A symmetric substructuring method for analyzing the natural frequencies of conical origami structures

Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness.

The Tension Cosmology, Largest Cosmic Structures and Explosions of Supernovae from SST

Here, using the Scale-Symmetric Theory (SST) we explain the cosmological tension and the origin of the largest cosmic structures. We show that a change in value of strong coupling constant for cold baryonic matter leads to the disagreement in the galaxy clustering amplitude, quantified by the parameter S8. Within the same model we described the Hubble tension. We described also the mechanism that transforms the gravitational collapse into an explosion—it concerns the dynamics of virtual fields that lead to dark energy. Our calculations concern the Type Ia supernovae and the core-collapse supernovae. We calculated the quantized masses of the progenitors of supernovae, emitted total energy during explosion, and we calculated how much of the released energy was transferred to neutrinos. Value of the speed of sound in the strongly interacting matter measured at the LHC confirms that presented here model is correct. Our calculations show that the Universe is cyclic.

Synthesis, Structure of a Symmetrically Substituted Stilbene with Strong Two-photon Absorption and Up-converted Blue Fluorescence

Efficient Ti-catalyzed reductive coupling methodology was first employed to synthesize the symmetrical bis-donor stilbene, trans-4, 4'-bis[diphenyl amino] stilbene (BDPAS). X-ray diffraction analyses reveal that this new crystal belongs to the triclinic crystal system of centro-symmetric P-1 space group. The DBPAS solution, with the linear transmission at wavelength of greater than or equal to 450 nm, possesses large two-photon absorption cross section as high as 39.4x10(-48) cm(4).s/photon resulting in strong two-photon induced blue fluorescence of 460 nm, pumped by 740 nm laser irradiation.

ON DECENTRALIZED STABILIZATION OF LINEAR LARGE SCALE SYSTEMS WITH SYMMETRIC CIRCULANT STRUCTURE

The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied.A few sufficient conditions on decentralized stabilization of such systems were proposed.For the continuous systems,by introducing a concept called the magnitude of interconnected structure,a very important property that the decentralized stabilization of such systems is fully determined by the structure of each isolated subsystem that is obtained when the magnitude of interconnected structure of the overall system is given.So the decentralized stabilization of such systems can be got by only appropriately designing or modifying the structure of each isolated subsystem,no matter how complicated the interconnected structure of the overall system is.A algorithm for obtaining decentralized state feedback to stabilize the overall system is given.The discrete systems were also discussed.The results show that there is a great dfference on decentralized stabilization between continuous case and discrete case.

A UNIFIED APPROACH FOR DEALING WITH THE EM SCATTERING FROM SYMMETRIC AND ANTI-SYMMETRIC STRUCTURES

It is of both the theoretical and practical importance to reduce the storage andCPU time of moment methods by utilizing the geometrical and physical features of the scatterer.An unified approach based on the group theory is presented to deal with the EM scattering fromsymmetric and anti-symmetric structures.

A NEW METHOD FOR STRESS ANALYSIS OF A CYCLICALLY SYMMETRIC STRUCTURE

In this paper, a computational method for finite element stress analysis of a cyclically symmetric structure subjected to arbitrary loads is provided. At first, using discrete Fourier transformation technique, the complete structure is analyzed by considering only one sector with appropriate complex constraints on its boundary with the adjacent sectors. Next, an imaginary structure which is composed of two identically overlapping sectors is constructed, and that the complex constraints mentioned above can be equivalently replaced by a set of real constraints on this imaginary structure is proved. Therefore, the stress analysis of a cyclically symmetric structure can be solved conveniently by most of finite element programs.

The effect of the horizontal structure for symmetric tropical cyclones on their movement

In this paper, using Holland's method, the effect of the horizontal structure of tropical cyclones on their motion is investigated. The 'characteristic radius', r0 characterized as the horizontal structure of a tropical cyclone,in which m and p are the parameters of the vortex, has been found by the author. And then it has been shown that there is but one 'characteristic radius' for each cyclone with horizontal structure. Two direct analytic solutions for the uniform and non-uniform basic flows in steady situations are presented with rc Results show that the change in the horizontal structure of the tropical cyclone itself will have obvious effect on the cyclone motion, on both its direction and speed. Therefore it must be considered in the research on the tropical cyclone motion.

Acoustic band pinning in the phononic crystal plates of anti-symmetric structure

Acoustic bands are studied numerically for a Lamb wave propagating in an anti-symmetric structure of a one- dimensional periodic plate by using the method of supercell plane-wave expansion. The results show that all the bands are pinned in pairs at the Brillouin zone boundary as long as the anti-symmetry remains and acoustic band gaps （ABGs） only appear between certain bands. In order to reveal the relationship between the band pinning and the anti-symmetry, the method of eigenmode analysis is introduced to calculate the displacement fields of different plate structures. Further, the method of harmony response analysis is employed to calculate the reference spectra to verify the accuracy of numerical calculations of acoustic band map, and both the locations and widths of ABGs in the acoustic band map are in good agreement with those of the reference spectra. The investigations show that the pinning effect is very sensitive to the anti-symmetry of periodic plates, and by introducing different types of breakages, more ABGs or narrow pass bands will appear, which is meaningful in band gap engineering.

