• Title/Summary/Keyword: Linear system of equations

Search Result 844, Processing Time 0.031 seconds

Analysis of Dynamic Deformation of 4-Bar Linkage Mechanism (1) Finite Element Analysis and Numerical Solution (4절 링크 기구의 동적 변형 해석 (I) 유한 요소 해석 및 수치해)

  • Cho, Sun-Whi;Park, Jong-Keun;Lee, Jin
    • Transactions of the Korean Society of Mechanical Engineers
    • /
    • v.16 no.4
    • /
    • pp.737-752
    • /
    • 1992
  • Analysis of elasto-dynamic deformation of flexible linkage mechanism is conducted using the finite element method. The equations of motion of the system are derived from the static structural problem in which dynamic inertia, gravitational and driving forces are treated as external loads. Linear spring model is included in the formulation of equation of motions to represent the effects of deformation of elastic bearings of revolute joints on the system behavior. A computer program is constructed and applied to analyze a specific crank-lever 4-bar mechanism. The algorithm of the program is as follows. First, the natural frequencies and the mode shapes of the system are calculated by solving the eigenproblem of the mechanism system which can be considered as a static structure by assuming the input shaft (crank shaft) to be fixed at any given configuration of mechanism. And finally, the elasto-dynamic deformation of the whole system is obtained using mode superposition method for the case of constant input speed. The effect of geometric stiffness on the mechamism is included in the program with the axial forces of links obtained through the quasi-static displacement analysis. It is found that the geometric stiffness exerts an important effect upon the elasto-dynamic behavior of the flexible linkage mechanism. Elastic deformation of bearing lowers the natural frequencies of the system, resulting smaller elastic displacement at the mid-point of the links and bigger elestic displacement at the ends of the links than rigid bearing. The above investigation of flexible linkage mechanism shows that the effects of the elastic deformation of bearing on the mechanism should be considered to design the mechanism which satisfies more preciously the purpose and the condition of design.

Forced vibrations of an elastic rectangular plate supported by a unilateral two-parameter foundation via the Chebyshev polynomials expansion

  • Zekai Celep;Zeki Ozcan
    • Structural Engineering and Mechanics
    • /
    • v.90 no.6
    • /
    • pp.551-568
    • /
    • 2024
  • The present study deals with static and dynamic behaviors including forced vibrations of an elastic rectangular nano plate on the two-parameter foundation. Firstly, the rectangular plate is assumed to be subjected to uniformly distributed and eccentrically applied concentrated loads. The governing equations of the problem are derived by considering the dynamic response of the plate, employing a series of the Chebyshev polynomials for the displacement function and applying the Galerkin method. Then, effects of the non-essential boundary conditions of the plate, i.e., the boundary conditions related to the shearing forces, the bending moments and the corner forces, are included in the governing equation of motion to compensate for the non-satisfied boundary conditions and increase the accuracy of the Galerkin method. The approximate numerical solution is accomplished using an iterative process due to the non-linearity of the unilateral property of the two-parameter foundation. The plate under static concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate and the foundation stiffnesses. Numerical treatment of the problem in the time domain is carried out by assuming a stepwise variation of the concentrated load and the linear acceleration procedure is employed in the solution of the system of governing differential equations derived from the equation of motion. Time variations of the contact region and those of the displacements of the plate are presented in the figures for various numbers of the two-parameter of the foundation, as well as the classical and nano parameters of the plate particularly focusing on the non-linearity of the problem due to the plate lift-off from the unilateral foundation. The effects of classical and nonlocal parameters and loading are investigated in detail. Definition of the separation between the plate and the two-parameter foundation is presented and applied to the given problem. The effect of the lift-off on the static and dynamic behavior of the rectangular plate is studied in detail by considering various loading conditions. The numerical study shows that the effect of nonlocal parameters on the behavior of the plate becomes significant, when nonlinearity becomes more profound, due to the lift-off of the plate. It is seen that the size effects are significant in static and dynamic analysis of nano-scaled rectangular plates and need to be included in the mechanical analyses. Furthermore, the corner displacement of the plate is affected more significantly from the lift-off, whereas it is less marked in the time variation of the middle displacement of the plate. Several numerical examples are presented to examine the sensibility of various parameters associated with nonlocal parameters of the plate and foundation. Both stiffening and softening nonlocal parameters behavior of the plate are identified in the numerical solutions which show that increasing the foundation stiffness decreases the extent of the contact region, whereas the stiffness of the shear layer increases the contact region and reduces the foundation settlement considerably.

