Stability and vibration of isotropic,orthotropic and laminated plates according to a higher-order shear deformation theory

A higher-order shear deformation theory is used to determine the natural frequencies and buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia. Exact solutions of simply supported plates are obtained and the results are compared with the exact solutions of three-dimensional elasticity theory, the first-order shear deformation theory, and the classical plate theory. The present theory predicts the frequencies and buckling loads more accurately when compared to the first-order and classical plate theories.     

General theory of micropolar elastic thin shells

The paper formulates general hypotheses of micropolar elastic thin shells that are given asymptotic validation. Using these hypotheses and three-dimensional Cosserat (micropolar, asymmetric) theory of elasticity, general two-dimensional applied models of micropolar elastic thin shells with independent displacement and rotation fields, constrained rotation and low shear rigidity are constructed to suit dimensionless physical parameters of the shell material. The constructed micropolar shell models take into complete account transverse shear strain and related strain. Models of micropolar elastic thin plates and beams are particular cases of the constructed micropolar shell models. An axially symmetric stress-strain state problem of a hinged cylindrical micropolar shell is considered. Numerical analysis is used to demonstrate effective strength and rigidity characteristics of micropolar elastic shells.     

Sound radiation from shear deformable stiffened laminated plates

Sound radiation from shear deformable stiffened laminated plates is studied theoretically. The equations of motion for the composite laminated plate are derived on the basis of the first-order shear deformation plate theory. Two sets of parallel stiffeners interact with the laminated plate only through the normal line forces. By using the Fourier wavenumber transform and the stationary phase method, the far-field sound pressure is described analytically. Sound pressure given by the first-order shear deformation plate theory and the classical thin plate theory is compared, and the differences of sound pressure are shown in the high frequency range for an isotropic plate. Sound pressure and the transverse displacement spectra are presented to illustrate the effects of force location, stiffeners and angle-ply layers. Sound radiation from symmetric and antisymmetric composite plates with multiple loadings is also investigated.     

A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach

Large-amplitude (geometrically non-linear) vibrations of circular cylindrical shells subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated. The Lagrange equations of motion are obtained by an energy approach, retaining damping through Rayleigh's dissipation function. Four different non-linear thin shell theories, namely Donnell's, Sanders-Koiter, Flügge-Lur’e-Byrne and Novozhilov's theories, which neglect rotary inertia and shear deformation, are used to calculate the elastic strain energy. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite shells. The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of the lowest natural frequency is computed for all these shell theories. Numerical responses obtained by using these four non-linear shell theories are also compared to results obtained by using the Donnell's non-linear shallow-shell equation of motion. A validation of calculations by comparison with experimental results is also performed. Both empty and fluid-filled shells are investigated by using a potential fluid model. The effects of radial pressure and axial load are also studied. Boundary conditions for simply supported shells are exactly satisfied. Different expansions involving from 14 to 48 generalized co-ordinates, associated with natural modes of simply supported shells, are used. The non-linear equations of motion are studied by using a code based on an arclength continuation method allowing bifurcation analysis.     

Acoustic radiation from shear deformable stiffened laminated cylindrical shells

An analytical model of acoustic radiation from shear deformable laminated cylindrical shells with initial axial loadings and doubly periodic rings is presented. The shear deformation and rotary inertia of the rings are taken into account and the rings interact with the cylindrical shell only through the normal forces. The far-field sound pressure is found by using the Fourier wavenumber transform and stationary phase method. High frequency limitation issues of the first-order shear deformation theory are discussed and the effects of the second set of rings, axial initial loadings and multiple external loadings on the far-field acoustic radiation are explored. Further, the helical wave spectra of the radial displacement and sound pressure are used to study the vibrational and acoustic characteristics of the laminated shells. Above the ring frequency, the profile of the helical wave spectra of the far-field sound pressure induced by the cylindrical shell is an ellipse and the patterns of the helical wave spectra of the far-field sound pressure keep unchanged. Moreover, the ellipse distinguishes the supersonic wavenumbers and subsonic wavenumbers from the helical wave spectra of the radial displacement and surface sound pressure in the wavenumber domain. The bright spots and highlights of the helical wave spectra show that the corresponding waves are dominant.     

