Mechanical property of cylindrical sandwich shell with gradient core of entangled wire mesh

To explore the wide-frequency damping and vibration-attenuation performances in the application of aerospace components,the cylindrical sandwich shell structure with a gradient core of entangled wire mesh was proposed in this paper.Firstly,the gradient cores of entangled wire mesh in the axial and radial directions were prepared by using an in-house Numerical Control weaving machine,and the metallurgical connection between skin sheets and the gradient core was performed using vacuum brazing.Secondly,to investigate the mechanical properties of cylindrical sandwich shells with axial or radial gradient cores,quasi-static and dynamic mechanical experiments were carried out.The primary evaluations of mechanical properties include secant stiffness,natural frequency,Specific Energy Absorption(SEA),vibration acceleration level,and so on.The results suggest that the vibration-attenuation performance of the sandwich shell is remarkable when the high-density core layer is at the end of the shell or abuts the inner skin.The axial gradient material has almost no influence on the vibration frequencies of the shell,whereas the vibration frequencies increase dramatically when the high-density core layer approaches the skin.Moreover,compared to the conventional sandwich shells,the proposed functional grading cylindrical sandwich shell exhibits more potential in mass reduction,stiffness designing,and energy dissipation.

NONLINEAR STABILITY OF TRUNCATED SHALLOW CONICAL SANDWICH SHELL WITH VARIABLE THICKNESS

The theory of nonlinear stability for a truncated shallow conical shell with variable thickness under the action of uniform pressure was presented. The fundamental equations and boundary conditions were derived by means of calculus of variations. An analytic solution for the critical buckling pressure of the shell with a hyperbolically varying thickness is obtained by use of modified iteration method. The results of numerical calculations are presented in diagrams, which show the influence of geometrical and physical parameters on the buckling behavior.

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITSAPPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

This paper applied the simplified theory.for multilayer sandwich shells undergoingmoderate small rotations in Ref [1] to shallow shells. The equilibrium equations andboundary conditions of large deflction of orthotropic and the special case. isotropicshells, are presented.

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION(III)──LARGE DEFLECTION AND POSTBUCKLING OF SHALLOW SHELLS

In this paper, exact solutions of large deflection of multilayer sandwich shallow shellsunder transverse forces and different boundary conditions are presented. Exact results ofpostbuckling of multilayer sandwich plates, shallow cylindrical shells and nonlineardeflection of general shallow shells such as spherical shells under inplane edge forcesare also obtained by the same procedure.

Mechanical Performance of Bio-inspired Bidirectional Corrugated Sandwich Pressure Shell Under External Hydrostatic Pressure

This paper aims to enhance the compression capacity of underwater cylindrical shells by adopting the corrugated sandwich structure of cuttlebone.The cuttlebone suffers uniaxial external compression,while underwater cylindrical shells are in a biaxial compressive stress state.To suit the biaxial compressive stress state,a novel bidirectional corrugated sandwich structure is proposed to improve the bearing capacity of cylindrical shells.The static and buckling analysis for the sandwich shell and the unstiffened cylindrical shell with the same volume-weight ratio are studied by numerical simulation.It is indicated that the proposed sandwich shell can effectively reduce the ratio between circumferential and axial stress from 2 to 1.25 and improve the critical buckling load by about 1.63 times.Numerical simulation shows that optimizing and adjusting the structural parameters could significantly improve the advantage of the sandwich shell.Then,the hydrostatic pressure tests for shell models fabricated by 3D printing are carried out.According to the experimental results,the overall failure position of the sandwich shell is at the center part of the sandwich shell.It has been found the average critical load of the proposed sandwich shell models exceeds two times that of the unstiffened shell models.Hence,the proposed bio-inspired bidirectional corrugated sandwich structure can significantly enhance the pressure resistance capability of cylindrical shells.

Vibration and Instability of Third⁃Order Shear Deformable FGM Sandwich Cylindrical Shells Conveying Fluid

The vibration and instability of functionally graded material(FGM)sandwich cylindrical shells conveying fluid are investigated.The Navier-Stokes relation is used to describe the fluid pressure acting on the FGM sandwich shells.Based on the third-order shear deformation shell theory,the governing equations of the system are derived by using the Hamilton’s principle.To check the validity of the present analysis,the results are compared with those in previous studies for the special cases.Results manifest that the natural frequency of the fluid-conveying FGM sandwich shells increases with the rise of the core-to-thickness ratio and power-law exponent,while decreases with the rise of fluid density,radius-to-thickness ratio and length-to-radius ratio.The fluid-conveying FGM sandwich shells lose stability when the non-dimensional flow velocity falls in 2.1-2.5,which should be avoided in engineering application.

Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields

The bending and free vibration of a rotating sandwich cylindrical shell are analyzed with the consideration of the nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields by use of the first-order shear deformation theory （FSDT） of shells. The governing equations of motion and the corresponding boundary conditions are established through the variational method and the Maxwell equation. The closed-form solutions of the rotating sandwich cylindrical shell are obtained. The effects of geometrical parameters, volume fractions of carbon nanotubes, applied voltages on the inner and outer piezoelectric layers, and magnetic and thermal fields on the natural frequency, critical angular velocity, and deflection of the sandwich cylindrical shell are investigated. The critical angular velocity of the nanocomposite sandwich cylindrical shell is obtained. The results show that the mechanical properties, e.g., Young＇s modulus and thermal expansion coefficient, for the carbon nanotube and matrix are functions of temperature, and the magnitude of the critical angular velocity can be adjusted by changing the applied voltage.

Buckling analysis of functionally graded material(FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations

An analytical solution for buckling of an eccentrically stiffened sandwich truncated conical shell is investigated. The shell consists of two functionally graded material （FGM） coating layers and a core layer which are metal or ceramic subjected to an axial compressive load and an external uniform pressure. Shells are reinforced by stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution. Two models of coated shell-stiffener arrangements are investigated. The change of the spacing between stringers in the meridional direction is taken into account. A couple set of three-variable- coefficient partial differential equations in terms of displacement components are solved by the Galerkin method. A closed-form expression for determining the buckling load is obtained. The numerical examples are presented and compared with previous works.

Critical velocity of sandwich cylindrical shell under moving internal pressure

Critical velocity of an infinite long sandwich shell under moving internal pressure is studied using the sandwich shell theory and elastodynamics theory. Propagation of axisymmetric free harmonic waves in the sandwich shell is studied using the sandwich shell theory by considering compressibility and transverse shear deformation of the core, and transverse shear deformation of face sheets. Based on the elastodynamics theory, displacement components expanded by Legendre polynomials, and position-dependent elastic constants and densities are introduced into the equations of motion. Critical velocity is the minimum phase velocity on the desperation relation curve obtained by using the two methods. Numerical examples and the finite element （FE） simulations are presented. The results show that the two critical velocities agree well with each other, and two desperation relation curves agree well with each other when the wave number k is relatively small. However, two limit phase velocities approach to the shear wave velocities of the face sheet and the core respectively when k limits to infinite. The two methods are efficient in the investigation of wave propagation in a sandwich cylindrical shell when k is relatively small. The critical velocity predicted in the FE simulations agrees with theoretical prediction.

Rotating sandwich cylindrical shells with an FGM core and two FGPM layers: free vibration analysis

The free vibration analysis of a rotating cylindrical shell with an analytical method is investigated. The shell is considered as a sandwich structure, where the middle layer is a functionally graded material(FGM) shell, and it is surrounded by two piezoelectric layers. Considering piezoelectric materials to be functionally graded(FG),the material properties vary along the thickness direction as one innovation of this study.Applying the first-order shear deformation theory(FSDT), the equations of motion of this electromechanical system are derived as the partial differential equations(PDEs) using Hamilton's principle. Then, the Galerkin procedure is used to discretize the governing equations, and the present results are compared with the previously published results for both isotropic and FGM shells to verify the analytical method. Finally, the effects of FGM and functionally graded piezoelectric material(FGPM) properties as well as the thickness ratio and the axial and circumferential wave numbers on the natural frequencies are studied. Moreover, the Campbell diagram is plotted and discussed through the governing equations. The present results show that increasing the non-homogeneous index of the FGM decreases the natural frequencies on the contrary of the effect of non-homogeneous index of the FGPM.

Nonlinear stability of functionally graded material(FGM)sandwich cylindrical shells reinforced by FGM stiffeners in thermal environment

In this paper, Donnell＇s shell theory and smeared stiffeners technique are improved to analyze the postbuckling and buckling behaviors of circular cylindrical shells of stiffened thin functionally graded material （FGM） sandwich under an axial loading on elastic foundations, and the shells are considered in a thermal environment. The shells are stiffened by FGM rings and stringers. A general sigmoid law and a general power law are proposed. Thermal elements of the shells and reinforcement stiffeners are considered. Explicit expressions to find critical loads and postbuckling load-deflection curves are obtained by applying the Galerkin method and choosing the three-term approximate solution of deflection. Numerical results show various effects of temperature, elastic foundation, stiffeners, material and geometrical properties, and the ratio between face sheet thickness and total thickness on the nonlinear behavior of shells.

