Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.

Optimization of the Water-Cooled Structure for the Divertor Plates in EAST Based on an Orthogonal Theory

An orthogoual experimental scheme was designed for optimizing a water-cooled structure of the divertor plate. There were three influencing factors： the radius R of the water- cooled pipe, and the pipe spacing L1 and L3. The influence rule of different factors on the cooling effect and thermal stress of the plate were studied, for which the influence rank was respectively R 〉 L1 〉 L3 and L3 〉 R 〉 L1. The highest temperature value decreased when R and L1 increased~ and the maximum thermal stress value dropped when R, L1 and L3 increased. The final optimized results can be summarized as： R equals 6 mm or 7 mm, L1 equals 19 mm, and L3 equals 20 mm. Compared with the initial design, the highest temperature value had a small decline~ and the maximum thermal stress value dropped by 19~ to 24~. So it was not ideal to improve the cooling effect by optimizing the geometry sizes of the water-cooled structure, even worse than increasing the flow speed, but it was very effective for dropping the maximum thermal stress value. The orthogoaal experimental method reduces the number of experiments by 80%, and thus it is feasible and effective to optimize the water-cooled structure of the divertor plate with the orthogonal theory.

Unconventional Hamilton-type variational principles for nonlinear elastodynamics of orthogonal cable-net structures

According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An ifnportant integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper, Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.

Modeling Approach and Analysis of the Structural Parameters of an Inductively Coupled Plasma Etcher Based on a Regression Orthogonal Design

The geometry of an inductively coupled plasma （ICP） etcher is usually considered to be an important factor for determining both plasma and process uniformity over a large wafer. During the past few decades, these parameters were determined by the ＂trial and error＂ method, resulting in wastes of time and funds. In this paper, a new approach of regression orthogonal design with plasma simulation experiments is proposed to investigate the sensitivity of the structural parameters on the uniformity of plasma characteristics. The tool for simulating plasma is CFD-ACE＋, which is commercial multi-physical modeling software that has been proven to be accurate for plasma simulation. The simulated experimental results are analyzed to get a regression equation on three structural parameters. Through this equation, engineers can compute the uniformity of the electron number density rapidly without modeling by CFD-ACE＋. An optimization performed at the end produces good results.

An Orthogonal Least Squares Based Approach to FIR Designs

This paper is concerned with the application of forward Orthogonal Least Squares (OLS) algorithm to the design of Finite Impulse Response (FIR) filters. The focus of this study is a new FIR filter design procedure and to compare this with traditional methods known as the fir2() routine provided by MATLAB.

Labyrinth Seal Design Optimization Based on Quadratic Regression Orthogonal Experiment

The influence of labyrinth seal structure parameters and their interaction on the characteristics of leakage amount are numerically investigated by conducting a quadratic regression orthogonal experiment. To determine the optimal structure parameters of the steam seal for minimizing the leakage amount, a reliable regression equation that does not lack of fit is established. The flow characteristics of the fluid in the labyrinth seal are analyzed in detail. Results show that the leakage amount is greatly influenced by seal cavity depth, convex platform height, seal tooth thickness, and tooth tip clearance, with the tip clearance having the most significant effect. The interaction among the four items exerts a certain impact on the leakage amount. The proposed regression equation exhibits a good significance and does not lack of fit. After optimization, the labyrinth seal demonstrates increased entropy and energy dissipation at the tip of the seal tooth, as well as decreased speed and inertia effect in the cavity, suggesting that the resistance leakage performance of the optimized labyrinth seal is improved.

Fabrication, Mechanical and Dielectric Characterization of 3D Orthogonal Woven Basalt Reinforced Thermoplastic Polyimide Composites

The 3D orthogonal woven basalt fiber reinforced polyimide (PI) composites were fabricated and characterized in this study. The PI film was firstly prepared to determine PI processing parameters. Fourier transform infrared (FTIR) analysis showed that 300°C was the suitable imidization temperature. Thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC) results showed relatively good thermal properties of the PI film. In the fabrication of composites, the multi-step impregnation method was applied. The bending properties of 3 mm-thick composite showed increasing trend in all and the second-time impregnated composite had much higher value than the first-time impregnated composite. Moreover, the bending fracture mode photos showed obvious creases except for the first-time impregnated materials, which agreed well with the bending property values. The dielectric constants for the composites were complex because they had not regular value following the mixing rule of the composites, which was mainly due to the interfacial polarization and other effects in the fabrication processing.

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric.The proper orthogonal decomposition(POD)analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1%of the turbulent kinetic energy,and hence their impact on the wake dynamics is studied.The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point.The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction.In addition,the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.