热力联合作用弹性薄圆板的弯曲与屈曲

 导出了热力联合作用下弹性薄圆板的弯曲动力响应控制方程,讨论了其弯曲变形特点及影响失效的因素。分析表明在短时热能沉积作用下,热屈曲是弹性薄板失效的主要方式之一;反鼓包或反冲塞是热屈曲的后继行为;增加外载和热能沉积功率水平都将加速热屈曲的发生;材料的温度相关性与热能沉积的时空分布对薄板的力学行为都有重要影响,同为产生和影响热剪切失效(反冲塞)的重要因素。     

Forced axisymmetric motion of circular,viscoelastic plates

Williams' method for forced motion of elastic systems is applied to circular, viscoelastic plates where the effects of rotatory inertia, transverse shear and time-dependent boundary conditions are included. The viscoelastic material is assumed to have a constant Poisson's ratio. A particular problem is solved for a symmetrically loaded, completely free plate. The material used is vulcanized rubber where the viscoelastic behavior in shear is used in specifying the material parameters of a three-element solid.     

DYNAMICS BEHAVIOR OF AXISYMMETRIC AND BEAM-LIKE ANISOTROPIC CYLINDRICAL SHELLS CONVEYING FLUID

The flow-induced vibration characteristics of anisotropic laminated cylindrical shells partially or completely filled with liquid or subjected to a flowing fluid are studied in this work for two cases of circumferential wave number, the axisymmetric, where n=0 and the beam-like, where n=1. The shear deformation effects are taken into account in this theory; therefore, the equations of motion are determined with displacements and transverse shear as independent variables. The present method is a combination of finite element analysis and refined shell theory in which the displacement functions are derived from the exact solution of refined shell equations based on orthogonal curvilinear co-ordinates. Mass and stiffness matrices are determined by precise analytical integration. A finite element is defined for the liquid in cases of potential flow that yields three forces (inertial, centrifugal and Coriolis) of moving fluid. The mass, stiffness and damping matrices due to the fluid effect are obtained by an analytical integration of the fluid pressure over the liquid element. The available solution based on Sanders' theory can also be obtained from the present theory in the limiting case of infinite stiffness in transverse shear. The natural frequencies of isotropic and anisotropic cylindrical shells that are empty, partially or completely filled with liquid as well as subjected to a flowing fluid, are given. When these results are compared with corresponding results obtained using existing theories, very good agreement is obtained.     

STRUCTURAL RESPONSE OF LAMINATED COMPOSITE SHELLS SUBJECTED TO BLAST LOADING: COMPARISON OF EXPERIMENTAL AND THEORETICAL METHODS

The results from a theoretical and experimental investigation of the dynamic response of cylindrically curved laminated composite shells subjected to normal blast loading are presented. The dynamic equations of motion for cylindrical laminated shells are derived using the assumptions of Love's theory of thin elastic shells. Kinematically admissible displacement functions are chosen to represent the motion of the clamped cylindrical shell and the governing equations are obtained in the time domain using the Galerkin method. The time-dependent equations of the cylindrically curved laminated shell are then solved by the Runge-Kutta-Verner method. Finite element modelling and analysis for the blast-loaded cylindrical shell are also presented. Experimental results for cylindrically curved laminated composite shells with clamped edges and subjected to blast loading are presented. The blast pressure and strain measurements are performed on the shell panels. The strain response frequencies of the clamped cylindrical shells subjected to blast load are obtained using the fast Fourier transformation technique. In addition, the effects of material properties on the dynamic behaviour are examined. The strain-time history curves show agreement between the experimental and analysis results in the longitudinal direction of the cylindrical panels. However, there is a discrepancy between the experimental and analysis results in the circumferential direction of the cylindrical panels. A good prediction is obtained for the response frequency of the cylindrical shell panels.     

