• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.543-559
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• 2002

In this paper we formulate the linear theory for compressible fluids in cylindrical geometry with small perturbation at the material interface. We derive the first order equations in the smooth regions, boundary conditions at the shock fronts and the contact interface by linearizing the Euler equations and Rankine-Hugoniot conditions. The small amplitude solution formulated in this paper will be important for calibration of results from full numerical simulation of compressible fluids in cylindrical geometry.

• Steel and Composite Structures
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• 제41권6호
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• pp.821-829
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• 2021

Nonlinear dynamic response of a sandwich beam considering porous core and nano-composite face sheet on nonlinear viscoelastic foundation with temperature-variable material properties is investigated in this research. The Hamilton's principle and beam theory are used to drive the equations of motion. The nonlinear differential equations of sandwich beam respect to time are obtained to solve nonlinear differential equations by Homotopy perturbation method (HPM). The effects of various parameters such as linear and nonlinear damping coefficient, linear and nonlinear spring constant, shear constant of Pasternak type for elastic foundation, temperature variation, volume fraction of carbon nanotube, porosity distribution and porosity coefficient on nonlinear dynamic response of sandwich beam are presented. The results of this paper could be used to analysis of dynamic modeling for a flexible structure in many industries such as automobiles, Shipbuilding, aircrafts and spacecraft with solar easured at current time step and the velocity and displacement were estimated through linear integration.

• 제어로봇시스템학회논문지
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• 제5권5호
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• pp.511-520
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• 1999

An anti-reset windup (ARW) based compensation method for state constrained control systems is studied. First, a linear controller is constructed to give a desirable nominal performance ignoring state-constraints of a plant. Then, an additional compensator is introduced to provide smooth performance degradation under state-constraints of the plant. This paper focuses on the effective design method of the additional compensator. By minimizing a reasonable performance index, the proposed compensator is expressed in terms of theplant and ocntroller parameters. The resulting dynamics of the compensated controller exhibits the dominant part of the linear closed-loop system which can be seen from the singular perturbation model reducton theory. THe proposed method guarantees total stability of overall resulting systems if linear controllers were constructed to meet certain condition.

• 대한전자공학회논문지
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• 제24권1호
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• pp.20-27
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• 1987

The hierarchical approach method is proposed to sperate each different time scale sub-systems from linear time invariant multi-parameter singular perturbation systems. By means of this proposal, the original multi-parameter singular perturbation systems is completely separated into independent subsystems with each different time scale. It is also investigated that the controllability of the system is invariant. And this paper applies singular perturbation methods to the minimum control effort problem for linear time invariant systems with constrained controls. Also near-optimum control theory, which is based on dividing the total time interval with the time scales respectively, is proposed. As a result, the time scale separation method is show to be particularly useful in a near optimum design which can be otained through a decentralized control structure.

• Structural Engineering and Mechanics
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• 제62권5호
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• pp.607-618
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• 2017

In this paper, an analytical procedure based on the perturbation technique is presented to study the free vibrations of annular viscoelastic plates by considering the first order shear deformation theory as the displacement field. The viscoelastic properties obey the standard linear solid model. The equations of motion are extracted for small deflection assumption using the Hamilton's principle. These equations which are a system of partial differential equations with variable coefficients are solved analytically with the perturbation technique. By using a new variable change, the governing equations are converted to equations with constant coefficients which have the analytical solution and they are appropriate especially to study the sensitivity analysis. Also the natural frequencies are calculated using the classical plate theory and finite elements method. A parametric study is performed and the effects of geometry, material and boundary conditions are investigated on the vibrational behavior of the plate. The results show that the first order shear deformation theory results is more closer than to the finite elements with respect to the classical plate theory for viscoelastic plate. The more results are summarized in conclusion section.

