• Title/Summary/Keyword: small unknowns

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Discretization Effects of Real-Time Input Shaping in Residual Vibration Reduction for Precise XY Stage (정밀 XY 스테이지 잔류진동 억제를 위한 실시간 입력성형에서의 이산화 효과에 관한 연구)

  • Park, Sang-Won;Choi, Hun-Seok;Singhose, William;Hong, Seong-Wook
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.16 no.4
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    • pp.71-78
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    • 2007
  • Input shaping is known to be a very effective tool for suppressing residual vibration without introducing any complicated sensors and feedback control. Real-time input shaping schemes necessitate a process such that the input command is discretized to deal with non-prescribed, real-time input. Thus parameters associated with input command discretization, such as time spacing and duration time, are unknowns which affect the performance of input shaping schemes, especially for small and fast XY stages. This paper investigates the effects of input command discretization parameters, such as time spacing and duration time, on the dynamic performance of XY stages subjected to real-time input shaping. An experimental system is developed which is equipped with an XY stage driven by servo-motors and real-time user command. Experiments are performed to investigate the dynamic performance of XY stage by changing these parameters and to yield a strategy to gain better performance.

Ultimate Strength Analysis of Framed Structures Using Idealized Structural Unit Method (이상화구조요소법에 의한 골조구조물의 최종강도해석에 관한 연구)

  • 백점기;임화규
    • Computational Structural Engineering
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    • v.4 no.1
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    • pp.83-94
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    • 1991
  • This paper presents an efficient and accurate method for nonlinear analysis of frame structures by idealized structural unit method. The main idea behind the present method is to minimize the computational effort by reducing the number of unknowns. An explicit form of the tangential elastic stiffness matrix of the element is derived by the principle of virtual work. The ultimate limit state of the element is judged on the basis of the formation of a plastic hinge mechanism. The elasto-plasto-plastic stiffness matrix of the element is derived by plastic node method and the post-ultimate stiffness equation is formulated under a simple analytic consideration. A comparison between the present solution and the existing experimental and other numerical result for unit column member and simple frame structure is made. If is clear from the result of this study that the present method is very useful because the computing time required is very small while giving the accurate solution.

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A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates

  • Bessaim, Aicha;Houari, Mohammed Sid Ahmed;Bernard, Fabrice;Tounsi, Abdelouahed
    • Structural Engineering and Mechanics
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    • v.56 no.2
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    • pp.223-240
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    • 2015
  • In this work, a nonlocal quasi-3D trigonometric plate theory for micro/nanoscale plates is proposed. In order to introduce the size influences, the Eringen's nonlocal elasticity theory is utilized. In addition, the theory considers both shear deformation and thickness stretching effects by a trigonometric variation of all displacements within the thickness, and respects the stress-free boundary conditions on the top and bottom surfaces of the plate without considering the shear correction factor. The advantage of this theory is that, in addition to considering the small scale and thickness stretching effects (${\varepsilon}_z{\neq}0$), the displacement field is modelled with only 5 unknowns as the first order shear deformation theory (FSDT). Analytical solutions for vibration of simply supported micro/nanoscale plates are illustrated, and the computed results are compared with the available solutions in the literature and finite element model using ABAQUS software package. The influences of the nonlocal parameter, shear deformation and thickness stretching on the vibration behaviors of the micro/nanoscale plates are examined.

Wave propagation investigation of a porous sandwich FG plate under hygrothermal environments via a new first-order shear deformation theory

  • Al-Osta, Mohammed A.
    • Steel and Composite Structures
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    • v.43 no.1
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    • pp.117-127
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    • 2022
  • This study investigates the wave propagation in porous functionally graded (FG) sandwich plates subjected to hygrothermal environments. A new simple three-unknown first-ordershear deformation theory (FSDT) incorporating an integral term is utilized in this paper. Only three unknowns are used to formulate the governing differential equation by applying the Hamilton principle. The FG layer of the sandwich plate is modeled using the power-law function with evenly distributed porosities to represent the defects of the manufacturing process. The plate is subjected to nonlinear hygrothermal changes across the thickness. The effects of the power-law exponent, core to thickness ratios, porosity volume, and the relations between volume fraction and wave properties of porous FG plate under the hygrothermal environment are investigated. The results showed that the waves' phase velocities increase linearly with the waves number in the FGM plate. The porosity of the FG materials plate has a noticeable impact on the phase velocity when considering the high ratios of the core layer. It has a negligible effect on small core layers. Finally, it is observed that changing temperatures and moistures do not influence the relationship between the power law and the phase velocity.