Rapid Nutrient Diagnosis of Tomato by Test Strips and a Chlorophyll Meter (Test strip과 chlorophyll meter를 이용한 토마토의 신속한 영양진단)

  • Kim, Kwon-Rae;Jeoung, Han-Ul;Kim, Kye-Hoon
    • Applied Biological Chemistry
    • /
    • v.46 no.2
    • /
    • pp.140-143
    • /
    • 2003
  • This study was performed to develop a more rapid and simple nutrient diagnosis method of plants than the conventional leaf analysis method. tomato (Lycopersicon esculentum Mill. cv. super momotaro) was planted in the mixed media produced by mixing perlite and rock wool at 1 . 1 (v/v) ratio. The Yamazakki nutrient solutions for cucumber and tomato were supplied to the media using the micro-drip irrigation system. Experimental plots produced consisted of no fertilization, deficient fertilization, adequate fertilization and surplus fertilization for N, P and K, respectively. Each experimental plot was replicated four times. Specific color different sensor values (SCDSV) measured by the chlorophyll meter were closely related to total-N concentrations in the leaves measured by the conventional method. Nitrate, $PO_4$ and K concentrations in petiole sap measured by test strips #(Reflectoquant^{\circledR},\;Merck,\;Germany)$ showed a significant relationship with total-N, p and K concentrations in leaves. The linear regression equations between $NO_3,\;PO_4$ and K concentrations in petiole sap and total-N, p and K concentrations in the leaves were prepared. The optimum levels of $NO_3,\;PO_4$ and K in petiole sap were obtained by plugging the optimum concentrations of total-N, p and K in the leaves by other researchers into the equations. In conclusion, the SCDSV by the chlorophyll meter and concentrations of NO3, p and K in petiole sap measured by the test strips would be suitable for rapid estimation of plant nutrient status.

Rapid Nutrient Diagnosis of Cucumber by Test Strip and Chlorophyll Meter (Test Strip과 Chlorophyll Meter를 이용한 오이의 신속한 영양진단)

  • Kim, Kwon-Rae;Kim, Kye-Hoon
    • Korean Journal of Soil Science and Fertilizer
    • /
    • v.36 no.5
    • /
    • pp.272-279
    • /
    • 2003
  • This study was performed to develop a more rapid and simple nutrient diagnosis method of plants than the conventional leaf analysis method. Cucumber (Cucumis sativus L. cv. jangil banbaek) was planted in the mixed media produced by mixing perlite and rock wool at 1:1 (v/v) ratio. The Yamazakki nutrient solution for cucumber was supplied to the media using micro-drip irrigation system. Experimental plots were consisted of no fertilization, deficient fertilization, adequate fertilization, and surplus fertilization for N, P and K. Specific color difference sensor value (SCDSV) measured by chlorophyll meter was closely related to total-N concentration in leaves measured by the conventional method. Nitrate, $PO_4$ and K concentration in petiole sap measured by test strips showed a significant relationship with total-N, P and K concentration in leaves. Linear regression equations between $NO_3$, $PO_4$ and K concentration in petiole sap and total-N, P and K concentration in the leaves were prepared. Optimum levels of $NO_{3}$, $PO_{4}$ and K in petiole sap were obtained by plugging the optimum concentrations of total-N, P and K in the leaves by other researchers into the equations. In conclusion, the SCDSV measured by chlorophyll meter and the concentration of $NO_3$, P and K in petiole sap measured by the test strips would be suitable for rapid estimation of plant nutrient status.

Application of Concurrent Engineering for Conceptual design of a Future Main Battle Tank (차세대 주력전차의 개념설계를 위한 동시공학의 적용)

