• Title/Summary/Keyword: linear differential system

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Experimental analyses of dynamical systems involving shape memory alloys

  • Enemark, Soren;Savi, Marcelo A.;Santos, Ilmar F.
    • Smart Structures and Systems
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    • 제15권6호
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    • pp.1521-1542
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    • 2015
  • The use of shape memory alloys (SMAs) in dynamical systems has an increasing importance in engineering especially due to their capacity to provide vibration reductions. In this regard, experimental tests are essential in order to show all potentialities of this kind of systems. In this work, SMA springs are incorporated in a dynamical system that consists of a one degree of freedom oscillator connected to a linear spring and a mass, which is also connected to the SMA spring. Two types of springs are investigated defining two distinct systems: a pseudoelastic and a shape memory system. The characterisation of the springs is evaluated by considering differential calorimetry scanning tests and also force-displacement tests at different temperatures. Free and forced vibration experiments are made in order to investigate the dynamical behaviour of the systems. For both systems, it is observed the capability of changing the equilibrium position due to phase transformations leading to hysteretic behaviour, or due to temperature changes which also induce phase transformations and therefore, change in stiffness. Both situations are investigated by promoting temperature changes and also pre-tension of the springs. This article shows several experimental tests that allow one to obtain a general comprehension of the dynamical behaviour of SMA systems. Results show the general thermo-mechanical behaviour of SMA dynamical systems and the obtained conclusions can be applied in distinct situations as in rotor-bearing systems.

LVDT를 이용한 범용 외경측정 모듈에 관한 연구 (A Study on the Universal Outer Diameter Measurement Module using LVDT)

  • 이능구;곽이구;김홍건
    • 한국기계가공학회지
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    • 제16권3호
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    • pp.100-106
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    • 2017
  • A universal outer diameter measurement module was developed using a linear variable differential transformer (LVDT). This outer diameter measurement module enables simultaneous measurement of outer diameter, displacement, and perpendicularity of bench-type high-precision products by combining analogue and digital measurement principles with mechanically precise and fine adjustment functions. The developed module showed a performance of 0.001mm in measurement resolution, 0.001mm in measurement accuracy, reference surface abrasion lower than Ra 0.1864, and measurement stability of 0.002mm. Therefore, we have acquired domestic measurement technology to improve productivity by securing technical competitiveness for universal diameter measurement technology, lower production costs through import substitution, and increased quality of products with more precise measurement technology. Furthermore, a substitution effect is expected for expensive import measurement system equipment used in production, research, and inspection sites in industries that produce precision processing products such as automobile and machine components.

A new and simple analytical approach to determining the natural frequencies of framed tube structures

  • Mohammadnejad, Mehrdad;Kazemi, Hasan Haji
    • Structural Engineering and Mechanics
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    • 제65권1호
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    • pp.111-120
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    • 2018
  • This paper presents a new and simple solution for determining the natural frequencies of framed tube combined with shear-walls and tube-in-tube systems. The novelty of the presented approach is based on the bending moment function approximation instead of the mode shape function approximation. This novelty makes the presented solution very simpler and very shorter in the mathematical calculations process. The shear stiffness, flexural stiffness and mass per unit length of the structure are variable along the height. The effect of the structure weight on its natural frequencies is considered using a variable axial force. The effects of shear lag phenomena has been investigated on the natural frequencies of the structure. The whole structure is modeled by an equivalent non-prismatic shear-flexural cantilever beam under variable axial forces. The governing differential equation of motion is converted into a system of linear algebraic equations and the natural frequencies are calculated by determining a non-trivial solution for the system of equations. The accuracy of the proposed method is verified through several numerical examples and the results are compared with the literature.

Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Levy white-noise

  • Di Paola, Mario;Pirrotta, Antonina;Zingales, Massimiliano
    • Structural Engineering and Mechanics
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    • 제28권4호
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    • pp.373-386
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    • 2008
  • In this study stochastic analysis of non-linear dynamical systems under ${\alpha}$-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ${\alpha}$-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ${\alpha}/2$- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ${\alpha}/2$-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ${\alpha}$-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.

Free vibration analysis of non-prismatic beams under variable axial forces

  • Saffari, H.;Mohammadnejad, M.;Bagheripour, M.H.
    • Structural Engineering and Mechanics
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    • 제43권5호
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    • pp.561-582
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    • 2012
  • Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

Lithium Ion Concentration Dependant Ionic Conductivity and Thermal Properties in Solid Poly(PEGMA-co-acrylonitrile) Electrolytes