Effect of shear stresses on the deflection and optimal configuration of a rectangular FGM structure

  • Ayoub El Amrani;Hafid Mataich;Jaouad El-Mekkaoui;Bouchta El Amrani
    • Coupled systems mechanics
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    • v.12 no.4
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    • pp.391-407
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    • 2023
  • This paper presents a static study of a rectangular functional graded material (FGM) plate, simply supported on its four edges, adopting a refined higher order theory that looks for, only,four unknowns,without taking into account any corrective factor of the deformation energy with the satisfaction of the zero shear stress conditions on the upper and lower faces of the plate. We will have determined the contribution of these stresses in the transverse deflection of the plate, as well as their effects on the axial stress within the interfaces between the layers(to avoid any problem of imperfections such as delamination) and on the top and bottom edges of the plate in order to take into account the fatigue phenomenon when choosing the distribution law of the properties used during the design of the plate. A numerical statement, in percentage, of the contribution of the shear effect is made in order to show the reliability of the adopted theory. We will also have demonstrated the need to add the shear effect when the aspect ratio is small or large. Code routines are programmed to obtain numerical results illustrating the validity of the model proposed in the theory compared to those available in the literature.

A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory

  • Mokhtar, Youcef;Heireche, Houari;Bousahla, Abdelmoumen Anis;Houari, Mohammed Sid Ahmed;Tounsi, Abdelouahed;Mahmoud, S.R.
    • Smart Structures and Systems
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    • v.21 no.4
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    • pp.397-405
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    • 2018
  • In this paper, a novel simple shear deformation theory for buckling analysis of single layer graphene sheet is formulated using the nonlocal differential constitutive relations of Eringen. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal elasticity theory is employed to investigate effects of small scale on buckling of the rectangular nano-plate. The equations of motion of the nonlocal theories are derived and solved via Navier's procedure for all edges simply supported boundary conditions. The results are verified with the known results in the literature. The influences played by Effects of nonlocal parameter, length, thickness of the graphene sheets and shear deformation effect on the critical buckling load are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model

  • Belkorissat, Ismahene;Houari, Mohammed Sid Ahmed;Tounsi, Abdelouahed;Bedia, E.A. Adda;Mahmoud, S.R.
    • Steel and Composite Structures
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    • v.18 no.4
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    • pp.1063-1081
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    • 2015
  • In this paper, a new nonlocal hyperbolic refined plate model is presented for free vibration properties of functionally graded (FG) plates. This nonlocal nano-plate model incorporates the length scale parameter which can capture the small scale effect. The displacement field of the present theory is chosen based on a hyperbolic variation in the in-plane displacements through the thickness of the nano-plate. By dividing the transverse displacement into the bending and shear parts, the number of unknowns and equations of motion of the present theory is reduced, significantly facilitating structural analysis. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG nano-plate are computed using Mori-Tanaka homogenization scheme. The governing equations of motion are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined four variable plate theory via Hamilton's principle. Analytical solution for the simply supported FG nano-plates is obtained to verify the theory by comparing its results with other available solutions in the open literature. The effects of nonlocal parameter, the plate thickness, the plate aspect ratio, and various material compositions on the dynamic response of the FG nano-plate are discussed.