  • 김진우;소한균
    • Journal of the Korea Institute of Military Science and Technology
    • /
    • v.2 no.1
    • /
    • pp.38-60
    • /
    • 1999
  • The main objective of this study is systemization of the technique of ROC quantification and optimization of baseline design by applying CE principle to the acquisition process of a weapon system. QFD and TOA techniques can be employed to a good working example of the conceptual design of a future main battle tank. In this paper, Product Planning Phase, the first phase of four QFD phases, is deployed in terms of eight steps including customer requirements and final product control characteristics. TOA is carried out considering only combat weight. In order to perform combat weight analysis and performance TOA, Preliminary Configuration Synthesis Methodology is used. Preliminary Configuration Synthesis Methodology employs the method of least squares and described linear equations of weight interrelation equation for each component of tank. As a result of QFD based upon the ROC, it was cleared that armor piercing power, main armament, type of ammunition, cruising range, combat weight, armor protection, power loading, threat detection and cost are primary factors influencing design and that combat weight is the most dominant one. The results of TOA based on the combat weight constraint show that 5100 lb reduction was required to satisfy the ROC. The baseline design of a future main battle tank is illustrated with assumption that all phases of QFD are employed to development and production process of subsystems, components, and parts of main battle tank. TOA is applied in iterative process between initial baseline design and ROC. The detailed design of each component is illustrated for a future main battle tank.

  • PDF

Buckling and free vibration analysis of tapered FG- CNTRC micro Reddy beam under longitudinal magnetic field using FEM

  • Mohammadimehr, M.;Alimirzaei, S.
    • Smart Structures and Systems
    • /
    • v.19 no.3
    • /
    • pp.309-322
    • /
    • 2017
  • In this paper, the buckling, and free vibration analysis of tapered functionally graded carbon nanotube reinforced composite (FG-CNTRC) micro Reddy beam under longitudinal magnetic field using finite element method (FEM) is investigated. It is noted that the material properties of matrix is considered as Poly methyl methacrylate (PMMA). Using Hamilton's principle, the governing equations of motion are derived by applying a modified strain gradient theory and the rule of mixture approach for micro-composite beam. Micro-composite beam are subjected to longitudinal magnetic field. Then, using the FEM, the critical buckling load, and natural frequency of micro-composite Reddy beam is solved. Also, the influences of various parameters including ${\alpha}$ and ${\beta}$ (the constant coefficients to control the thickness), three material length scale parameters, aspect ratio, different boundary conditions, and various distributions of CNT such as uniform distribution (UD), unsymmetrical functionally graded distribution of CNT (USFG) and symmetrically linear distribution of CNT (SFG) on the critical buckling load and non-dimensional natural frequency are obtained. It can be seen that the non-dimensional natural frequency and critical buckling load decreases with increasing of ${\beta}$ for UD, USFG and SFG micro-composite beam and vice versa for ${\alpha}$. Also, it is shown that at the specified value of ${\alpha}$ and ${\beta}$, the dimensionless natural frequency and critical buckling load for SGT beam is more than for the other state. Moreover, it can be observed from the results that employing magnetic field in longitudinal direction of the micro-composite beam increases the natural frequency and critical buckling load. On the other hands, by increasing the imposed magnetic field significantly increases the stability of the system that can behave as an actuator.

Mechanical and thermal stability investigation of functionally graded plates resting on visco-Pasternak foundation

  • Samira Hassiba Tagrara;Mohamed Mehdi hamri;Mahmoud Mohamed Selim Saleh;Mofareh Hassan Ghazwani;Abdelbaki Chikh;Abdelmoumen Anis Bousahla;Abdelhakim Kaci;Fouad Bourada;Abdelouahed Tounsi
    • Steel and Composite Structures
    • /
    • v.46 no.6
    • /
    • pp.839-856
    • /
    • 2023
  • This work presents a simple four-unknown refined integral plate theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on Visco-Pasternak foundations. The proposed refined high order shear deformation theory has a new displacement field which includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Governing equations are deduced from the principle of minimum total potential energy and a Navier type analytical solution is adopted for simply supported FG plates. The Visco-Pasternak foundations is considered by adding the impact of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The accuracy of the present model is demonstrated by comparing the computed results with those available in the literature. Some numerical results are presented to show the impact of material index, elastic foundation type, and damping coefficient of the foundation, on the mechanical and thermal buckling behaviors of FG plates.