DYNAMIC STABILITY OF CURVED PANELS WITH CUTOUTS

The parametric instability behaviour of curved panels with cutouts subjected to in-plane static and periodic compressive edge loadings are studied using finite element analysis. The first order shear deformation theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to Sanders' first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The effects of static and dynamic load factors, geometry, boundary conditions and the cutout parameters on the principal instability regions of curved panels with cutouts are studied in detail using Bolotin's method. Quantitative results are presented to show the effects of shell geometry and load parameters on the stability boundaries. Results for plates are also presented as special cases and are compared with those available in the literature.     

Vibration of cylindrical shells of bimodulus composite materials

A theory is formulated for the small amplitude free vibration of thick, circular cylindrical shells laminated of bimodulus composite materials, which have different elastic properties depending upon whether the fiber-direction strain is tensile or compressive. The theory used is the dynamic, shear deformable (moderately thick shell) analog of the Sanders best first approximation thin shell theory. By means of tracers, the analysis can be reduced to that of various simpler shell theories, namely Love's first approximation, and Donnell's shallow shell theory. As an example of the application of the theory, a closed form solution is presented for a freely supported panel or complete shell. To validate the analysis, numerical results are compared with existing results for various special cases. Also, the effects of the various shell theories, thickness shear flexibility, and bimodulus action are investigated.     

Dynamic analysis of ring-stiffened circular cylindrical shells

A numerical method is developed for the dynamic analysis of ring-stiffened circular cylindrical thin elastic shells. Only circular symmetric vibrations of the shell segments and radial and torsional vibrations of the rings are considered. The geometric and material properties of the shell segments and the rings may vary from segment to segment. Free vibrations or forced vibrations due to harmonic pressure loading are treated with the aid of dynamic stiffness influence coefficients for shell segments and rings. Forced vibrations due to transient pressure loading are treated with the aid of dynamic stiffness influence coefficients for shell segments and rings defined in the Laplace transform domain. The time domain response is then obtained by a numerical inversion of the transformed solution. The effect of external viscous or internal viscoelastic damping is also investigated by the proposed method. In all the cases, the dynamic problem is reduced to a static-like form and the “exact” solution of the problem is numerically obtained.     

均匀流中剪切变形加筋层合板声与振动特性研究

基于一阶剪切变形理论, 建立了分析均匀流中周期加筋层合板声振特性的理论模型. 该模型应用对流波动方程及边界条件精确考虑了均匀流与层合板的耦合作用, 加强筋通过法向线力及扭矩与层合板相互作用, 利用傅里叶波数变换和稳相法, 得到了位移谱和辐射声压的解析表达式. 计算结果与已有公开数据符合良好, 验证了模型的有效性. 数值结果表明, 在高频段不能忽略剪切变形和加强筋扭转运动的影响; 增大均匀流速度可降低结构的辐射声压; 适当调整板厚和加强筋间距可有效避开结构的辐射声压波峰. 关键词： 均匀流 第一阶剪切变形理论 层合板 波数变换     

Influence of physical non-linearity on the dynamic behavior of composite plates

Influence of the physically non-linear property is investigated for three types of motion in laminated plates, namely harmonic waves, free vibrations and shock waves. Only the non-linearity in the transverse shear deformation is included.     

Unsteady fluid dynamic forces on a simply-supported circular cylinder of finite length conveying a flow,with applications to stability analysis

An exact analytic expression for the unsteady fluid pressure acting on the internal walls of a simply-supported circular cylindrical tube of finite length, carrying flow, is presented. The generalized force coefficients corresponding to specific modes of deformation are given explicitly. The results are applied to two problems: (1) the interaction of flow and buckling of thin-walled cylindrical shells subjected to lateral pressure and/or end thrust; (2) the aeroelastic stability of the shells. The second problem is aimed at resolving some controversy about post-divergence flutter oscillation of cylindrical shells or plates exposed to a subsonic flow. The shell equation, of the Morley type, is solved by Galerkin's method and an analytic approach is used to examine the stability of the system. It is important that damping be taken into account in the analysis. The undeformed configuration is always unstable when the flow speed exceeds the minimum divergence boundary.     