Analysis of the Naemorhedus caudatus Population in Odaesan National Park - The Goral Individually Identification and Statistical Analysis Using the Sensor Camera - (오대산국립공원 산양(Naemorhedus caudatus) 개체 수 분석 - 무인센서카메라 분석을 이용한 개체 구분 및 통계 분석 -)

  • Kim, Gyu-cheol;Lee, Yong-hak;Lee, Dong-un;Son, Jang-ick;Kang, Jae-gu;Cho, Chea-un
    • Korean Journal of Environment and Ecology
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    • v.34 no.1
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    • pp.1-8
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    • 2020
  • This study conducted a full survey of the goral population using sensor cameras to identify the exact habitat of the gorals that inhabit Odaesan National Park and for restoration and habitat management-focused conservation projects following the population growth. We surveyed Odaesan National Park for a year in 2018 and selected18 grids (2km×2km) first based on the survey results. We then further divided each grid into four small grids (1km×1km) and installed a total of 62 sensor cameras in 38 small girds divided by four grids(1km×1km). The survey resulted in a total of 5,096 photographed wild animals, 2,268 of which were gorals, and the analysis by the classification table of goral (horn shape (Ⓐ), ring pattern (Ⓑ), ring formation ratio (Ⓒ), and facial color (Ⓓ)) identified a total of 95 animals. The ratio of male and female was 35 males (36.8%), 46 females (48.4%), and 14 sex unknowns (14.7%), while the ratio of female and male excluding sex unknowns was 4 (male):6 (female). The horn shape (Ⓐ) and face color (Ⓓ) were the important factors for distinguishing male and female and identifying individuals. The analysis of the correlation of 81 individuals, excluding 14 individuals of unknown sex, showed a significant difference (r=-0.635, p<0.01). Since the goral population in Odaesan National Park has reached a minimum viable population, it is necessary to change the focus of the management policy of Odaesan National Park from restoration to conservation.

The Variation of Natural Population of Pinus densiflora S. et Z. in Korea (III) -Genetic Variation of the Progeny Originated from Mt. Chu-wang, An-Myon Island and Mt. O-Dae Populations- (소나무 천연집단(天然集團)의 변이(變異)에 관(關)한 연구(硏究)(III) -주왕산(周王山), 안면도(安眠島), 오대산(五臺山) 소나무집단(集團)의 차대(次代)의 유전변이(遺傳變異)-)