Effect of the Acceleration and Deceleration on the Dynamic Characteristics of an Air Stage (에어 스테이지의 동적 특성에 미치는 가속도 및 감속도의 영향)

  • Park, Sang Joon;Lee, Jae Hyeok;Park, Sang-Shin;Kim, Gyu Ha
    • Tribology and Lubricants
    • /
    • v.36 no.1
    • /
    • pp.39-46
    • /
    • 2020
  • Air stages are usually applied to precision engineering in sectors such as the semiconductor industry owing to their excellent performance and extremely low friction. Since the productivity of a semiconductor depends on the acceleration and deceleration performance of the air stage, many attempts have been made to improve the speed of the stage. Even during sudden start or stop sequences, the stage should maintain an air film to avoid direct contact between pad and the rail. The purpose of this study is to quantitatively predict the dynamic behavior of the air stage when acceleration and deceleration occur. The air stage is composed of two parts; the stage and the guide-way. The stage transports objects to the guideway, which is supported by an externally pressurized gas bearing. In this study, we use COMSOL Multiphysics to calculate the pressure of the air film between the stage and the guide-way and solve the two-degree-of-freedom equations of motion of the stage. Based on the specified velocity conditions such as the acceleration time and the maximum velocity of stage, we calculate the eccentricity and tilting angle of the stage. The result shows that the stiffness and damping of the gas bearing have non-linear characteristics. Hence, we should consider the operating conditions in the design process of an air stage system because the dynamic behavior of the stage becomes unstable depending on the maximum velocity and the acceleration time.

Summer season temperature-humidity index threshold for infrared thermography in Hanwoo (Bos taurus coreanae) heifers

  • Kim, Na Yeon;Moon, Sang Ho;Kim, Seong Jin;Kim, Eun Kyung;Oh, Mirae;Tang, Yujiao;Jang, Se Young
    • Asian-Australasian Journal of Animal Sciences
    • /
    • v.33 no.10
    • /
    • pp.1691-1698
    • /
    • 2020
  • Objective: The study sought to estimate the relationship between body surface temperature (BST) and temperature humidity index (THI) and to present the validity of THI as a heat stress index in the field. Methods: Eight Hanwoo heifers (20 to 32 month) were examined in a field trial, with a space allowance of 10 ㎡ per head. The BST was measured using an infrared thermographic camera. The BST of five body regions (eyes, hindquarters, nose, part of horns, and ears), ambient temperature (AT), and relative humidity (RH) were measured 7 times daily (07, 09, 11, 13, 15, 17, and 19 h) during each season with three replicates. Results: The THI ranged 34.0 to 56.9 during spring (AT, -1.0℃ to 13.4℃), 75.1 to 84.7 during summer (AT, 24.9℃ to 33.6℃), 55.8 to 70.9 during autumn (AT, 13.0℃ to 26.0℃) and 17.5 to 39.2 during winter (AT, -10.4℃ to 1.0℃). In the regression analysis, the coefficient of determination (R2) between THI and BST was 0.88, 0.72, 0.83, 0.86, and 0.85 for the eyes, hindquarters, nose, part of horn, and ears area, respectively. This indicates that BST has a strong correlation with AT and RH. Expression equations were estimated as Y (THI) = 31.54+0.1085X (BST of eyes) and Y (THI) = 30.48+0.1147X (BST of hindquarters) by simple linear regression analysis in this experiment. Conclusion: Consequently, the upper bound for heat stress estimation can be specified ranging from THI of 65 (eyes) to 70 (hindquarters). From this we can expect a precise feeding system for Korean native cattle in the field.

Experimental and numerical study on coupled motion responses of a floating crane vessel and a lifted subsea manifold in deep water

  • Nam, B.W.;Kim, N.W.;Hong, S.Y.
    • International Journal of Naval Architecture and Ocean Engineering
    • /
    • v.9 no.5
    • /
    • pp.552-567
    • /
    • 2017
  • The floating crane vessel in waves gives rise to the motion of the lifted object which is connected to the hoisting wire. The dynamic tension induced by the lifted object also affects the motion responses of the floating crane vessel in return. In this study, coupled motion responses of a floating crane vessel and a lifted subsea manifold during deep-water installation operations were investigated by both experiments and numerical calculations. A series of model tests for the deep-water lifting operation were performed at Ocean Engineering Basin of KRISO. For the model test, the vessel with a crane control system and a typical subsea manifold were examined. To validate the experimental results, a frequency-domain motion analysis method is applied. The coupled motion equations of the crane vessel and the lifted object are solved in the frequency domain with an additional linear stiffness matrix due to the hoisting wire. The hydrodynamic coefficients of the lifted object, which is a significant factor to affect the coupled dynamics, are estimated based on the perforation value of the structure and the CFD results. The discussions were made on three main points. First, the motion characteristics of the lifted object as well as the crane vessel were studied by comparing the calculation results. Second, the dynamic tension of the hoisting wire were evaluated under the various wave conditions. Final discussion was made on the effect of passive heave compensator on the motion and tension responses.