Nonlinear dynamic responses of sandwich functionally graded porous cylindrical shells embedded in elastic media under 1:1 internal resonance

In this article, the nonlinear dynamic responses of sandwich functionally graded(FG) porous cylindrical shell embedded in elastic media are investigated. The shell studied here consists of three layers, of which the outer and inner skins are made of solid metal, while the core is FG porous metal foam. Partial differential equations are derived by utilizing the improved Donnell's nonlinear shell theory and Hamilton's principle. Afterwards, the Galerkin method is used to transform the governing equations into nonlinear ordinary differential equations, and an approximate analytical solution is obtained by using the multiple scales method. The effects of various system parameters,specifically, the radial load, core thickness, foam type, foam coefficient, structure damping,and Winkler-Pasternak foundation parameters on nonlinear internal resonance of the sandwich FG porous thin shells are evaluated.

Nonlinear thermo-mechanical stability of eccentrically stiffened functionally graded material sandwich doubly curved shallow shells with general sigmoid law and power law according to third-order shear deformation theory

In this paper, the nonlinear analysis of stability of functionally graded ma- terial （FGM） sandwich doubly curved shallow shells is studied under thermo-mechanical loads with material properties obeying the general sigmoid law and power law of four ma- terial models. Shells are reinforced by the FGM stiffeners and rest on elastic foundations. Theoretical formulations are derived by the third-order shear deformation theory （TSDT） with the von Karman-type nonlinearity taking into account the initial geometrical im- perfection and smeared stiffener technique. The explicit expressions for determining the critical buckling load and the post-buckling mechanical and thermal load-deflection curves are obtained by the Galerkin method. Two iterative algorithms are presented. The effects of the stiffeners, the thermal element, the distribution law of material, the initial imper- fection, the foundation, and the geometrical parameters on buckling and post-buckling of shells are investigated.

FINITE STRIP DYNAMIC ANALYSIS OF CYLINDRICAL SHELL SANDWICH STRUCTURES

A rectangular, singly curved and finite strip element for curved sandwich dynamic analysis is developed. The convergence and speed of the method, the strip element density and the reduction of the degrees of freedom etc . are discussed through free vibration analysis of a honeycomb cylindrical shell pan-el. The results show that the frequencies and modal shapes obtained agree very well with the analytical solutions for the symmetrical honeycomb sandwich under the simply supported end conditions.

Free vibration of circular cylindrical shell with constrained layer damping

Free vibration characteristics of circular cylindrical shell with passive constrained layer damping （PCLD）are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders＇ thin shell theory. Nu- merical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.

NONLINEAR BENDING THEORY OF DIAGONAL SQUARE PYRAMID RETICULATED SHALLOW SHELLS

Double-deck reticulated shells are a main form of large space structures. One of the shells is the diagonal square pyramid reticulated shallow shell, whose its upper and lower faces bear most of the load but its core is comparatively flexible. According to its geometrical and mechanical characteristics, the diagonal square pyramid reticulated shallow shell is treated as a shallow sandwich shell on the basis of three basic assumptions. Its constitutive relations are analyzed from the point of view of energy and internal force equivalence. Basic equations of the geometrically nonlinear bending theory of the diagonal square pyramid reticulated shallow shell are established by means of the virtual work principle.

基于分层法的功能梯度三明治壳线性弯曲无网格分析

基于3D连续壳理论和一阶剪切变形理论,采用分层法,提出了一种求解功能梯度三明治壳线性弯曲问题的移动最小二乘无网格法.通过映射技术,将随动坐标系上的二维无网格节点信息映射到三维壳中,并在随动坐标系上形成移动最小二乘近似的形函数.因基于3D连续壳理论的壳数值解答无法像特定壳一样给出其厚度方向的显式表达式,该文将功能梯度三明治材料壳结构中材料参数变化的部分划分成若干层,得到每层的材料参数为常数.利用最小势能原理,推导出了功能梯度三明治壳线性弯曲的无网格控制方程.通过引入一个厚度方向的线性变换,使得每层厚度方向的Gauss积分均在-1至1区间内,不违背一阶剪切变形理论.采用完全转化法施加本质边界条件.以功能梯度三明治板、柱壳、双曲扁壳经典几何形状壳为例,讨论了不同梯度系数、径厚比和曲率半径等对数值结果的影响,并将计算结果与文献解对比.研究表明,该方法在求解不同形状的功能梯度三明治壳线性弯曲问题时,具有收敛性好、计算精度高的特点.

