Development and Evaluation of a Groundnut In-Shell Grader

Groundnuts marketed from farms are generally referred to as groundnuts in-shell. When freshly harvested, they may contain some dirt, vines and other foreign materials. Grades of these stocks are established based on intended use. Groundnut producers and commercial buyers use the grade as guidelines for trading. Grading aims at raising the quality and value of the product. Grading is generally limited to measurement of physical properties, such as, size distributions of the pods and percentage by weight of shelled kernels in the undecorticated groundnuts and percentage by weight of foreign materials. A groundnut grader was designed and developed. It was designed to sort three selected groundnut varieties commonly cultivated in Nigeria into three grades based on the geometric dimensions of the selected varieties. These varieties are SAMNUT 10, 14 and 18.Analyses of grading trials indicate that while SAMNUT 10 exhibits the three grades, the other varieties (SAMNUT 14 and 18) can only be graded into two grades. The grader has a rated capacity of grading 224 th-1 of undercorticated pods. The maximum ranges within each grade when all the varieties were considered were: grade I—15.81 mm to 18.05 mm, grade II—12.44 mm to 15.78 mm and grade III—10.60 mm to 13.30 mm.

Wrinkling in graded core/shell systems using symplectic formulation

Wrinkles in flat graded elastic layers have been recently described as a timevarying Hamiltonian system by the energy method.Cylindrical core/shell structures can also undergo surface instabilities under the external pressure.In this study,we show that by treating the radial direction as a pseudo-time variable,the graded core/shell system with radially decaying elastic properties can also be described within the symplectic framework.In combination with the shell buckling equation,the present paper addresses the surface wrinkling of graded core/shell structures subjected to the uniform external pressure by solving a series of ordinary differential equations with varying coefficients.Three representative gradient distributions are showcased,and the predicted critical pressure and critical wave number are verified by finite element simulations.The symplectic framework provides an efficient and accurate approach to understand the surface instability and morphological evolution in curved biological tissues and engineered structures.

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 para- meters 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.

Sound radiation of a functionally graded material cylindrical shell in water by mobility method

Based on the fundamental dynamic equations of functionally graded material (FGM) cylindrical shell, this paper investigates the sound radiation of vibrational FGM shell in water by mobility method. This model takes into account the exterior fluid loading due to the sound press radiated by the FGM shell. The FGM cylindrical shell was excited by a harmonic line radial force uniformly distributing along the generator. The FGM shell equations of motion, the Helmholtz equation in the exterior fluid medium and the continuity equation at fluid-shell interface are used in this vibroacoustic problem. The expressions of sound radiation efficiency and sound field of the FGM shell have been derived by mobility method. Radiation efficiency, modal mobility and the directivity pattern of the sound field are solved numerically. In particular, radiation efficiency and directivity pattern with various power law index are analyzed.

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.

Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities

The free thermal vibration of functionally graded material(FGM) cylindrical shells containing porosities is investigated. Both even distribution and uneven distribution are taken into account. In addition, three thermal load types, i.e., uniform temperature rise(UTR), nonlinear temperature rise(NLTR), and linear temperature rise(LTR), are researched to explore their effects on the vibration characteristics of porous FGM cylindrical shells. A modified power-law formulation is used to describe the material properties of FGM shells in the thickness direction. Love’s shell theory is used to formulate the straindisplacement equations, and the Rayleigh-Ritz method is utilized to calculate the natural frequencies of the system. The results show that the natural frequencies are affected by the porosity volume fraction, constituent volume fraction, and thermal load. Moreover,the natural frequencies obtained from the LTR have insignificant differences compared with those from the NLTR. Due to the calculation complexity of the NLTR, we propose that it is reasonable to replace it by its linear counterpart for the analysis of thin porous FGM cylindrical shells. The present results are verified in comparison with the published ones in the literature.

Thermal buckling analysis of functionally graded cylindrical shells

Thermal buckling behavior of cylindrical shell made of functionally graded material（FGM） is studied. The material constituents are composed of ceramic and metal.The material properties across the shell thickness are assumed to be graded according to a simple power law distribution in terms of the volume fraction rule of mixtures. Based on the Donnell shell theory, a system of dimensionless partial differential equations of buckling in terms of displacement components is derived. The method of separation of variables is used to transform the governing equations to ordinary differential equations（ODEs）. A shooting method is used to search for the numerical solutions of the differential equations under two types of boundary conditions. Effects of the power law index, the dimensionless geometrical parameters, and the temperature ratio on the critical buckling temperature are discussed in detail.