Vibration analysis of laminated cross-ply oval cylindrical shells

Here, free vibrations and transient dynamic response analyses of laminated cross-ply oval cylindrical shells are carried out. The formulation is based on higher order theory that accounts for the transverse shear and the transverse normal deformations, and includes zig-zag variation in the in-plane displacements across the thickness of the multi-layered shells. The contributions of inertia effect due to in-plane and rotary motions, and the higher order function arising from the assumed displacement models are included. The governing equations obtained using Lagrangian equations of motion are solved through finite element approach. A detailed parametric study is conducted to bring out the influence of different shell geometry, ovality parameter, lay-up and loading environment on the vibration characteristics related to different modes of vibrations of oval shell.     

Exact closed-form solutions for the natural frequencies and stability of elastically connected multiple beam system using Timoshenko and high-order shear deformation theory

A general procedure for the determination of the natural frequencies and buckling load for a set of beam system under compressive axial loading is investigated using Timoshenko and high-order shear deformation theory. It is assumed that the set beams of the system are simply supported and continuously joined by a Winkler elastic layer. The model of beam includes the effects of axial loading, shear deformation and rotary inertia. In the special case of identical beams, explicit expressions for the natural frequencies and the critical buckling load are determined using a trigonometric method. The influences of the compressive axial loading and the number of beams in the system on the natural frequencies and the critical buckling load are discussed. These results are of considerable practical interest and have wide application in engineering practice of frameworks.     

考虑铺层角的复合材料圆柱壳自由振动三维弹性准确解

为了获得任意角度铺层的多层复合材料圆柱壳的自由振动准确解,在三维弹性理论的基础上,结合分层理论和状态空间法,建立横向位移和应力的传递矩阵,轴向和环向位移采用双螺旋模式的位移函数,对任意角度铺层复合材料圆柱壳简支边界条件下的自由振动进行了理论推导,得到了自由振动方程的精确形式。与文献理论解和有限元计算结果对比,结果表明,关注频率在2倍的环频率以下时,薄壳的固有频率计算精度能控制在1%以内,厚壳的固有频率计算精度能控制在2%以内。对于厚壳的计算可将壳体沿厚度方向划分为多层来处理,这样能有效提高计算精度。计算分析了铺层角对壳体固有频率的影响,环向模态数较低时,固有频率随着铺层角的增加呈抛物线变化趋势;环向模态数较高时,固有频率随着铺层角的增大单调递增。该理论方法同样适用于均质各向同性壳和正交各向异性圆柱壳。      

Buckling of 2D-FG Cylindrical Shells under Combined External Pressure and Axial Compression

This paper presents the stability of two-dimensional functionally graded (2D-FG) cylindrical shells subjected to combined external pressure and axial compression loads, based on classical shell theory. The material properties of functionally graded cylindrical shell are graded in two directional (radial and axial) and determined by the rule of mixture. The Euler's equation is employed to derive the stability equations, which are solved by GDQ method to obtain the critical mechanical buckling loads of the 2D-FG cylindrical shells. The effects of shell geometry, the mechanical properties distribution in radial and axial direction on the critical buckling load are studied and compared with a cylindrical shell made of 1D-FGM. The numerical results reveal that the 2D-FGM has a significant effect on the critical buckling load.     

Comparisons of displacement-based theories for waves and vibrations in laminated and sandwich composite plates

A semi-analytical method incorporating various displacement-based formulations has been developed to investigate propagation of time harmonic waves and vibrations in fiber reinforced polymer composite laminated and sandwich plates. Various displacement-based models starting from the first order shear deformation theory to the fourth order theory have been developed using combinations of linear, quadratic, cubic and quartic variation of axial and transverse displacements through the thickness of a lamina or a mathematical sub-layer. These displacement-based formulations have been validated by comparing their results with the analytical solutions available in the literature. Results of all the displacement models have been compared with those obtained by displacement model using quartic variation of in-plane and transverse displacements for vibration problem. Higher order displacement-based theory using cubic variation of in-plane and transverse displacements through the thickness of sub-layer has been found to yield converging results for wave propagation in laminated composite plates as well as for vibration problems. All the investigations performed indicate the importance of higher order theories for analysis of wave propagation and vibrations in composite laminated and sandwich plates.