基于夹层结构各层协同优化的聚合物基复合介质储能性能

近年来,聚合物基纳米复合介质因其具有可塑性强和功率密度大且稳定性好等优点而受到广泛关注。但由于其自身能量密度小且耐击穿能力有限,不能满足现代电气化时代高精密储能器件的要求。为了获得兼具高击穿强度和高储能密度的聚合物基复合介质,研究设计了一种新的夹层结构,将铁电聚合物聚(偏氟乙烯-三氟乙烯-氯氟乙烯)(PVTC)与线性聚合物聚甲基丙烯酸甲酯(PMMA)共混作为外部绝缘层,将具高介电常数的核壳结构BT@AO@PDA纳米纤维添加到PVTC中作为中间极化层,构筑的正向夹层结构(绝缘层-极化层-绝缘层)实现了击穿强度和介电常数的协同提升。其中,PMMA质量分数为25%的PMMA/PVTC复合介质和3%的BT@AO@PDA/PVTC复合介质构成的正向夹层结构在562.7 MV/m电场下获得了17.25 J/cm3的高储能密度,并且具有优异的充放电循环稳定性和1.42μs的超快放电速率。该工作为制备高储能柔性介质薄膜电容器提供了一种简便且有效的策略。

A comparative study on mechanical and vibroacoustic performance of sandwich cylindrical shells with positive,negative,and zero Poisson’s ratio cellular cores

Deep-sea submersibles are significant mobile platforms requiring multi-functional capabilities that are strongly determined by the constituent materials.Their cylindrical protective cover can be advanced by designing their sandwiched cellular materials whose physical properties can be readily parameterized and flexibly tuned.Porous honeycomb materials are capable of possessing tuned positive,negative,or zero Poisson’s ratios(PPR,NPR,and ZPR),which is expected to produce distinct physical performance when utilized as a cellular core of cylindrical shells for the deep-sea submersibles.A novel cylindrical meta-structure sandwiched with the semi-re-entrant ZPR metamaterial has been designed as well as its similarly-shaped sandwich cylindrical shell structures with PPR and NPR honeycombs.The mechanical and vibroacoustic performance of sandwich cylindrical shells with cellular materials featuring a full characteristic range of Poisson’s ratios are then compared systematically to explore their potential for engineering applications on submerged pressure-resistant structures.The respective unit cells are designed to feature an equivalent load-bearing capability.Physical properties of pressure resistance,buckling,and sound insulation are simulated,respectively,and the orders of each property are then generalized by systematic comparison.The results indicate that the PPR honeycomb core takes advantage of higher structural strength and stability while the ZPR one yields better energy absorption and sound insulation behavior.The NPR one yields moderate properties and has the potential for lower circumferential deformation.The work explores the application of cellular materials with varied Poisson’s ratios and provides guidance for the multi-functional design of sandwich cylindrical meta-structures.

重复冲击载荷下泡沫铝夹芯壳的动态响应

通过数值模拟研究了泡沫铝夹芯壳在重复冲击载荷作用下的变形和能量耗散机理,分析了曲率半径、前后面板厚度分配、芯层厚度和冲击能量梯度对结构抗重复冲击性能和能量吸收能力的影响规律。结果表明:在重复冲击载荷作用下,泡沫铝夹芯壳结构的变形不断累积,前面板局部弯曲变形,芯层局部压缩,后面板整体弯曲变形。随着冲击次数的增加,冲击力峰值逐渐增大,冲击持续时间缩短,结构能量吸收能力降低,整体抗弯刚度增大。每次冲击能量相同时,泡沫铝夹芯壳结构曲率越大,能量吸收能力越强,同时前、后面板5次重复冲击后的中点挠度大于曲率较小的夹芯壳结构。5次重复冲击载荷作用下,前面板厚度较大且后面板厚度较小时,结构的比吸能较低,但后面板中点挠度较小。泡沫铝芯层厚度越大,结构的后面板挠度越小,但总比吸能降低。3种不同梯度的冲击能量作用下,递增能量工况下结构的吸能最多,前、后面板的挠度较大,递减能量工况下结构的吸能最少,前、后面板的挠度较小。