薄膜结构气弹动力稳定性研究

将扁壳的无矩理论和流体的理想势流理论结合起来对薄膜结构的气弹动力稳定性进行了研究,提出了结构失稳的判别准则,确定了结构失稳临界风速。首先应用扁壳的无矩理论建立了薄膜结构的动力平衡方程。然后假设来流为均匀的理想势流,考虑流固耦合作用,对风向沿结构拱向和垂向时分别采用不同的气弹模型确定了作用于薄膜表面的气动力,得到了两种情况下薄膜结构的气弹动力耦合作用方程。利用Bubnov-Galerkin方法将此耦合作用方程转化为一常系数二阶微分方程,并根据Routh-Hurwitz稳定性准则确定了薄膜的失稳临界风速。最后通过对临界风速的影响因素进行分析,得到了一些重要结论,并提出了防止薄膜结构气弹失稳的一些基本措施。     

Supersonic flutter prediction of functionally graded conical shells

Aero-thermoelastic analysis of a simply supported functionally graded truncated conical shell subjected to supersonic air flow is performed to predict the flutter boundaries. The temperature-dependent properties of the FG shell are assumed to be graded through the thickness according to a simple rule of mixture and power-law function of volume fractions of material constituents. Through the thickness steady-state heat conduction is considered for thermal analysis. To perform the stability analysis, the general nonlinear equations of motion are first derived using the classical Love’s shell theory and the von Karman–Donnell-type of kinematic nonlinearity together with the linearized first-order piston theory for aerodynamic loading. Then the nonlinear equations of motion are linearized to obtain the linear equilibrium and aeroelastic equations. The equilibrium equations are solved using power series method to obtain the initial stresses induced by aerodynamic and thermal loadings. The results are then used as an input to the aeroelastic stability equations which are finally solved with the generalized Galerkin method. The flutter boundaries are obtained for the FG conical shells with different semi-vertex cone angles, different temperature distributions, and different volume fraction indices.     

Transient dynamic and free vibration analysis of functionally graded truncated conical shells with non-uniform thickness subjected to mechanical shock loading

This paper is focused on the transient dynamic and free vibration analysis of functionally graded (FG) axisymmetric truncated conical shells with non-uniform thickness. Two numerically efficient and accurate solution methods are presented to study the transient dynamic responses of FG shells subjected to either internal or external mechanical shock loading. Employing the displacement-based layerwise theory in conjunction with the Hamilton’s principle, the transversely discretized equations of motion are obtained. The differential quadrature method (DQM) is used to discretize the resulting equations in the axial direction. To solve the developed time-dependent equations, either DQM (named LWDQ) or Newmark’s time integration scheme (named LWDQN) is employed. The material properties are graded continuously in the thickness direction according to a volume fraction power-law distribution. The developed results are successfully compared with those obtained by ANSYS and also with the available results in the literature. The comparisons demonstrate the accuracy and effectiveness of the aforementioned methods on achievement of fast convergence rate with relatively low computational cost. Finally, the effects of different geometric and material parameters on the dynamic behavior of the FG shells are investigated. Due to high accuracy of the method, the results can be used as benchmarks for future research.     

Finite element method applied to the supersonic flutter of circular cylindrical shells

The application of the finite element method to the supersonic flutter of circular cylindrical shells subjected to internal pressure and axial compression is presented. A circular cylindrical shell element is used. The element stiffness, mass and initial stiffness matrices are given. The element aerodynamic matrix is derived based on a first order high Mach number approximation to the linear potential flow theory. The eigenvalue problem is solved by the QR algorithm. Numerical results are presented and these are compared with analytical solutions and experimental data.     

Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment

The free vibration analysis of rotating functionally graded (FG) cylindrical shells subjected to thermal environment is investigated based on the first order shear deformation theory (FSDT) of shells. The formulation includes the centrifugal and Coriolis forces due to rotation of the shell. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The initial thermo-mechanical stresses are obtained by solving the thermoelastic equilibrium equations. The equations of motion and the related boundary conditions are derived using Hamilton’s principle. The differential quadrature method (DQM) as an efficient and accurate numerical tool is adopted to discretize the thermoelastic equilibrium equations and the equations of motion. The convergence behavior of the method is demonstrated and comparison studies with the available solutions in the literature are performed. Finally, the effects of angular velocity, Coriolis acceleration, temperature dependence of material properties, material property graded index and geometrical parameters on the frequency parameters of the FG cylindrical shells with different boundary conditions are investigated.     

Thermoelastic analysis of rotating laminated functionally graded cylindrical shells using layerwise differential quadrature method

An accurate and efficient solution procedure based on the elasticity theory is employed to investigate the thermoelastic behavior of rotating laminated functionally graded (FG) cylindrical shells in thermal environment. The material properties are assumed to be temperature dependent and graded in the thickness direction. In order to accurately model the variation of the field variables across the thickness, the shell is divided into a set of mathematical layers. The differential quadrature method (DQM) is adopted to discretize the governing differential equations of each layer together with the related boundary and compatibility conditions at the interface of two adjacent layers. Using the DQM enables one to accurately and efficiently discretize the partial differential equations, especially along the graded direction, and also implement the boundary and compatibility conditions in their strong forms. After demonstrating the convergence and accuracy of the presented approach, the effects of material and geometrical parameters and also temperature dependence of material properties on the stresses and displacement components of rotating laminated FG cylindrical shells are studied.     

Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory

A two-dimensional (2D) higher-order deformation theory is presented for vibration and buckling problems of circular cylindrical shells made of functionally graded materials (FGMs). The modulus of elasticity of functionally graded (FG) shells is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal deformations, and rotatory inertia is derived through Hamilton’s principle. Several sets of truncated Mth order approximate theories are applied to solve the eigenvalue problems of simply supported FG circular cylindrical shells. In order to assure the accuracy of the present theory, convergence properties of the fundamental natural frequency for the fundamental mode r=s=1 are examined in detail. A comparison of the present natural frequencies of isotropic and FG shells is also made with previously published results. Critical buckling stresses of simply supported FG circular cylindrical shells subjected to axial stress are also obtained and a relation between the buckling stress and natural frequency is presented. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. Modal transverse shear and normal stresses are calculated by integrating the three-dimensional (3D) equations of motion in the thickness direction satisfying the stress boundary conditions at the outer and inner surfaces. The 2D higher-order deformation theory has an advantage in the analysis of vibration and buckling problems of FG circular cylindrical shells.     

Analytical model of sound transmission through relatively thick FGM cylindrical shells considering third order shear deformation theory

This work presents an analytical solution for acoustic transmission through relatively thick FGM cylindrical shells using third order shear deformation theory (TSDT). An infinitely long FGM cylindrical shell composed of metal and ceramic with power-law distribution of volume fraction through the thickness is considered. The shell is immersed in a fluid with an external airflow and an oblique plane wave impinges on the external sidewall of the shell. Comparing the results of present study with those of previous models (CST and FSDT) for thin shells, similar results are observed due to limited effects of shear and rotation on transmission loss (TL). However, for relatively thick shells where the shear and rotation effects become more important in lower R/h, TSDT presents more accurate results caused by its higher order model. In addition, the results show proportional change in TL according to distribution of material properties through the thickness of FG cylindrical shells.     

Three-Dimensional Solutions of Functionally Graded Piezo-Thermo-Elastic Shells and Plates Using a Modified Pagano Method

A modified Pagano method is developed for the three-dimensional (3D) coupled analysis of simply-supported, doubly curved functionally graded (FG) piezo-thermo-elastic shells under thermal loads. Four different loading conditions, applied on the lateral surfaces of the shells, are considered. The material properties of FG shells are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependent on this. The Pagano method, conventionally used for the analysis of multilayered composite elastic plates/shells, is modified to be feasible for the present analysis of FG piezo-thermo-elastic plates/shells. The modifications include that a displacement-based formulation is replaced by a mixed formulation, a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions, a successive approximation (SA) method is adopted and introduced in the present analysis, and the propagator matrix method is developed for the heat conduction analysis and the coupled piezo-thermo-elastic analysis of the FG shells. The influence of the material-property gradient index on the field variables, induced in the FG piezo-thermo-elastic shells and plates under the thermal load, is studied.     

