• Title/Summary/Keyword: a LU decomposition

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Recovering structural displacements and velocities from acceleration measurements

  • Ma, T.W.;Bell, M.;Lu, W.;Xu, N.S.
    • Smart Structures and Systems
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    • v.14 no.2
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    • pp.191-207
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    • 2014
  • In this research, an internal model based method is proposed to estimate the structural displacements and velocities under ambient excitation using only acceleration measurements. The structural response is assumed to be within the linear range. The excitation is assumed to be with zero mean and relatively broad bandwidth such that at least one of the fundamental modes of the structure is excited and dominates in the response. Using the structural modal parameters and partial knowledge of the bandwidth of the excitation, the internal models of the structure and the excitation can be respectively established, which can be used to form an autonomous state-space representation of the system. It is shown that structural displacements, velocities, and accelerations are the states of such a system, and it is fully observable when the measured output contains structural accelerations only. Reliable estimates of structural displacements and velocities are obtained using the standard Kalman filtering technique. The effectiveness and robustness of the proposed method has been demonstrated and evaluated via numerical simulations on an eight-story lumped mass model and experimental data of a three-story frame excited by the ground accelerations of actual earthquake records.

Analytical solutions for vibrations of rectangular functionally graded Mindlin plates with vertical cracks

  • Chiung-Shiann Huang;Yun-En Lu
    • Structural Engineering and Mechanics
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    • v.86 no.1
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    • pp.69-83
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    • 2023
  • Analytical solutions to problems are crucial because they provide high-quality comparison data for assessing the accuracy of numerical solutions. Benchmark analytical solutions for the vibrations of cracked functionally graded material (FGM) plates are not available in the literature because of the high level of complexity of such solutions. On the basis of first-order shear deformation plate theory (FSDT), this study proposes analytical series solutions for the vibrations of FGM rectangular plates with side or internal cracks parallel to an edge of the plates by using Fourier cosine series and the domain decomposition technique. The distributions of FGM properties along the thickness direction are assumed to follow a simple power law. The proposed analytical series solutions are validated by performing comprehensive convergence studies on the vibration frequencies of cracked square plates with various crack lengths and under various boundary condition combinations and by performing comparisons with published results based on various plate theories and the theory of three-dimensional elasticity. The results reveal that the proposed solutions are in excellent agreement with literature results obtained using the Ritz method on the basis of FSDT. The paper also presents tabulations of the first six nondimensional frequencies of cracked rectangular Al/Al2O3 FGM plates with various aspect ratios, thickness-to-width ratios, crack lengths, and FGM power law indices under six boundary condition combinations, the tabulated frequencies can serve as benchmark data for assessing the accuracy of numerical approaches based on FSDT.

Experimental validation of a multi-level damage localization technique with distributed computation

  • Yan, Guirong;Guo, Weijun;Dyke, Shirley J.;Hackmann, Gregory;Lu, Chenyang
    • Smart Structures and Systems
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    • v.6 no.5_6
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    • pp.561-578
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    • 2010
  • This study proposes a multi-level damage localization strategy to achieve an effective damage detection system for civil infrastructure systems based on wireless sensors. The proposed system is designed for use of distributed computation in a wireless sensor network (WSN). Modal identification is achieved using the frequency-domain decomposition (FDD) method and the peak-picking technique. The ASH (angle-between-string-and-horizon) and AS (axial strain) flexibility-based methods are employed for identifying and localizing damage. Fundamentally, the multi-level damage localization strategy does not activate all of the sensor nodes in the network at once. Instead, relatively few sensors are used to perform coarse-grained damage localization; if damage is detected, only those sensors in the potentially damaged regions are incrementally added to the network to perform finer-grained damage localization. In this way, many nodes are able to remain asleep for part or all of the multi-level interrogations, and thus the total energy cost is reduced considerably. In addition, a novel distributed computing strategy is also proposed to reduce the energy consumed in a sensor node, which distributes modal identification and damage detection tasks across a WSN and only allows small amount of useful intermediate results to be transmitted wirelessly. Computations are first performed on each leaf node independently, and the aggregated information is transmitted to one cluster head in each cluster. A second stage of computations are performed on each cluster head, and the identified operational deflection shapes and natural frequencies are transmitted to the base station of the WSN. The damage indicators are extracted at the base station. The proposed strategy yields a WSN-based SHM system which can effectively and automatically identify and localize damage, and is efficient in energy usage. The proposed strategy is validated using two illustrative numerical simulations and experimental validation is performed using a cantilevered beam.

Parallel solution of linear systems on the CRAY-2 using multi/micro tasking library (CRAY-2에서 멀티/마이크로 태스킹 라이브러리를 이용한 선형시스템의 병렬해법)

  • Ma, Sang-Back
    • The Transactions of the Korea Information Processing Society
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    • v.4 no.11
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    • pp.2711-2720
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    • 1997
  • Multitasking and microtasking on the CRAY machine provides still another way to improve computational power. Since CRAY-2 has 4 processors we can achieve speedup up to 4 properly designed algorithms. In this paper we present two parallelizations of linear system solution in the CRAY-2 with multitasking and microtasking library. One is the LU decomposition on the dense matrices and the other is the iterative solution of large sparse linear systems with the preconditioner proposed by Radicati di Brozolo. In the first case we realized a speedup of 1.3 with 2 processors for a matrix of dimension 600 with the multitasking and in the second case a speedup of around 3 with 4 processors for a matrix of dimension 600 with the multitasking and in the second case a speedup of around 3 with 4 processors for a matrix of dimension 8192 with the microtasking. In the first case the speedup is limited because of the nonuniform vector lenghts. In the second case the ILU(0) preconditioner with Radicati's technique seem to realize a reasonable high speedup with 4 processors.

