基于能量法研究刚性质量块轴向撞击圆柱壳的屈曲

基于能量法,考虑应力波效应,研究了刚性质量块撞击圆柱壳的屈曲问题。建立拉格朗日函数,将其和计算获得的符合边界条件的准试函数代入第二类拉格朗日方程,得到二阶线性偏微分方程,分析方程解的特性,得到刚性质量块撞击圆柱壳屈曲临界速度的解析表达式。算例分析讨论了临界长度、冲击质量、轴向模态数、环向模态数、径厚比对屈曲的影响。结果表明:应力波效应、初始冲击动能、径厚比对圆柱壳的动力屈曲有明显影响;高速冲击易激发屈曲的高阶模态、也容易在径厚比较小时激发圆柱壳的屈曲。     

Hypervelocity penetration modeling: momentum vs. energy and energy transfer mechanisms

Analytic penetration modeling usually relies on either a momentum balance or an energy-rate balance to predict depth of penetration by a penetrator based on initial geometry and impact velocity. In recent years, fairly sophisticated models of penetration have arisen that develop the three-dimensional flow field within a target. Based on the flow field and constitutive assumptions, it is then possible to derive a momentum or an energy-rate balance. This paper examines the use of assumed flow fields within a target created by impact and then examines the resulting predicted behavior based on either momentum conservation or energy conservation. It is shown that for the energy-rate balance to work, the details of the energy transfer mechanisms must be included in the model. In particular, how the projectile energy is initially transferred into target kinetic energy and elastic compression energy must be included. As impact velocity increases, more and more energy during the penetration event is temporarily deposited within the target as elastic compression and target kinetic energy. This energy will be dissipated by the target at a later time, but at the time of penetration it is this transfer of energy that defines the forces acting on the projectile. Thus, for an energy rate balance approach to successfully model penetration, it must include the transfer of energy into kinetic energy within the target and the storage of energy by elastic compression. Understanding the role of energy dissipation in the target clarifies the various terms in analytic models and identifies their origin in terms of the fundamental physics. Understanding the modes of energy transfer also assists in understanding the hypervelocity result that penetration depth only slowly increases with increasing velocity even though the kinetic energy increases as the square of the velocity.     

Field equations, equations of motion, and energy functionals for thick shells of revolution with arbitrary curvature and variable thickness from a three-dimensional theory

Summary This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.     

One class of analytical self-similar solutions to the system of radiative transfer and energy equations for a homogeneous medium

The known class of analytical self-similar solutions of the traveling heat wave type for a nonlinear integro-differential system of equations which describes nonstationary spectral transfer of radiant energy in a kinetic model is generalized to a homogeneous medium. The solutions are constructed in three-dimensional Cartesian geometry with specially chosen absorption and scattering coefficients. No additional terms that might distort the essence of the physical phenomena being described are introduced into the original equations, and the solution is almost completely determined by the functional dependence on a self-similar variable. This class of exact solutions is also applicable to the “gray matter” approximation and can be used to test numerical methods for calculating direct and inverse problems of radiative transfer. Examples of test calculations are given.     

Combined design and load shifting for distributed energy system

Renewable distributed energy generation (DEG) system plays an important role in future power developments and is one of the options to reduce energy consumption. It is envisaged that energy efficiency of DEG systems can be improved via load shifting (LS). This study proposed a heuristic-based numerical approach to perform LS analysis on renewable stand-alone DEG systems. The technique is an extension from a method known as the Electric System Cascade Analysis (ESCA). The new technique, which focuses on efficient electricity utilisation is able to determine the optimal: (i) load profiles, (ii) capacity of power generator, (iii) capacity and power of energy storage (ES) and (iv) charging/discharging schedule of ES. The stage-wise technique allows user to compare and determine the optimal design in a flexible way while having a better understanding of the selection of options. The application of ESCA-LS on a case study revealed that after incorporation of direct LS (load manipulation) in addition to LS by ES (supply manipulation), the power generators and ES capacity can be further reduced. While reduction of 3.1 % for solar-PV installation area and 3.9 % for biomass power generator is recorded, ES power-related capacity and energy-related capacity managed a higher reduction of up to 19.0 and 13.2 % for the main case study     