Dynamic responses of functionally graded magneto-electro-elastic shells with open-circuit surface conditions

Three-dimensional (3D) free-vibration analysis of simply supported, doubly curved functionally graded (FG) magneto-electro-elastic shells with open-circuit surface conditions is studied using an asymptotic approach. The material properties of the FG shells are regarded as heterogeneous through the thickness coordinate. The 29 basic equations of 3D magneto-electro-elasticity are firstly reduced to a system of 10 state space vector equations in terms of 10 primary variables in elastic, electric and magnetic fields. Apart from the regular asymptotic expansion in the early paper on static analysis, the method of multiple time scales is used to eliminate the secular terms and to make the asymptotic expansion feasible. Through a straightforward derivation, we finally decompose the present 3D problem as recursive sets of two-dimensional (2D) problems with motion equations of the coupled classical shell theory (CCST). The orthonormality and solvability conditions for various order problems are derived. With these conditions, it is shown that the 3D asymptotic solutions can be obtained by repeatedly solving the CCST-type motion equations order-by-order in a systematic and hierarchic manner. The influence of the gradient index of material properties on the natural frequencies and their corresponding modal field variables of various FG piezoelectric and magneto-electro-elastic shells is presented.     

On a problem of the vibration of functionally graded conical shells with mixed boundary conditions

This paper presents a theoretical approach to solve vibration problems of functionally graded (FG) truncated conical shells under mixed boundary conditions. The material properties of FG shell are assumed to vary continuously through the thickness of the conical shell. The fundamental relations, motion and strain compatibility equations of FG truncated conical shells are derived by means of the Airy stress function method. Two cases of mixed boundary conditions are investigated. The basic equations are solved by using Galerkin method and fundamental cyclic frequencies of FG truncated conical shells are obtained. The results are compared and validated with the results available in the literature. The detailed parametric studies are carried out to investigate the influences of radius-to-thickness ratio, lengths-to-radius ratio, material composition and mixed boundary conditions on the fundamental cyclic frequencies of truncated conical shells.     

Postbuckling of functionally graded fiber reinforced composite laminated cylindrical shells, Part I: Theory and solutions

Buckling and postbuckling behavior are presented for fiber reinforced composite (FRC) laminated cylindrical shells subjected to axial compression or a uniform external pressure in thermal environments. Two kinds of fiber reinforced composite laminated shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The governing equations are based on a higher order shear deformation shell theory with von Kármán-type of kinematic non-linearity and including the extension-twist, extension-flexural and flexural-twist couplings. The thermal effects are also included, and the material properties of FRC laminated cylindrical shells are estimated through a micromechanical model and are assumed to be temperature dependent. The non-linear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths of FRC laminated cylindrical shells.     

On the vibration and stability of shear deformable FGM truncated conical shells subjected to an axial load

The aim of present study is to investigate the vibration and stability of functionally graded (FG) conical shells under a compressive axial load using the shear deformation theory (SDT). The basic equations of shear deformable FG conical shells are derived using Donnell shell theory and solved using Galerkin's method. The novelty of this study is to achieve closed-form solutions for the dimensionless frequencies and critical axial loads for freely-supported FG truncated conical shells on the basis of the SDT. Parametric studies are made to investigate effects of shear stresses, compositional profiles and conical shell characteristics on the critical parameters. Some comparisons with the various studies have been performed in order to show the accuracy of the present study.     

Influences of elastic foundations and shear deformations on the buckling behavior of functionally graded material truncated conical shells under axial compression

This article presents an investigation on the buckling of functionally graded (FG) truncated conical shells under an axial load resting on elastic foundations within the shear deformation theory (SDT). The governing equations are solved using the Galerkin method, and the closed-form solution of the axial buckling load for FG conical shells on elastic foundations within the SDT is obtained. Various numerical examples are presented and discussed to verify the accuracy of the closed-form solution in predicting dimensionless buckling loads for FG conical shells on the Winkler–Pasternak elastic foundations within the SDT.     