  • Kim, Kyung-Chan;Roh, Sae-Weon;Ryu, Sang-Woog
    • Journal of Electrochemical Science and Technology
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    • 제1권1호
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    • pp.57-62
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    • 2010
  • The lithium ion concentration dependant ionic conductivity and thermal properties of poly(ethylene glycol) methyl ether methacrylate (PEGMA)/acrylonitrile-based copolymer electrolytes with $LiClO_4$ have been studied by differential scanning calorimetry (DSC), linear sweep voltammetry (LSV) and AC complex impedance measurements. In systems with 11 wt% of acrylonitrile all liquid electrolytes were obtained regardless of lithium ion concentration. Complex impedance measurements with stainless steel electrodes give ambient ionic conductivities $8.1\times10^{-6}\sim1.4\times10^{-4}S cm^{-1}$. On the other hand, a hard and soft films at ambient temperature were obtained in copolymer electrolyte system consists of 15 wt% acrylonitrile with 6 : 1 and 3 : 1 of [EO] : [Li] ratio, respectively. DSC measurements indicate the crystalline melting temperature of poly(PEGMA) disappeared completely after addition of $LiClO_4$ in this system due to the complex formation between ethylene oxide (EO) unit and lithium salt. As a result, free standing film with room temperature ionic conductivity of $1.7\times10^{-4}S cm^{-1}$ and high electrochemical stability up to 5.5V was obtained by controlling of acrylonitrile and lithium salt concentration.

Bi-stability in a vertically excited rectangular tank with finite liquid depth

  • Spandonidis, Christos C.;Spyrou, Kostas J.
    • Ocean Systems Engineering
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    • 제2권3호
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    • pp.229-238
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    • 2012
  • We discuss the bi - stability that is possibly exhibited by a liquid free surface in a parametrically - driven two-dimensional (2D) rectangular tank with finite liquid depth. Following the method of adaptive mode ordering, assuming two dominant modes and retaining polynomial nonlinearities up to third-order, a nonlinear finite-dimensional nonlinear modal system approximation is obtained. A "continuation method" of nonlinear dynamics is then used in order to elicit efficiently the instability boundary in parameters' space and to predict how steady surface elevation changes as the frequency and/or the amplitude of excitation are varied. Results are compared against those of the linear version of the system (that is a Mathieu-type model) and furthermore, against an intermediate model also derived with formal mode ordering, that is based on a second - order ordinary differential equation having nonlinearities due to products of elevation with elevation velocity or acceleration. The investigation verifies that, in parameters space, there must be a region, inside the quiescent region, where liquid surface instability is exhibited. There, behaviour depends on initial conditions and a wave form would be realised only if the free surface was substantially disturbed initially.

CaO MgO.$2SiO_2-Al_2O_3$ 계의 고용체 생성에 관한 연구 (A Study on the Forming of Solid Solution in CaO.MgO.$2SiO_2-Al_2O_3$ System)

  • 안영필;김복희
    • 한국세라믹학회지
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    • 제20권1호
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    • pp.25-30
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    • 1983
  • This experiment was studied in the system of (1-x) CaO MgO $2SiO-Al_2O_3$ to investigate forming of solid solution. The technique empolyed was the well known water-quenching method. Differential thermal analysis of the each glass water quenched indicated that under 30 mole% $Al_2O_3$ was lowered with increasing of the amount of $Al_2O_3$ It was supposed by X-ray diffraction patterns of each specimen sintered at various temperature that only solid solution was formed under the 30mole % $Al_2O_3$ compositions solid solution and anorthite were formed at the 20mole% $Al_2O_3$ composition anorthite solid solution and spinel$(MgAl_2O_4)$ were formed over the 40mole% $Al_2O_3$ compositions. The maximum density and thermal expanison coefficient was 2.89g/cm 7.74x106./C$^{\circ}$ respectively in the composi-tion of 10 mole% $Al_2O_3$ . All the specimens showed linear thermal expansion behavior. Microhardness was as high as 850kg/nm2 in the composition of 5, 10, 20 mole % $Al_2O_3$ and dielectric constant was 7.3-6.9.

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Flapwise and non-local bending vibration of the rotating beams

  • Mohammadnejad, Mehrdad;Saffari, Hamed
    • Structural Engineering and Mechanics
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    • 제72권2호
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    • pp.229-244
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    • 2019
  • Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

Numerical Simulations of Subcritical Reactor Kinetics in Thermal Hydraulic Transient Phases

  • J. Yoo;Park, W. S.
    • 한국원자력학회:학술대회논문집
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    • 한국원자력학회 1998년도 춘계학술발표회논문집(1)
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    • pp.149-154
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    • 1998
  • A subcritical reactor driven by a linear proton accelerator has been considered as a nuclear waste incinerator at Korea Atomic Energy Research Institute(KAERI). Since the multiplication factor of a subcritical reactor is less than unity, to compensate exponentially decreasing fission neutrons from spallation reactions are essentially required for operating the reactor in its steady state. furthermore, the profile of accelerator beam currents is very important in controlling a subcritical reactor, because the reactor power varies in accordance of the profile of external neutrons. We have developed a code system to find numerical solutions of reactor kinetics equations, which are the simplest dynamic model for controlling reactors. In a due course of our previous numerical study of point kinetics equations for critical reactors, however, we learned that the same code system can be used in studying dynamic behavior of the subcritical reactor. Our major motivation of this paper is to investigate responses of subcritical reactors for small changes in thermal hydraulic parameters. Building a thermal hydraulic model for the subcritical reactor dynamics, we performed numerical simulations for dynamic responses of the reactor based on point kinetics equations with a source term. Linearizing a set of coupled differential equations for reactor responses, we focus our research interest on dynamic responses of the reactor to variations of the thermal hydraulic parameters in transient phases.

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