多层隔振系统的动力学模型

在微振动的前提下，从推导空间刚体的动能及隔振器的势能及耗散能着手，利用拉格朗日方程建立了考虑隔振器上下安装点位置的多层隔振系统的动力学方程组。在推导中使用平移变换矩阵T和旋转变换矩阵R以及用TR矩阵的形式描述了多层隔振系统的动能表达式、势能表达式及耗散能表达式。中给出了一个浮筏隔振系统模型的算例，计算结果表明，所推导的多层隔振系统的动力学模型有良好的计算精度，能满足高质量工程设计的要求。     

Momentum and energy propagation in tapered granular chains

We study momentum and energy propagation in 1D tapered chains of spherical granules which interact according to a Hertz potential. In this work we apply the binary collision approximation, which is based on the assumption that transfer of energy along the chain occurs via a succession of two-particle collisions. Although the binary theory correctly captures the trends of increase or decrease of kinetic energy and momentum, the actual values of these quantities are not in good quantitative agreement with those obtained by numerically integrating the full equations of motion. To address this difficulty we have developed a mixed numerical/analytical correction algorithm to provide an improved estimate of the velocity of the particles during pulse propagation. With this corrected velocity we are in turn able to correctly predict the momentum and kinetic energy along the chain for several tapering configurations, specifically for forward linear, forward exponential, backward linear and backward exponential tapering.     

Nonlinear coupled problems in dynamics of shells

The coupled system of three partial differential equations governing a flexible shallow shell dynamics is analysed. No any prior assumptions about the temperature distribution through the shell thickness are applied. The efficiency of the method used here when applied to the solution of integral-differential equations with different dimensions (three-dimensional equations related to the Kirchhoff-Love model) and of different type (heat transfer equations and the hyperbolic equations of shell theory) is demonstrated. Many computational results are reported and discussed.     

Electric energy generator

This study reports an extremely cost-effective mechanism for converting wind energy into electric energy using piezoelectric bimorph actuators at small scale. The total dimensions of the electric energy generator are 5.08 x 11.6 x 7.7 cm3. The rectangular, box-shaped body of the overall structure is made using 3.2-mm thick plastic. Slits are made on two opposite faces of the box so that two columns and six rows of bimorph actuators can be inserted. Each row of bimorph actuators is separated from each other by a gap of 6 mm, and the two columns of bimorphs are separated from each other by a gap of 6.35 mm. In between the two columns, a cylindrical rod is inserted consisting of six rectangular hooks. The hooks are positioned in such a way that each of them just touches the two bimorphs on either side in a particular row. As the wind flows across the generator, it creates a rotary motion on the attached fan that is converted into vertical motion of the cylindrical rod using the cam-shaft mechanism. This vertical motion of the cylindrical rod creates oscillating stress on the bimorphs due to attached hooks. The bimorphs produce output voltage proportional to the applied oscillating stress through piezoelectric effect. The prototype fabricated in this study was found to generate 1.2 mW power at a wind speed of 12 mph across the load of 1.7 komega.     

冲击块与金属圆柱壳相互作用的缓冲吸能分析

应用Johnson Cook本构方程, 结合Singace叠缩模型,考虑冲击作用引起材料的应变强化效应、应变率强化效应和温度效应,研究了冲击物体和金属圆柱壳相互作用的能量转化过程。运用角度增量叠缩法计算了圆柱壳的塑性变形能,根据冲击块和圆柱壳所组成系统能量守恒得到了冲击块速度位移、冲击块和圆柱壳之间瞬时载荷的解析表达式,以及圆柱壳塑性变形引起的温度分布函数。通过对不同材质的金属圆柱壳在冲击作用下塑性变形过程的计算分析,并和有限元计算结果比较,证明了本文计算方法的正确性。     

Electromagnetic energy harvester for harvesting acoustic energy

This paper reports a suspended coil, electromagnetic acoustic energy harvester (AEH) for extracting acoustical energy. The developed AEH comprises Helmholtz resonator (HR), a wound coil bonded to a flexible membrane and a permanent magnet placed in a magnet holder. The harvester’s performance is analyzed under different sound pressure levels (SPLs) both in laboratory and in real environment. In laboratory, when connected to 50 Ω load resistance and subjected to an SPL of 100 dB, the AEH generated a peak load voltage of 198.7 mV at the resonant frequency of 319 Hz. When working under the optimum load resistance, the AEH generated an optimum load power of 789.65 µW. In real environment, the developed AEH produced a maximum voltage of 25 mV when exposed to the acoustic noise of a motorcycle and generated an optimum voltage of 60 mV when it is placed in the surroundings of a domestic electrical generator.     