Static behavior of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux

Three-dimensional (3D) static behavior of doubly curved functionally graded (FG) magneto-electro-elastic shells under the mechanical load, electric displacement and magnetic flux is studied by an asymptotic approach. Without loss of generality, the material properties of the shells are regarded as heterogeneous through the thickness coordinate. The edge boundary conditions are considered as the full simple supports. The basic equations of 3D magneto-electro-elasticity are firstly reduced to the state-space vector equations by means of direct elimination. By introducing a geometric perturbation parameter and following the regular asymptotic expansion, we finally decompose the 3D problem as recursive sets of two-dimensional (2D) problems with governing equations of the coupled classical shell theory (CCST). It is shown that the 3D solutions can be obtained by repeatedly solving the CCST-type equations order-by-order in view of the recursive property among various order problems. Parametric studies for both the coupling magneto-electro-elastic effect and the influence of the gradient index of material properties on the structural behavior of various FG shells under magneto-electro-mechanical loads are presented.     

Postbuckling of nanotube-reinforced composite cylindrical shells under combined axial and radial mechanical loads in thermal environment

A postbuckling analysis is presented for nanocomposite cylindrical shells reinforced by single-walled carbon nanotubes (SWCNTs) subjected to combined axial and radial mechanical loads in thermal environment. Two types of carbon nanotube-reinforced composite (CNTRC) shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The material properties of FG-CNTRCs are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations are based on a higher order shear deformation shell theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. A boundary layer theory and associated singular perturbation technique are employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, FG-CNTRC cylindrical shells under combined action of external pressure and axial compression for different values of load-proportional parameters. The results for UD-CNTRC shell, which is a special case in the present study, are compared with those of the FG-CNTRC shell.     

小垂度薄膜屋盖的气弹动力耦合作用方程

薄膜结构自重轻、刚度小、自振频率低,对风的作用非常敏感,一般认为在风荷载作用下会产生较大的位移和加速度反应,并可能引起局部流场的变化甚至诱发气弹失稳,所以应在考虑风与结构的耦合作用基础上分析结构的风振反应。研究了风与薄膜屋盖的耦合作用方程。从弹性薄壳的无矩理论出发,考虑薄膜结构的几何非线性,并引入扁壳理论的假定建立了小垂度薄膜屋盖的平衡方程和相容方程。然后采用流体力学中的势流理论并参考空气动力学中的薄翼型理论确定了作用于封闭薄膜屋盖外侧的动气压,从而建立了风与薄膜屋盖的动力耦合作用方程。为下一步的研究提供了解析模型。     

弹性圆柱薄壳在流体中的变形与内力分析

应用薄壳弹性理论及流体力学基本方程,给出了圆柱壳在流体中流固耦合问题的基本关系式。阐述并应用相容拉格朗日-欧拉方法推导出流体绕壳横向流动时弹性圆柱薄壳的小弯曲变形问题的方程,并求解了流场的速度势和壳体的变形及内力分布。通过具体算例,绘出了流场分布图,讨论了有关参数变化对圆柱壳变形和表面压力系数的影响。     

Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments,Part I: Axially-loaded shells

A postbuckling analysis is presented for nanocomposite cylindrical shells reinforced by single-walled carbon nanotubes (SWCNTs) subjected to axial compression in thermal environments. Two kinds of carbon nanotube-reinforced composite (CNTRC) shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The material properties of FG-CNTRCs are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations are based on a higher order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of axially-loaded, perfect and imperfect, FG-CNTRC cylindrical shells under different sets of thermal environmental conditions. The results for UD-CNTRC shell, which is a special case in the present study, are compared with those of the FG-CNTRC shell. The results show that the linear functionally graded reinforcements can increase the buckling load as well as postbuckling strength of the shell under axial compression. The results reveal that the CNT volume fraction has a significant effect on the buckling load and postbuckling behavior of CNTRC shells.     

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.