Investigation on Fabric and Air Permeability in Relation to Its Structure

Five parameters of fabric structure are selected to study the relationship between fabric structure and fabric air permeability by orthogonal test . The influencing rule and influencing order of these factors on air permeability are obtained.

Effect of Rare Earth Elements on Structure and Electrochemical Properties of PuNi_3-type Hydrogen Storage Alloys

Structure and electrochemical properties of (La, Ce, Pr, Nd)_2MgNi_9 hydrogen storage alloys were investigated through orthogonal design experiments, and the alloys were obtained through induction melting followed by annealing treatment. The structure of main phase in alloys belongs to PuNi_3-type with a space group R3m. Rare earth elements, as a substitute of lanthanum, have a significant effect on phase structure of alloys, elements of cerium and neodymium are beneficial to the formation of Gd_2Co_7-type phase with a space group P 6_3/mmc. Rare earth elements can decrease the unit cell volume of main phase of alloys dramatically, and increase the axis ratio. The results of electrochemical experiment showed that the discharge capacity of alloy electrodes ranged from 342.97 to 380.68 mAh·g -1, and elements of cerium and neodymium can reduce the discharge capacity of alloy electrodes significantly. Compared to the electrode of La_2MgNi_9 alloy, the substitution of lanthanum by rare earth elements did not improve the cyclic stability of alloy electrodes due to the anisotropic structure change of unit cell. While rare-earth elements can improve the high rate dischargeability of alloy electrodes, the high rate dischargeability of alloy electrodes could reach the maximum when the unit cell volume of PuNi_3-type structure was about 0532 nm.

3D Woven Structures and Their Weave Design with Changing Cross-section on Warp and Weft Direction

With 3D orthogonal and pseudo-orthogonal weaves, woven sructures with lengthwise and widthwise changing cross section on one side or both sides of the structure can be constructed. The weave formation and the looming draft creation are discussed in this paper which can be used as references to manufacture woven preforms with changing cross sections.

Ultrasonic C-scan inspection of brazed joint in thin panel honeycomb structure

The non-destructive testing of brazed joint in honeycomb structure with thin panel （ thickness ： 0. 2 mm） was studied by ultrasonic C-scan method. Samples with different types of artificial defect were designed; the characteristic signal and the main parameters of the test were determined by the pre-experiment, and then parameters were optimized by orthogonal design, finally the optimum process was verified by a single panel sample. The multiple reflection echoes were chosen as the characteristic signal. The optimal C-scan results were achieved when the 20 MHz focus probe was used, and the pass band range for received signal were selected as 8 - 17. 5 MHz. The defects such as incomplete penetration and core damage can be detected with ultrasonic C-scan, and the detection accuracy can reach to 1 ram.

ON A GENERALIZED GEOMETRIC CONSTANT AND SUFFICIENT CONDITIONS FOR NORMAL STRUCTURE IN BANACH SPACES

In this paper, we introduce a new geometric constant C;（a, X） of a Banach space X, which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant. Subsequently, we present several sufficient conditions for normal structure of a Banach space in terms of this new constant, the generalized James constant, the generalized Garc′?a-Falset coefficient and the coefficient of weak orthogonality of Sims. Our main results of the paper generalize some known results in the recent literature.

LINEAR ACTIVE STRUCTURES AND MODES (Ⅱ) —DISCRETE SYSTEMS AND BEAMS

The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.

Constructing orthogonally structured graphene nanointerface on SiC nanowires reinforced carbon/carbon composites to boost mechanical strength and strength retention rate

Carbon/carbon composites with higher mechanical strength and better reliability at elevated tempera-tures are urgently needed to satisfy the practical applications requirements.SiC nanowires(SiCNWs)modified C/C(SC-CC)composites have attracted an abundance of attention for their excellent mechanical performance.To further boost the mechanical strengths of composites and maximize the reinforcing efficiency of SiCNWs,we introduce orthogonally structured graphene nanosheets(OGNs)into SC-CC composites,in which OGNs are grafted on the SiCNWs via chemical vapor deposition(CVD)method,forming SC-G-CC composites.Benefiting from the nano-interface effects,uniform stress distribution,strong SiCNWs/PyC interfacial bonding and elevated stress propagation efficiency in the PyC matrix are achieved,thus SC-G-CC composites accomplish brilliant mechanical properties before and after 1,600℃ heat treatment.As temperature rises to 2,100℃,SiCNWs lose efficacy,whereas OGNs with excellent thermal stability continue to play the nano-interface role in the PyC matrix.Therefore,SC-G-CC com-posites show better mechanical performance after 2,100℃ heat treatment,and the mechanical strength retention rate(MSR)of interlaminar shear strength,out-of-plane and in-plane compressive strength of SC-G-CC composites reach 61.0%,55.7%and 55.3%,respectively.This work proposes an alternative thought for maximizing the potentiality of nanomaterials and edifies the mechanical modification of composites.