Crystal Structure, DFT and Electrochemical Property of a Novel C3-symmetrical 1,3,5-Tri（9-ethyl-6-nitrocarbazol-3-yl） Benzene

A novel C3-symmetrical molecule, 1,3,5-tri(9-ethyl-6-nitrocarbazol-3-yl) benzene(IV), was synthesized and characterized by 1 H NMR, 13 C NMR and UV-vis spectroscopy, elemental analyses and X-ray single crystal diffraction analysis. For this complex: C48 H36 N6 O6, Mr = 792.83, triclinic system, space group P1, a = 11.568(6), b = 13.158(7), c = 17.856(10) ?, α = 95.419(9), β = 107.345(8), γ = 114.682(8)o, V = 2281(2) ?3, Z = 2, Dc = 1.154 g/cm3, λ = 0.71073 ?, F(000) = 828, S = 1.083, R = 0.0836 and wR = 0.1926 for 3304 observed reflections with I > 2ζ(I). The compound possesses good thermal stability with the decomposition temperature(Td) of 265 ℃. The absorption and emission spectra show that the compound can emit blue light in CHCl3, and the quantum yield of compound IV in EtOH was 0.66. Furthermore, the electrochemical properties of compound IV were also studied by cyclic voltammetry(CV) method, and the results correspond to the data of theoretical calculation by the Gaussian 09 software.

Analysis of flow around impermeable groynes on one side of symmetrical compound channel:An experimental study

This paper presents the results of an experimental study on the influences of floodplain impermeable groynes on flow structure, velocity, and water depth around the groyne（s）. A wooden symmetrical compound channel was used. Groyne models with three different groyne relative lengths, 0.5, 0.75, and 1.0, were used on one floodplain with single and series arrangements. Analysis of the experimental results using the measured flow velocity and water depth values showed that flow structure, velocity, and water depth mainly depend on groyne relative length and the relative distance between series groynes. The flow velocity at the main channel centerline increased by about 40%, 60%, and 85%, and in other parts on the horizontal plane at the floodplain mid-water, depth by about 75%, 125%, and 175% of its original value in eases of one-side floodplain groyne（s） with relative lengths of 0.5, 0.75, and 1.0, respectively. The effective distance between two groynes in series arrangement ranges from 3 to 4 times the groyne length. Using an impermeable groyne with a large relative length in river floodplains increases the generation of eddy and roller zones downstream of the groyne, leading to more scouring and deposition. To avoid that, the groyne relative length must be kept below half the floodplain width,

REDUCTION APPROACHES FOR VIBRATION CONTROL OF REPETITIVE STRUCTURES

The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way so that the control system posses the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputs, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.

Synthesis and Crystal Structure of Chiral Spiro{1-bromo-4-hydroxy-5-N-cyclohexyl-butyrolactam-6-oxo-dirings[3.1.0]hexane-2,3′-(4′-diphenylcarbinol-5′-menthyloxy-butyrolatone)}

A novel compound of chiral spiro{1-bromo-4-hydroxy-5-N-cyclohexyl-butyro-lactam-6-oxo-dirings[3.1.0]hexane-2,3＇-（4＇-diphenylcarbinol-5＇-menthyloxy-butyrolatone）} was synthesized via tandem nucleophilic substitution reaction under mild conditions, and its structure was determined by IR, ^1H NMR, elemental analysis and X-ray diffraction. The crystal structure of this compound is of monoclinic system, space group P21 with a = 9.7356（9）, b = 12.2760（12）, c = 14.9577（14） A, β = 101.0300（10）°, Mr = 680.66, Z = 2, V = 1754.6（3） A^3, Dc = 1.288 g/cm^3, p（MoKα） = 1.216 mm^-1, F（000） = 716, the final R = 0.0434 and wR = 0.0996.

Crosscumulants Based Approaches for the Structure Identification of Volterra Models

In this paper, we address the problem of structure identification of Volterra models. It consists in estimating the model order and the memory length of each kernel. Two methods based on input-output crosscumulants are developed. The first one uses zero mean independent and identically distributed Caussian input, and the second one concerns a symmetric input sequence. Simulations are performed on six models having different orders and kernel memory lengths to demonstrate the advantages of the proposed methods.