Three-dimensional magneto-thermo-elastic analysis of functionally graded cylindrical shell

The present paper presents the three-dimensional magneto-thermo-elastic analysis of the functionally graded cylindrical shell immersed in applied thermal and magnetic fields under non-uniform internal pressure. The inhomogeneity of the shell is assumed to vary along the radial direction according to a power law function, whereas Poisson＇s ratio is supposed to be constant through the thickness. The existing equations in terms of the displacement components, temperature, and magnetic parameters are derived, and then the effective differential quadrature method （DQM） is used to acquire the analytical solution. Based on the DQM, the governing heat differential equations and edge boundary conditions are transformed into algebraic equations, and discretized in the series form. The effects of the gradient index and rapid temperature on the displacement, stress components, temperature, and induced magnetic field are graphically illustrated. The fast convergence of the method is demonstrated and compared with the results obtained by the finite element method （FEM）.

Nonlinear analysis on dynamic buckling of eccentrically stiffened functionally graded material toroidal shell segment surrounded by elastic foundations in thermal environment and under time-dependent torsional loads

The nonlinear analysis with an analytical approach on dynamic torsional buckling of stiffened functionally graded thin toroidal shell segments is investigated. The shell is reinforced by inside stiffeners and surrounded by elastic foundations in a thermal environment and under a time-dependent torsional load. The governing equations are derived based on the Donnell shell theory with the yon Karman geometrical nonlinearity, the Stein and McElman assumption, the smeared stiffeners technique, and the Galerkin method. A deflection function with three terms is chosen. The thermal parameters of the uniform temperature rise and nonlinear temperature conduction law are found in an explicit form. A closed-form expression for determining the static critical torsional load is obtained. A critical dynamic torsional load is found by the fourth-order Runge-Kutta method and the Budiansky-Roth criterion. The effects of stiffeners, foundations, material, and dimensional parameters on dynamic responses of shells are considered.

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.

ANALYSIS OF THE DYNAMIC STABILITY OF ELECTRICAL GRADED PIEZOELECTRIC CIRCULAR CYLINDRICAL SHELLS

A system of Mathieu–Hill equations have been obtained for the dynamic stability analysis of electrical graded piezoelectric circular cylindrical shells subjected to the combined loading of periodic axial compression and radial pressure and electric ?eld. Bolotin’s method is then employed to obtain the dynamic instability regions. It is revealed that the piezoelectric e?ect, the piezoelectric graded e?ect and the electric ?eld only have minor e?ect on the unstable region. In contrast, the geometric parameters, the rigidity of constituent materials and the external loading play a dominant role in determining the unstable region.

Natural frequencies of rotating functionally graded cylindrical shells

Love＇s first approximation theory is used to analyze the natural frequencies of rotating functionally graded cylindrical shells. To verify the validity of the present method, the natural frequencies of the simply supported non-rotating isotropic cylindrical shell and the functionally graded cylindrical shell are compared with available published results. Good agreement is obtained. The effects of the power law index, the wave numbers along the x- and O-directions, and the thickness-to-radius ratio on the natural frequencies of the simply supported rotating functionally graded cylindrical shell are investigated by several numerical examples. It is found that the fundamental frequencies of the backward waves increase with the increasing rotating speed, the fundamental frequencies of the forward waves decrease with the increasing rotating speed, and the forward and backward waves frequencies increase with the increasing thickness-to-radius ratio.

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.

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.

巴旦木分级破壳机设计与试验

为解决巴旦木破壳机械生产效率低、破壳率低和核仁损伤量大等问题,通过研究坚果破壳原理,选用适宜机械加工的大巴旦木(‘莎车3号’)为研究对象,设计了巴旦木分级破壳机,同时进行巴旦木尺寸、破壳力加载方向及加载速度、巴旦木含水率的物料特性分析。结果表明:破壳机破壳辊间隙和含水率对巴旦木破壳力和变形量影响显著。使用试验法优化了巴旦木分级破壳机构工作参数,当两轧辊间距离调整为Ⅰ级14 mm、Ⅱ级13 mm和Ⅲ级12 mm,含水率控制在9.8%~10.5%范围内,转速为1 000 r·min^(-1)时,测得平均破壳率为95.57%,平均破损率为3.37%,满足实际生产需求。

