压电层合纤维层间的连续性条件和外表面的应力边界条件,通过有限Hankel积分变换和Laplace变换求解压电层合纤维的力电耦合的动力学方程,给出了压电层合纤维在动载荷作用下的应力和电势瞬态响应的解析解。从解析表达式和算例,可以得到在径向动载荷下层合压电纤维的应力和电势的瞬态响应历程和实心处动态集中效应的规律。     

强厚度叠层连续闭口圆柱壳轴对称问题的精确解

抛弃任何有关位移或应力模式的假设，在文献［１］、［２］的基础上，引入δ－函数，导出连续闭口厚圆柱壳轴对称问题的状态方程；给出薄的、中厚的和强厚的叠层连续闭口圆柱壳的统一的精确解。     

流体作用下正交各向异性圆锥壳的自由振动

给出了流体载荷作用下正交各向异性圆锥壳体的自由振动理论模型。通过波传播法和Galerkin法得到了流体载荷作用下截锥壳体自由振动的解。流体载荷作用下的锥壳被划分为好几段,并且每个小圆锥段被当作一个小圆柱段。通过确定每个小圆柱段的流体载荷,来确定锥壳的流体载荷。这样,作用在锥壳上的流体载荷逐段加载。流体载何以及没有流体载荷作用的各向同性和正交各向异性圆锥壳的数值结果被计算出来阐述求解过程的有效性。     

Three-dimensional nonlinear thermo-elastic analysis of functionally graded cylindrical shells with piezoelectric layers by differential quadrature method

Three-dimensional nonlinear thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads is carried out. The strain–displacement relations are based on the nonlinear Lagrangian strain–displacement relations; that is, nonlinear terms containing derivatives of the displacement in the radial direction are included. Material properties of the shell are assumed to be graded in the radial direction according to a power law but the Poisson’s ratio is assumed to be constant. Cylindrical shells are assumed to be under the effect of pressure loading in cosine form, ring pressure loads, electric and temperature fields. Numerical results of stress, displacement, electric and thermal fields are obtained by using two versions of the differential quadrature methods, namely polynomial and Fourier quadrature methods. The convergence of the solution is studied, and results of the axisymmetric loadings are verified with reported results for a cylindrical shell with material properties obeying a power law. Effects of the grading index of material properties, the temperature difference, the ratio of the mean radius to the thickness of the shell, boundary conditions, the thickness of piezoelectric layers and electric excitation on stress, displacement, electric and temperature fields are presented.     

外压作用下椭圆截面柱壳的弹性屈曲

基于能量法推导了外压作用下椭圆截面柱壳弹性屈曲临界荷载的理论解,推导中考虑了椭圆截面连续变化的曲率,引入带有衰减系数的位移函数以反映外压作用下椭圆柱壳的变形特点,并利用里兹法求解外压椭圆柱壳的能量方程。由椭圆柱壳理论解退化求得的圆柱壳外压屈曲荷载与已有文献的经典解吻合良好,与有限元分析结果的比较进一步验证了该文理论解的准确性。基于理论解的参数分析表明:在外压作用下,椭圆柱壳具备比圆柱壳更优越的力学性能;椭圆柱壳的外压屈曲荷载随椭圆截面比的增大而增大,随壳体名义径厚比的减小而增大;椭圆柱壳的外压屈曲荷载随壳体长度的增大而降低,但当名义长径比大于1左右后,屈曲荷载基本保持不变。     

Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation

In this study, the mechanical buckling of functionally graded material cylindrical shell that is embedded in an outer elastic medium and subjected to combined axial and radial compressive loads is investigated. The material properties are assumed to vary smoothly through the shell thickness according to a power law distribution of the volume fraction of constituent materials. Theoretical formulations are presented based on a higher-order shear deformation shell theory (HSDT) considering the transverse shear strains. Using the nonlinear strain–displacement relations of FGMs cylindrical shells, the governing equations are derived. The elastic foundation is modelled by two parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The boundary condition is considered to be simply-supported. The novelty of the present work is to achieve the closed-form solutions for the critical mechanical buckling loads of the FGM cylindrical shells surrounded by elastic medium. The effects of shell geometry, the volume fraction exponent, and the foundation parameters on the critical buckling load are investigated. The numerical results reveal that the elastic foundation has significant effect on the critical buckling load.     

An energy conservative symplectic methodology for buckling of cylindrical shells under axial compression

This study concerns a theoretical analysis on the buckling of cylindrical shells under axial compression in a new energy conservative symplectic system. By introducing four pairs of dual variables and employing the Legendre transformation, the governing equations that are expressed in stress function and radial displacement are re-arranged into Hamiltonian’s canonical equations. The critical loads and buckling modes are reduced to solving for symplectic eigenvalues and eigensolutions, respectively. The obtained results conclude that buckling solutions are mainly grouped into two types according to their nature of different buckling modes: non-uniform buckling with deflection localized at the vicinity of the ends and uniform buckling with deformation waves distributed uniformly along the axial direction, and the complete solving space only consists of the basic eigensolutions. The influence of geometric parameters and boundary conditions on the critical loads and buckling modes is discussed in detail, and some insights into this problem are analyzed.     

Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory

A new higher order shear deformation theory for elastic composite/sandwich plates and shells is developed. The new displacement field depends on a parameter “m”, whose value is determined so as to give results closest to the 3D elasticity bending solutions. The present theory accounts for an approximately parabolic distribution of the transverse shear strains through the shell thickness and tangential stress-free boundary conditions on the shell boundary surface. The governing equations and boundary conditions are derived by employing the principle of virtual work. These equations are solved using Navier-type, closed form solutions. Static and dynamic results are presented for cylindrical and spherical shells and plates for simply supported boundary conditions. Shells and plates are subjected to bi-sinusoidal, distributed and point loads. Results are provided for thick to thin as well as shallow and deep shells. The accuracy of the present code is verified by comparing it with various available results in the literature.     

Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory

A new higher order shear deformation theory for elastic composite/sandwich plates and shells is developed. The new displacement field depends on a parameter “m”, whose value is determined so as to give results closest to the 3D elasticity bending solutions. The present theory accounts for an approximately parabolic distribution of the transverse shear strains through the shell thickness and tangential stress-free boundary conditions on the shell boundary surface. The governing equations and boundary conditions are derived by employing the principle of virtual work. These equations are solved using Navier-type, closed form solutions. Static and dynamic results are presented for cylindrical and spherical shells and plates for simply supported boundary conditions. Shells and plates are subjected to bi-sinusoidal, distributed and point loads. Results are provided for thick to thin as well as shallow and deep shells. The accuracy of the present code is verified by comparing it with various available results in the literature.     

Transient wave propagation and early short time transient responses of laminated composite cylindrical shells

The generalized ray method (GRM) and the method of reverberation ray matrix (MRRM) have been successfully used to study the transient elastic wave transmission in the beams, planar trusses, space frames and infinite layered media. In this paper, the GRM and MRRM are extended to investigate the early short time transient responses of laminated composite cylindrical shells with finite size under impact load. Using the Laplace transformation, the ray groups transmitting in the laminated cylindrical shells under the shock load are yielded by means of the boundary conditions. The reverberation-ray matrix representing the multi-reflected and scattered waves in the laminated cylindrical shells with finite structural size is deduced. Using FFT algorithm, the transient response corresponding to each ray group can be derived. Through the numerical simulations, it is seen that the early short time transient accelerations of the laminated composite cylindrical shells under impact loads are very large, but the early short time transient shear strain and displacement are very small. Furthermore, the effects of the stacking sequence, thickness of the composite cylindrical shells and different shock loads on the early short time transient responses of the laminated composite cylindrical shells with finite size are also analyzed.     

Buckling of thick orthotropic spherical shells

This paper is concerned with the semi-analytical solution for the axisymmetric buckling for perfect complete thick orthotropic spherical shells and hemispherical shells under various edge conditions, subjected to uniform full external pressures. The meridional and radial mid-surface displacements and the circumferential cross-sectional rotation are expressed as an expansion in Legendre polynomials respectively in the meridional coordinate. Transverse shear strain effects are included in the energy formulation of small strains. The solutions are achieved directly by use of the Ritz method without considering the force and moment equilibrium and solving the complicated governing equations. Critical buckling loads and the various modes are found from the equations by use of orthogonality and some integral relations.     

Response and control of functionally graded laminated piezoelectric shells under thermal shock and moving loadings

Based on the first-order shear deformation theory (FSDT), approximate solution for FG (functionally graded) laminated piezoelectric cylindrical shells under thermal shock and moving mechanical loads is given utilizing Hamilton’s principle. The thin piezoelectric layers embedded on inner and outer surfaces of the functionally graded layer are acted as distributed sensor and actuator to control dynamic characteristics of the FG laminated cylindrical shells. Here, the modal analysis technique and Newmark’s integration method are used to calculate the dynamic response of FG laminated cylindrical shells. Constant-gain negative velocity feedback approach is used for active vibration control. The active vibration control to a single moving concentrated loading, thermal shock loading and a continuous stream of moving concentrated loadings is, respectively, investigated. Results indicate that the control gain and velocity of moving loadings have significant effects on the dynamic response and resonance of the system.     

Mixed Formulation Solution and Optical Based Experimental Methods in the Deformation Analysis of Radially Loaded Cylindrical Shells

Abstract: A mixed formulation in the characterization of internal forces and displacements in cylindrical shells, subjected to radial forces is presented. This numerical approach is proposed as an alternative to the irreducible formulation, where in some problems this solution leads to stress distribution presenting some discontinuity along the edge joining shell modules with different geometry as, for example, curved pipes with tangent terminations. The mixed formulation here proposed prescribes the continuity in the stress field at shell adjacent sections, while practically ensures similar accuracy in the displacement and stress fields. The force and displacement formulations are carried out by combining unknown analytic functions with trigonometric expansions. The solution can be applied to recurrent problems in piping design as is the case of edge forces and radial loads. Examples considering these external parameters are developed and results are compared with an experimental method based on optical interferometric techniques. These procedures were applied with video recording of the interferometric pattern and allow the displacement field assessment with a non‐contact procedure.