Load management as a smart grid concept for sizing and designing of hybrid renewable energy systems

Optimal sizing of hybrid renewable energy systems (HRES) to satisfy load requirements with the highest reliability and lowest cost is a crucial step in building HRESs to supply electricity to remote areas. Applying smart grid concepts such as load management can reduce the size of HRES components and reduce the cost of generated energy considerably. In this article, sizing of HRES is carried out by dividing the load into high- and low-priority parts. The proposed system is formed by a photovoltaic array, wind turbines, batteries, fuel cells and a diesel generator as a back-up energy source. A smart particle swarm optimization (PSO) algorithm using MATLAB is introduced to determine the optimal size of the HRES. The simulation was carried out with and without division of the load to compare these concepts. HOMER software was also used to simulate the proposed system without dividing the loads to verify the results obtained from the proposed PSO algorithm. The results show that the percentage of division of the load is inversely proportional to the cost of the generated energy.     

载流悬臂柱壳的非线性数值分析

针对在电磁场和机械场耦合作用下的载流柱壳的非线性变形问题的数值解法进行了研究。给出了载流柱壳在耦合场作用下的几何方程、物理方程、二维电动力学方程、磁弹性非线性运动方程和洛仑兹力表达式,建立了差分格式和线性化迭代方程,给出了这些方程的数值解系统,并以悬臂柱壳为例,计算了该壳在电磁场和机械载荷耦合作用下的应力及变形;讨论了其应力及变形与外加电磁参量之间的关系;证明了变化电磁参量可以对壳的工作状态实施控制。     

大型复合材料夹芯筒屈曲分析中芯材剪切变形与壳体锥度的影响

针对某卫星结构中的大型复合材料夹芯承力筒进行屈曲分析。首先分别建立柱壳段、锥壳段和框段的几何方程、物理方程与应变能表达式,以及给定载荷条件下的外力势能表达式。然后根据位移边界条件采用正交完备的三角级数构造承力筒的位移模态,最后根据最小势能原理求解临界载荷。通过对比计及与不计及芯材剪切变形和壳体锥度时临界载荷的计算结果,发现对于该承力筒而言,芯材剪切变形与壳体锥度对临界载荷计算结果的影响均小于10%。该分析结果为承力筒在设计阶段的简化计算提供了理论依据。     

METHOD OF INITIAL FUNCTIONS FOR THE ANALYSIS OF LAMINATED CIRCULAR CYLINDRICAL SHELLS UNDER AXISYMMETRIC LOADING

The method of initial functions has been used for the static analysis of an infinite and simply supported, orthotropic, and laminated, circular cylindrical shell of revolution subjected to axisymmettic load. In this method the three-dimensional state equations for an individual ply of a laminated shell are established without making any a priori assumptions regarding the distribution of stresses and displacements across the thickness of the shell By using the continuity conditions of displacements and stresses on each interface between adjacent layers, the state equation far the laminate is obtained. Using the Cayley-Hamilton theorem, the transfer matrix that maps the initial state vector into the field is evaluated explicitly, leading to an exact solution of the problem (MIF—exact). Alternatively, depending on the number of terms retained in the series expansion of the transfer matrix, different-order theories of MIF are derived. The results of different-order MIF theories, classical theories, and shear deformation shell theories are compared with the results of MIF—exact to assess their accuracy and limitations.     