• Advances in nano research
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• 제15권3호
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• pp.215-224
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• 2023

Nonlinearity plays an important role in control systems and the application of design. For this reason, in addition to linear vibrations, nonlinear vibrations of the stepped nanobeam are also discussed in this manuscript. This study investigated the vibrations of stepped nanobeams according to Eringen's nonlocal elasticity theory. Eringen's nonlocal elasticity theory was used to capture the nanoscale effect. The nanoscale stepped Euler Bernoulli beam is considered. The equations of motion representing the motion of the beam are found by Hamilton's principle. The equations were subjected to nondimensionalization to make them independent of the dimensions and physical structure of the material. The equations of motion were found using the multi-time scale method, which is one of the approximate solution methods, perturbation methods. The first section of the series obtained from the perturbation solution represents a linear problem. The linear problem's natural frequencies are found for the simple-simple boundary condition. The second-order part of the perturbation solution is the nonlinear terms and is used as corrections to the linear problem. The system's amplitude and phase modulation equations are found in the results part of the problem. Nonlinear frequency-amplitude, and external frequency-amplitude relationships are discussed. The location of the step, the radius ratios of the steps, and the changes of the small-scale parameter of the theory were investigated and their effects on nonlinear vibrations under simple-simple boundary conditions were observed by making comparisons. The results are presented via tables and graphs. The current beam model can assist in designing and fabricating integrated such as nano-sensors and nano-actuators.

• Journal of the Korean Physical Society
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• 제73권12호
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• pp.1800-1807
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• 2018

In this paper, we study the gravitational perturbation of traversable wormhole spacetime, especially the Morris-Thorne wormhole spacetime, by using the linearized theory of gravity. We restrict our interest to the first order term and ignore the higher order terms. We assume that the perturbation is axisymmetric. We also assume that the time dependence follows the Fourier decomposition and the angular dependence is expressed in terms of the Legendre functions. As a result, we derive the gravitational perturbation equation of traversable wormhole in terms of a single linear second-order differential equation. As a consequence, we could analyze the unstability of the spacetime with the effective potentials. Furthermore, we consider the interaction between the external gravitational perturbation and the exotic matter, constituting traversable wormholes and its effect on the stability of traversable wormholes.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1017-1031
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• 2009

The problem of interaction of surface water waves by small undulation at the bottom of a laterally unbounded sea is treated on the basis of linear water wave theory for both normal and oblique incidences. Perturbation analysis is employed to obtain the first order corrections to the reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. Fourier transform method and residue theorem are applied to obtain these coefficients. As an example, a patch of sinusoidal ripples is considered in both the cases as the shape function. The principal conclusion is that the reflection coefficient is oscillatory in the ratio of twice the surface wave number to the wave number of the ripples. In particular, there is a Bragg resonance between the surface waves and the ripples, which is associated with high reflection of incident wave energy. The theoretical observations are validated computationally.

• 천문학회보
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• 제44권1호
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• pp.55.5-55.5
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• 2019

We present our first attempt at understanding the dual impact of the large-scale density and velocity environment on the formation of very first astrophysical objects in the Universe. Following the recently developed quasi-linear perturbation theory on this effect, we introduce the publicly available initial condition generator of ours, BCCOMICS (Baryon Cold dark matter COsMological Inital Condition generator for Small scales), which provides so far the most self-consistent treatment of this physics beyond the usual linear perturbation theory. From a suite of uniform-grid simulations of N-body+hydro+BCCOMICS, we find that the formation of first astrophysical objects is strongly affected by both the density and velocity environment. Overdensity and streming-velocity (of baryon against cold dark matter) are found to give positive and negative impact on the formation of astrophysical objects, which we quantify in terms of various physical variables.

• 천문학회보
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• 제44권2호
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• pp.52.3-52.3
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• 2019

We present our first attempt at understanding the dual impact of the large-scale density and velocity environment on the formation of very first astrophysical objects in the Universe. Following the recently developed quasi-linear perturbation theory on this effect, we introduce the publicly available initial condition generator of ours, BCCOMICS (Baryon Cold dark matter COsMological Inital Condition generator for Small scales), which provides so far the most self-consistent treatment of this physics beyond the usual linear perturbation theory. From a suite of uniform-grid simulations of N-body+hydro+BCCOMICS, we find that the formation of first astrophysical objects is strongly affected by both the density and velocity environment. Overdensity and streming-velocity (of baryon against cold dark matter) are found to give positive and negative impact on the formation of astrophysical objects, which we quantify in terms of various physical variables.