基于EDEM的核桃壳仁混合物振动筛分级工艺优化

为提高核桃壳仁混合物的分级效果,对现有核桃壳仁混合物分级设备进行三维实体建模,利用EDEM软件模拟核桃壳仁混合物的分级过程,以筛面上物料的运动速度、质量以及各等级颗粒在统计区域的数量为指标,以振幅、振动频率、振动方向角、筛面倾角为考察因素,对振动筛分级工艺进行优化。结果表明:在振动频率12 Hz、振幅5 mm、振动方向角45°、筛面倾角4°的工艺参数组合下,各等级核桃壳仁的透筛率最高,分级效果最好。

弹性支撑功能梯度微圆柱壳模态频率的研究

在建立弹性支撑功能梯度薄壁微圆柱壳模型的基础上,基于修正的偶应力理论和一阶剪切变形理论,推导了微圆柱壳的模态频率方程,讨论了弹性支撑、尺寸效应、温度梯度、材料组分指数、孔隙以及几何尺寸等参数对微圆柱壳模态频率的影响。结果表明:微尺度下,弹性刚度系数在0~105N/m^(3)范围内对微圆柱壳的模态频率基本无影响,剪切刚度系数在0~5×10^(4)N/m范围内对模态频率的影响较大,且增大剪切刚度系数有益于提高微圆柱壳的模态频率;由修正的偶应力理论得到的模态频率大于由经典连续体理论得到的模态频率;在弹性支撑和尺寸效应有无考虑的4种组合下,模态频率随温度梯度和微圆柱壳长度的增大而减小,随陶瓷体积分数指数的增大而增大,随孔隙体积分数和微圆柱壳厚度的变化规律不同;温度梯度对考虑尺寸效应或弹性基础的微圆柱壳模态频率影响较大,而孔隙调节具弹性支撑微圆柱壳的模态频率尤其显著。

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.

磁性功能梯度圆柱壳磁热弹性超谐波共振研究

研究温度场和磁场中功能梯度(functionally graded, FG)圆柱薄壳1∶3阶超谐波共振问题。针对金属-陶瓷FG圆柱薄壳,采用热传导方程表征一维温度场沿壳体厚度分布特性;结合热弹性理论,并考虑几何非线性,确定了壳体物理中面下的本构关系;基于磁弹性理论,建立磁场环境下壳体所受洛伦兹力和磁化力模型。应用哈密顿变分原理推得磁热弹耦合非线性振动方程。利用伽辽金积分法得到两端简支FG圆柱薄壳的无量纲化非线性振动微分方程,确定了由静磁力和热内力所产生的静挠度特征方程。应用多尺度法对系统的1∶3阶超谐波共振问题进行近似解析求解,得到系统稳态运动下的幅频响应方程,并应用李雅普诺夫稳定性理论对稳态解进行稳定性分析。通过数值算例,得到不同物理和几何参数影响下系统的共振幅值变化曲线图、动相轨迹图及多值解的区域划分图。结果表明:系统体现为硬弹簧特性;增大激励力幅值、陶瓷侧温度,临界多值解的分岔点右移,共振区域变大;增大磁场强度,稳定解振幅减小。

任意边界条件下旋转功能梯度锥-柱连接壳行波模态分析

连接壳结构广泛应用于船舶推进系统中,其边界条件复杂,而且在旋转运动下会产生行波模态,对推进器的动力学性能具有重要影响。为了推进功能梯度材料在船舶海洋工程中的应用,本文通过弹簧模拟壳体结构的边界条件,建立旋转功能梯度锥-柱连接壳的动力学模型,探讨旋转功能梯度锥-柱连接壳的行波模态特性。基于Love薄壳理论,运用弹簧模拟结构两端的边界条件以及圆锥壳和圆柱壳连接界面的连续性条件,推导考虑旋转运动引发的科氏力和离心力的功能梯度连接壳能量方程;以Chebyshev多项式为基底构造位移函数,建立旋转功能梯度连接壳的模态频率方程;利用Rayleigh-Ritz法求解连接壳的行波模态频率;通过收敛性分析确定边界弹簧和接触弹簧的刚度取值范围以及Chebyshev多项式所需要展开的项数;分析环向波数、陶瓷体积分数指数、圆锥角、转速以及任意边界对行波模态频率的影响。结果表明:旋转转速越大,连接壳的前后行波分叉行为越明显;轴向弹簧刚度对行波模态频率影响最大;相比于传统的能量法,采用弹簧模拟边界提高了计算效率,而且连接壳在弹性边界下的行波特性变化较大,说明了采用弹簧模拟任意边界的必要性。