Synthesis and Characterization of a New Symmetric Dinucleating Ligand and Its Dizinc(Ⅱ)Complex with Alkoxo and Carboxylate Bridges

A novel dinuclear zinc（II） complex [Zn2L（μ-OAc）]（PF6）2（CH3OH） has been synthesized from a new symmetrical compartmental ligand HL in which the pendant arms, bearing pyridyl groups, are bridged by 1,3-diaminopropan-2-ol. X-ray crystal structure shows that the two zinc atoms reside within the adjacent ligand compartments and are bridged by the endogenous alkoxo-O from ligand and one exogenous carboxylate from acetate with a syn-syn mode. The coordination geometry of two zinc atoms is a distorted trigonal bipyramid with the pyridyl-N atoms and bridging alkoxo-O atom providing the equatorial donor set. Such coordination geometry observed in this complex is similar to that found in the dinuclear unit ofphospholipase C.

Solving a Generalized Jaynes-Cummings Model by Supersymmetric Unitary Transformation

For the generalized Jaynes-Cummings model Hamiltonian which can describe two collectively radiation atoms,we find its supersymmetric structure.Based on supersymmetric quantum mechanics theory,we introduce a supersymmetric unitary transformation,in which the supersymmetric unitary transformation operator can be constructed by supersymmetric generators of the super-Lie algebra,to diagonalize the Hamiltonian.On doing so,its eigenvalue and eigenstates are obtained.

Hidden Properties of Mathematical Physics Equations. Double Solutions. The Realization of Integrable Structures. Emergence of Physical Structures and Observable Formations

With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.

Spontaneous Emergence of Physical Structures and Observable Formations: Fluctuations, Waves, Turbulent Pulsations and So on

As it is known, the closed inexact exterior form and associated closed dual form make up a differential-geometrical structure. Such a differential-geometrical structure describes a physical structure, namely, a pseudostructure on which conservation laws are fulfilled (A closed dual form describes a pseudostructure. And a closed exterior form, as it is known, describes a conservative quantity, since the differential of closed form is equal to zero). It has been shown that closed inexact exterior forms, which describe physical structures, are obtained from the equations of mathematical physics. This process proceeds spontaneously under realization of any degrees of freedom of the material medium described. Such a process describes an emergence of physical structures and this is accompanied by an appearance of observed formations such as fluctuations, waves, turbulent pulsations and so on.

对称悬架混联轮腿机器人结构设计与参数优化

为了实现机器人在地下空间低能耗的灵活运动,文中设计了一种对称悬架混联轮腿机器人,并针对其腿部参数优化问题,提出了一种基于沙猫群算法的性能均衡优化方法(简称均衡优化方法)。结合对称四边形机构与悬架系统,设计了一种对称悬架混联式轮腿结构,并建立其运动学和动力学模型,分析了腿部杆长对单轮腿运动空间和灵活性指标的影响,预优化确定了腿部初始杆长均为0.3 m。在满足轮腿越障规划空间及高灵活性的基础上,为了实现低能耗,建立了轮腿性能均衡优化评价指标,采用均衡优化方法对腿部杆长进行了优化研究。数值计算结果表明:大腿和小腿杆长最优值分别为0.23 m和0.3 m,该轮腿运动能耗为23.18 J,运动空间为0.1322 m2,灵活性指标变化范围为(0.2,1)。优化后灵活性保持不变,运动空间减小了24.54%,能耗降低了22.60%,验证了该方法合理有效,为轮腿机器人的设计与优化提供了一种新的思路。

关于集合环的教学方法探讨

集合的运算性质是集合论课程的基础,通过引入集合环概念及其性质的讲授,帮助学生们理解集合代数运算的性质,促进对抽象代数结构的理解.在对称差运算满足结合律性质的证明过程中,启发学生们积极思考,从集合论的角度理解代数结构,锻炼学生们的抽象思维能力.

基于改进矩量法的风电机无源干扰快速计算

准确快速计算风电机的散射电场,是解决风电机无源干扰的基本前提。采用传统矩量法求解电大尺寸风电机散射电场时,需要极为庞大的计算资源导致难以求解。为此,考虑风电机工作时叶片的周期对称性以及风电机叶片大曲率、复杂的异形曲面,改进了传统矩量法中求解风电机无源干扰的面元剖分方法,引入基于曲面三角面元的矩量法基函数,并且利用叶片结构的对称性简化阻抗矩阵填充过程,准确快速计算出了风电机表面感应电流产生的散射电场,实现了风电机无源干扰的快速计算。为验证所提方法的正确性及有效性,开展了基于电波暗室风电机缩比模型实验,结果表明,该方法计算的结果与实验测量结果较为一致。以实际金风GW82/1500型风电机为例,将所提方法计算的不同方位角下风电机叶片无源干扰水平与传统矩量法相比,表明该方法与其吻合良好,所提方法矩阵元素计算内存减少了34.64倍,矩阵元素求解效率提高了37.95倍。为后续广域空间下风电场中大规模风电机阵列动态电磁散射理论研究奠定了理论与技术基础。