  • Yim, Kyong Bin;Kwon, Ki Won
    • Journal of Korean Society of Forest Science
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    • v.32 no.1
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    • pp.36-63
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    • 1976
  • The purpose of this study is to elucidate the genetic variation of the natural forest of Pinus densiflora. Three natural populations of the species, which are considered to be superior quality phenotypically, were selected. The locations and conditions of the populations are shown in table 1 and 2. The morphological traits of tree and needle and some other characteristics were presented already in our first report of this series in which population and family differences according to observed characteristics were statistically analyzed. Twenty trees were sampled from each populations, i.e., 60 trees in total. During the autumn of 1974, matured cones were collected from each tree and open-pollinated seeds were extracted in laboratory. Immediately after cone collection, in closed condition, the morphological characteristics were measured. Seed and seed-wing dimensions were also studied. In the spring of 1975, the seeds were sown in the experimental tree nursery located in Suweon. And in the April of 1976, the 1-0 seedlings were transplanted according to the predetermined experimental design, randomized block design with three replications. Because of cone setting condition. the number of family from which progenies were raised by populations were not equal. The numbers of family were 20 in population 1. 18 in population 2 and 15 in population 3. Then, each randomized block contained seedlings of 53 families from 3 populations. The present paper is mainly concerned with the variation of some characteristics of cone, seed, needle, growth performance of seedlings, and chlorophyll and monoterpene compositions of needles. The results obtained are summerized as follows. 1. The meteorological data obtained by averaging the records of 30 year period, observed from the nearest station to each location of populations, are shown in Fig. 3, 4, and 5. The distributional pattern of monthly precipitation are quite similar among locations. However, the precipitation density on population 2, Seosan area, during growing season is lower as compared to the other two populations. Population 1. Cheong-song area, and population 3, Pyong-chang area, are located in inland, but population 2 in the western seacoast. The differences on the average monthly air temperatures and the average monthly lowest temperatures among populations can hardly be found. 2. Available information on the each mother trees (families) studied, such as age, stem height, diameter at breast height, clear-bole-length, crown conditions and others are shown in table 6,7, and 8. 3. The measurements of fresh cone weight, length and the widest diameter of cone are given in Tab]e 9. All these traits arc concerned with the highly significant population differences and family differences within population. And the population difference was also found in the cone-index, that is, length-diameter ratio. 4. Seed-wing length and seed-wing width showed the population differences, and the family differences were also found in both characteristics. Not discussed in this paper, however, seed-wing colours and their shapes indicate the specificity which is inherent to individual trees as shown in photo 3 on page 50. The colour and shape are fully the expression of genetic make up of mother tree. The little variations on these traits are resulted from this reason. The significant differences among populations and among families were found in those characteristics, such as 1000-seed weight, seed length, seed width, and seed thickness as shown in table 11. As to all these dimensions, the values arc always larger in population 1 which is younger in age than that of the other two. The population differences evaluated by cone, seed and seed-wing sizes could partly be attributed to the growth vigorousity. 5. The values of correlation between the characteristics of cone and seed are presented in table 12. As shown, the positive correlations between cone diameter and seed-wing width were calculated in all populations studied. The correlation between seed-wing length and seed length was significantly positive in population 1 and 3 but not in population 2, that is, the r-value is so small as 0.002. in the latter. The correlation between cone length and seed-wing length was highly significant in population 1, but not in population 2. 6. Differences among progenies in growth performances, such as 1-0 and 1-1 seedling height and root collar diameter were highly singificant among populations as well as families within population(Table 13.) 7. The heritability values in narrow sense of population characteristics were estimated on the basis of variance components. The values based on seedling height at each age stage of 1-1 and 1-0 ranged from 0.146 to 0.288 and the values of root collar diameter from 0.060 to 0.130. (Table 14). These heritability values varied according to characteristics and seedling ages. Here what must be stated is that, for calculation of heritability values, the variance values of population was divided by the variance value of environment (error) and family and population. The present authors want to add the heritability values based on family level in the coming report. It might be considered that if the tree age is increased in furture, the heritability value is supposed to be altered or lowered. Examining the heritability values studied previously by many authors, in pine group at age of 7 to 15, the values of height growth ranged from 0.2 to 0.4 in general. The values we obtained are further below than these. 8. The correlation between seedling growth and seed characteristics were examined and the values resulted are shown in table 16. Contrary to our hypothetical premise of positive correlation between 1-0 seedling height and seed weight, non-significance on it was found. However, 1-0 seedling height correlated positively with seed length. And significant correlations between 1-0 and 1-1 seedling height are calculated. 9. The numbers of stomata row calculated separately by abaxial and adaxial side showed highly significant differences among populations, but not in serration density. On serration density, the differences among families within population were highly significant. (Table 17) A fact must be noted is that the correlation between stomata row on abaxial side and adaxial side was highly significant in all populations. Non-significances of correlation coefficient between progenies and parents regarding to stomata row on abaxial side were shown in all populations studied.(Table 18). 10. The contents of chhlorophyll b of the needle were a little more than that of chlorophyll a irrespective of the populations examined. The differences of chlorophyll a, b and a plus b contents were highly significant but not among families within populations as shown in table 20. The contents of chlorophyll a and b are presented by individual trees of each populations in table 21. 11. The occurrence of monoterpene components was examined by gas liquid chromatography (Shimazu, GC-1C type) to evaluate the population difference. There are some papers reporting the chemical geography of pines basing upon monoterpene composition. The number of populations studied here is not enough to state this problem. The kinds of monoterpene observed in needle were ${\alpha}$-pinene, camphene, ${\beta}$-pinene, myrcene, limonene, ${\beta}$-phellandrene and terpinolene plus two unknowns. In analysis of monoterpene composition, the number of sample trees varied with population, I.e., 18 families for population 1, 15 for population 2 and 11 for population3. (Table 22, 23 and 24). The histograms(Fig. 6) of 7 components of monoterpene by population show noticeably higher percentages of ${\alpha}$-pinene irrespective of population and ${\beta}$-phellandrene in the next order. The minor Pinus densiflora monoterpene composition of camphene, myrcene, limonene and terpinolene made up less than 10 percent of the portion in general. The average coefficients of variation of ${\alpha}$-pinene and ${\beta}$-phellandrene were 11 percent. On the contrary to this, the average coefficients of variation of camphene, limonene and terpinolene varied from 20 to 30 percent. And the significant differences between populaiton were observed only in myrcene and ${\beta}$-phellandrene. (Table 25).

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