Three-dimensional multi-field equations of a functionally graded piezoelectric thick shell with variable thickness, curvature and arbitrary nonhomogeneity

The present research develops a three-dimensional multi-field formulation of a functionally graded piezoelectric thick shell of revolution by using tensor analysis. An orthogonal curvilinear coordinate system was employed, and basic geometric equations were derived for an arbitrary thick shell of revolution with variable thickness and curvature. Mechanical and electrical properties were assumed to vary along a three-dimensional orthogonal coordinate system with arbitrary functional distribution. The functional of the introduced shell was derived by using kinetic and potential energy of the structure based on three orthogonal displacement components, electric potential and material properties. The final differential equations were derived in general state for every arbitrary structure and material property distributions. The obtained equations were reduced for functionally graded and functionally graded piezoelectric cylindrical shells and the mentioned reduced equations were verified by comparison with the literature. Trueness and generality of the present results can be justified by capability of these equations for different geometries and material properties.     

Numerical study of asteroid impact on the earth’s surface with allowance for gravitation and radiation energy transfer

The study presents a procedure for numerical modeling and results of gasdynamic calculations of asteroid impact on the surface in a two-dimensional axisymmetric formulation for impact velocities of ∼ 50 km/sec and asteroid dimensions of ∼ 1 km. The effect of gravity and radiation energy transfer are taken into account. Radiation transfer is calculated using the equations of radiation diffusion in the multigroup approximation with respect to the photon energy (10 spectral groups). The equations of radiation diffusion are solved by the method of alternating directions.     

Refined resultant thermomechanics of shells

The resultant two-dimensional (2D) balance laws of mass, linear and angular momentum, and energy as well as the entropy inequality for shells are derived by direct through-the-thickness integration of corresponding 3D laws of continuum thermomechanics. It is indicated that the resultant shell stress power cannot be expressed exactly through the 2D shell stress and strain measures alone. Hence, an additional stress power called an interstitial working is added to the resultant 2D balance of energy. The new, refined, resultant balance of energy and entropy inequality derived here are regarded to be exact implications of corresponding global 3D laws of rational thermodynamics. The kinematic structure of our shell theory is that of the Cosserat surface, while our refined resultant laws of thermomechanics contain three additional surface fields somewhat similar to those present in 3D extended thermodynamics. We briefly analyse the restrictions imposed by our refined resultant entropy inequality on the forms of 2D constitutive equations of viscous shells with heat conduction and of thermoelastic shells. It is shown, in particular, that in such shells the refined resultant entropy inequality allows one to account for some longer-range spatial interactions. We also present several novel forms of 2D kinetic constitutive equations compatible with the resultant shell equations.     

Enhancing the transfer of inductive energy to imploding plasma loads with a single-step meatgrinder circuit

The transfer of magnetic energy to an uncoupled load inductor using a novel inductive storage and transfer circuit (single-step meatgrinder) is compared with two classical inductive circuits. The first is the inductor-inductor transfer via an opening switch. The second is a transformer circuit where the primary circuit is opened and energy is transfered to the secondary and the uncoupled load. For identical loads the new circuit is shown to provide a 90-percent improvement over the two conventional circuits in energy transferred to the uncoupled load. A low-current low-voltage experiment, where 35.4 percent of the initial inductive energy is transferred to an uncoupled load using the new circuit, is discussed. A physical design for the Air Force Weapons Laboratory Shiva bank, which accounts for voltage holding, coupling, and parasitic inductance in the switches, is also described.     

结构倒塌时楼板碰撞效应的简化评估方法

针对上楼板、下楼板碰撞的两种极限状态 -- 完全塑性碰撞和完全刚性碰撞,开展了碰撞过程中动能转移量的理论分析,考察了上板、下板质量比对动能转移量的影响,同时进行了2种极限状态下动能转移量的数值计算;提出了结构倒塌时上板、下板碰撞效应的一种简化评估方法,具体包括2个步骤：1) 下板的非线性静力分析;2) 采用能量平衡原理估算上板的最大允许重力荷载。研究表明：上板、下板质量比等于1时,完全塑性碰撞后的总动能转移百分比和下板动能转移百分比分别为33.3%和16.7%;完全刚性碰撞后的下板动能转移百分比与碰撞前上板速度、碰撞后上板周边反弹速度等参数有关,上板、下板质量比等于1时下板动能转移百分比为44.4%~97.1%;采用通用软件ABAQUS计算得到的两种极限状态对应的下板动能转移百分比,总体上与理论分析结果较为接近。