• Steel and Composite Structures
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• v.38 no.3
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• pp.293-304
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• 2021

The aim of this paper is to analyze the nonlinear bending of functionally graded (FG) curved nanobeams reinforced by carbon nanotubes (CNTs) in thermal environment. Chen-Yao's surface elastic theory and geometric nonlinearity are also considered. The nanobeams are subjected to uniform loadings and placed on three-parameter substrates. The Euler-Lagrange equations are employed to deduce the equations of equilibrium. Then, the asymptotic solutions and boundary value problems are analytically determined by utilizing the two-step perturbation technique. Finally, the effects of the surface parameters, geometric factors, foundation stiffness, volume fraction, thermal effects and layout type of CNTs on the nonlinear bending of the nanobeams are discussed.

• Advances in nano research
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• v.12 no.6
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• pp.617-627
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• 2022

In the current study, the nonlinear impact of the Von-Kármán theory on the vibrational response of nonhomogeneous structures of functionally graded (FG) nano-scale tubes is investigated according to the nonlocal theory of strain gradient theory as well as high-order Reddy beam theory. The inhomogeneous distributions of temperature-dependent material consist of ceramic and metal phases in the radial direction of the tube structure, in which the thermal stresses are applied due to the temperature change in the thickness of the pipe structure. The general motion equations are derived based on the Hamilton principle, and eventually, the acquired equations are solved and modeled by the Meshless approach as well as a computer simulation via intelligent mathematical methodology. The attained results are helpful to dissect the stability of the MEMS and NEMS.

• Geomechanics and Engineering
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• v.31 no.3
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• pp.329-337
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• 2022

In this paper, the thermal post-buckling characteristics of functionally graded (FG) pipes with initial geometric imperfection are studied. Considering the influence of initial geometric defects, temperature and geometric nonlinearity, Euler-Lagrange principle is used to derive the nonlinear governing equations of the FG pipes. Considering three different boundary conditions, the two-step perturbation method is used to solve the nonlinear governing equations, and the expressions of thermal post-buckling responses are also obtained. Finally, the correctness of this paper is verified by numerical analyses, and the effects of initial geometric defects, functional graded index, elastic foundation, porosity, thickness of pipe and boundary conditions on thermal post-buckling response are analyzed. It is found that, bifurcation buckling exists for the pipes without initial geometric imperfection. In contrast, there is no bifurcation buckling phenomenon for the pipes with initial geometric imperfection. Meanwhile, the elastic stiffness can significantly improve thermal post-buckling load and thermal post-buckling strength. The larger the porosity, the greater the thermal buckling load and the thermal buckling strength.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.2
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• pp.165-174
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• 2007

Variable displacement type piston pump uses various controllers for controlling more than one state quantity like pressure, flow, power, and so on. These controllers need the mathematical model closely expressing dynamic behavior of pump for analyzing the stability of control systems which usually use various kinds of state variables. This paper derives the nonlinear mathematical model for variable displacement type piston pump. This model consists of two 1st oder differential equations by the continuity equations and one 2nd oder differential equation by the motion equation. To simplify the model we obtain the linear state variable model by differentiating the three nonlinear equations. And we verify this linearized model by comparison of simulation with experimentation and analyze the stability for the flow/pressure control. Finally this paper suggests the design compensation to ensure the stability of the systems.

• Structural Engineering and Mechanics
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• v.63 no.1
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• pp.37-46
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• 2017

This paper is concerned with the numerical study on the resonance response of a rigid spar-type floating platform in coupled heave and pitch motion. Spar-type floating platforms, widely used for supporting the offshore structures, offer an economic advantage but those exhibit the dynamically high sensitivity to external excitations due to their shape at the same time. Hence, the investigation of their dynamic responses, particularly at resonance, is prerequisite for the design of spar-type floating platforms which secure the dynamic stability. Spar-type floating platform in 2-D surface wave is assumed to be a rigid body having 2-DOFs, and its coupled dynamic equations are analytically derived using the geometric and kinematic relations. The motion-variance of the metacentric height and the moment of inertia of floating platform are taken into consideration, and the hydrodynamic interaction between the wave and platform motions is reflected into the hydrodynamic force and moment and the frequency-dependent added masses. The coupled nonlinear equations governing the heave and pitch motions are solved by the RK4 method, and the frequency responses are obtained by the digital Fourier transform. Through the numerical experiments to the wave frequency, the resonance responses and the coupling in resonance between heave and pitch motions are investigated in time and frequency domains.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.289-304
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• 2012