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Crystal Structure and Thermal Stability Study on Tetrabutylammonium Hexamolybdate [n-Bu4N]2[Mo6O19](TBAM)

  • Zhao, Pu Su;Zhao, Zhan Ru;Jian, Fang Fang;Lu, Lu De
    • Journal of the Korean Chemical Society
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    • v.47 no.6
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    • pp.553-558
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    • 2003
  • The crystal structure of $[n-Bu_4N]_2[Mo_6O_{19}]$(TBAM) (n-Bu4N=tetrabutylammonium) has been determined by X-ray crystallography. It crystallizes in the monoclinic system, space group C2/c, with lattice parameters ${\alpha}$=16.314(5), b=17.288(5), c=17.776(4)${\AA}$ ${\beta}$=101.47(3), and Z=4. In $[Mo_6O{19}]^{2-}$ anion, Mo atoms occupy six vertices of octahedron and each Mo atom is coordinated by six oxygen atoms to adopt distorted octahedral coordination geometry. The average bond distance of Mo-Ot (terminal), Mo-Ob (bridged) and Mo-Oc (central) are 1.680 ${\AA}$, 1.931 ${\AA}$ and 2.325 ${\AA}$ respectively. In $[n-Bu_4N]^+$ cation, the N atom possesses a slightly distorted tetrahedral geometry. There are some potential extensive C-H ${\cdots}$ O hydrogen bonds in the lattice, by which connecte molecules and stabilize the crystal structure. Thermogravimetric analysis suggests that thermal decomposition of the title compound includes two transitions and it loses weight at 356.0 and 803.5 $^{\circ}$, respectively, and the residue presumable be $Mo_2O_2$. Accordingly, the title compound has high thermal stability.

Structural and Thermal Characteristics of a High-Nitrogen Energetic Material: G(AHDNE)

  • Lu, Lei;Xu, Kangzhen;Zhang, Hang;Wang, Gang;Huang, Jie;Wang, Bozhou;Zhao, Fengqi
    • Bulletin of the Korean Chemical Society
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    • v.33 no.7
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    • pp.2352-2358
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    • 2012
  • A high-nitrogen energetic salt, 1-amino-1-hydrazino-2,2-dinitroethylene guanidine salt [G(AHDNE)], was synthesized by reacting of 1-amino-1-hydrazino-2,2-dinitroethylene (AHDNE) and guanidine hydrochloride in sodium hydroxide aqueous solution. The theoretical investigation on G(AHDNE) was carried out by B3LYP/$6-311+G^*$ method. The thermal behaviors of G(AHDNE) were studied with DSC and TG-DTG methods, and the result presents an intense exothermic decomposition process. The enthalpy, apparent activation energy and pre-exponential constant of the process are $-1060J\;g^{-1}$, $148.7kJ\;mol^{-1}$ and $10^{15.90}s^{-1}$, respectively. The critical temperature of thermal explosion of G(AHDNE) is $152.63^{\circ}C$. The specific heat capacity of G(AHDNE) was studied with micro-DSC method and theoretical calculation method, and the molar heat capacity is $314.69J\;mol^{-1}K^{-1}$ at 298.15 K. Adiabatic time-to-explosion of G(AHDNE) was calculated to be a certain value between 60-72 s. The detonation velocity and detonation pressure were also estimated. G(AHDNE) presents good performances.

A Study on the friction and Wear Characteristics of C-N Coated SCM415 Steel (C-N코팅 SCM415강의 마찰$\cdot$마모 특성에 관한 연구)

  • Lyu Sung-ki;Lu Long;Jin Tai-yu;Lian Zhe-Man;Cao Xing-Jin;Cho Sung-Min
    • Journal of the Korean Society of Safety
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    • v.20 no.1 s.69
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    • pp.18-23
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    • 2005
  • This study deals with the friction and wear characteristics of C-N coated SCM415 steel. The PSII(plasma source ion implantation) apparatus was built and a SCM415 test piece with steel substrate was treated with carbon nitrogen by this apparatus. The composition and structure of the surface layer were analyzed and compared with that of PVD(physical vapor decomposition) coated TiN layer. It was found that both of friction coefficient of C-N coating and TiN coating decreased with increasing load, however, C-N coating showed relatively lower faction coefficient than that of TiN coating. The micro-vickers hardness of C-N film is 3200 Hv, which is $32\~43\%$ higher than that of TiN film. The critical load of C-N film is 52N, which is $25\%$ higher than that of TiN film. The hardness of C-N film fabricated by Plasma ion implantation is $61\~70\%$ higher than that of base material, and faction coefficient is $14\~50\%$ lower than that of base material. It is also interesting to note that the friction was changed from adhesive wear mode to light oxidizing wear mode.