基于刚度折减法的岸边集装箱起重机结构损伤模拟

岸边集装箱桥式起重机是码头集装箱进行装卸的专业设备,其前大梁、梯形架和拉杆往往受到交变载荷、冲击载荷,且在露天码头环境下受到锈蚀、涂膜剥离、裂纹等故障的侵袭,这会对其结构的刚度产生较大影响。鉴于此,文中以岸边集装箱起重机为研究对象,提出了一种基于刚度折减法的岸边集装箱起重机损伤模拟方法 ,建立有限元模型对岸边集装箱起重机的前大梁、梯形架和拉杆分别进行损伤模拟,得到不同刚度折减程度下损伤状态的位移、应变等响应;同时,考虑到这3种损伤并不独立发生,采用正交试验方法基于该损伤模型对这3种损伤进行分组模拟,得到多损伤条件下的响应数据,从而进一步反映岸边集装箱起重机实际工况下的损伤规律。

Analysis of coherent structures in drag-reducing polymer solution flow based on proper orthogonal decomposition

Direct numerical simulation(DNS) of forcing homogeneous isotropic turbulence with polymers was performed.In order to understand the polymers effect on turbulent coherent structures,proper orthogonal decomposition was performed to identify coherent structures based on DNS data,so as to analyze the remarkable difference due to the addition of polymers.The results showed that the numbers for eigenmodes required for capturing coherent structures were 32 and 24 for the Newtonian fluid and polymer solution flows,respectively,which means the decrease of the complexity in polymer solution flow.Through the POD energy spectrum,it was found that the turbulent kinetic energy is distributed onto a large number of eigenmodes whether in the Newtonian fluid flow or polymer solution flow,suggesting that polymer solution flow is still turbulent in one aspect.Besides,the POD eigenmodes were investigated,which found that the small-scale structures are inhibited in polymer solution flow.

Influence of Heat Setting on Mechanical and Structural Properties of Polypropylene Hernia Mesh

Heat setting has important effects on mechanical and structural properties of polypropylene( PP) mesh. However,there is no systematic study on the effects of heat setting. In this paper,the orthogonal array was designed for heat setting,and the influences of heat setting on structural, mechanical properties and flexural rigidity of PP mesh were studied. The experimental results showed that temperature had larger influence than tension and time on thickness,tensile strength,bursting strength, tear strength and bending stiffness of PP meshes, except the fabric weight. The optimum heat setting parameters were as follows: temperature was120 ℃, time was 10 min,and tension was small. These results will provide guideline for the selection of heat setting parameters.

Partition of Forecast Error into Positional and Structural Components

Weather manifests in spatiotemporally coherent structures.Weather forecasts hence are affected by both positional and structural or amplitude errors.This has been long recognized by practicing forecasters(cf.,e.g.,Tropical Cyclone track and intensity errors).Despite the emergence in recent decades of various objective methods for the diagnosis of positional forecast errors,most routine verification or statistical post-processing methods implicitly assume that forecasts have no positional error.The Forecast Error Decomposition(FED)method proposed in this study uses the Field Alignment technique which aligns a gridded forecast with its verifying analysis field.The total error is then partitioned into three orthogonal components:(a)large scale positional,(b)large scale structural,and(c)small scale error variance.The use of FED is demonstrated over a month-long MSLP data set.As expected,positional errors are often characterized by dipole patterns related to the displacement of features,while structural errors appear with single extrema,indicative of magnitude problems.The most important result of this study is that over the test period,more than 50%of the total mean sea level pressure forecast error variance is associated with large scale positional error.The importance of positional error in forecasts of other variables and over different time periods remain to be explored.

基于正交试验的民用飞机抗爆结构参数敏感性分析

最小风险炸弹位置(LRBL)结构是放置飞机上可疑爆炸物的装置,探究结构尺寸和炸药位置对其抗爆性能的影响程度可为其改进设计提供参考。基于正交试验设计与数值模拟相结合的方法,以LRBL结构各危险部位的最大应变和变形为评价指标,分别运用极差分析法和方差分析法对LRBL结构的罐体壁厚、底盖厚度、连接凸台厚度、剪切销直径和炸药位置5个影响因素开展参数敏感性分析。结果表明:在200 g炸药当量的工况下,各因素对LRBL结构的抗爆性能的影响显著程度从大到小为炸药位置、罐体壁厚、底盖厚度、凸台厚度和剪切销直径;结合评价指标综合分析得到各个因素最优水平下的LRBL结构设计方案。