In this paper, we study asymptotic behaviour of solutions of the following higher order nonlinear dynamic equations $$S_n^{\Delta}(t,x)+{\delta}p(t)f(x(g(t)))=0$$ and $$S_n^{\Delta}(t,x)+{\delta}p(t)f(x(h(t)))=0$$ on an arbitrary time scale $\mathbb{T}$ with sup $\mathbb{T}={\infty}$, where n is a positive integer, ${\delta}=1$ or -1 and $$S_k(t,x)=\{\array x(t),\;if\;k=0,\\a_k(t)S_{{\kappa}-1}^{\Delta}(t),\;if\;1{\leq}k{\leq}n-1,\\a_n(t)[S_{{\kappa}-1}^{\Delta}(t)]^{\alpha},\;if\;k=n,$$ with ${\alpha}$ being a quotient of two odd positive integers and every $a_k$ ($1{\leq}k{\leq}n$) being positive rd-continuous function. We obtain some sufficient conditions for the equivalence of the oscillation of the above equations.

• Journal of Mechanical Science and Technology
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• v.15 no.8
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• pp.1165-1173
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• 2001

This paper deals with dynamic analysis of Pipeline Inspection Gauge (PIG) flow control in natural gas pipelines. The dynamic behaviour of PIG depends on the pressure differential generated by injected gas flow behind the tail of the PIG and expelled gas flow in front of its nose. To analyze dynamic behaviour characteristics (e.g. gas flow, the PIG position and velocity) mathematical models are derived. Tow types of nonlinear hyperbolic partial differential equations are developed for unsteady flow analysis of the PIG driving and expelled gas. Also, a non-homogeneous differential equation for dynamic analysis of the PIG is given. The nonlinear equations are solved by method of characteristics (MOC) with a regular rectangular grid under appropriate initial and boundary conditions. Runge-Kutta method is used for solving the steady flow equations to get the initial flow values and for solving the dynamic equation of the PIG. The upstream and downstream regions are divided into a number of elements of equal length. The sampling time and distance are chosen under Courant-Friedrich-Lewy (CFL) restriction. Simulation is performed with a pipeline segment in the Korea gas corporation (KOGAS) low pressure system. Ueijungboo-Sangye line. The simulation results show that the derived mathematical models and the proposed computational scheme are effective for estimating the position and velocity of the PIG with a given operational condition of pipeline.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.3
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• pp.205-211
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• 2005

In this study, a new numerical procedure for the generation of a nonlinear tailored group of waves is presented. The procedure is based on the transient wave group technique. In order to integrate the nonlinearity during the wave propagation in the computational method, the Navier-Stokes equations are applied as governing equations. The governing equations are discretized by finite volume approximation. The deformation of the free water surface in each time step is pursued with a moving grid. A two-dimensional, numerical wave tank for the simulation of the wave propagation is developed and tested in detail. The numeric results are compared first with analytical wave theories and with measurements, in order to examine the correctness of the numerical wave tank. Wave surface elevation and associated fields of velocity and pressure are numerically computed and compared with measurements. Very good agreements show up.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.777-789
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• 2016

In this paper, we establish some new oscillation criteria for the second-order forced nonlinear functional dynamic equations with damping term $$(r(t)x^{\Delta}(t))^{\Delta}+q({\sigma}(t))x^{\Delta}(t)+p(t)f(x({\tau}(t)))=e(t)$$, and $$(r(t)x^{\Delta}(t))^{\Delta}+q(t)x^{\Delta}(t)+p(t)f(x({\sigma}(t)))=e(t)$$, on a time scale ${\mathbb{T}}$, where r(t), p(t) and q(t) are real-valued right-dense continuous (rd-continuous) functions [1] defined on ${\mathbb{T}}$ with p(t) < 0 and ${\tau}:{\mathbb{T}}{\rightarrow}{\mathbb{T}}$ is a strictly increasing differentiable function and ${\lim}_{t{\rightarrow}{\infty}}{\tau}(t)={\infty}$. No restriction is imposed on the forcing term e(t) to satisfy Kartsatos condition. Our results generalize and extend some pervious results [5, 8, 10, 11, 12] and can be applied to some oscillation problems that not discussed before. Finally, we give some examples to illustrate our main results.

• Structural Engineering and Mechanics
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• v.42 no.4
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• pp.589-608
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• 2012

In this study, the effect of in-plane deformations on the dynamic behavior of laminated plates is investigated. For this purpose, the displacement-time and strain-time histories obtained from the large deflection analysis of laminated plates are compared for the cases with and without including in-plane deformations. For the first one, in-plane stiffness and inertia effects are considered when formulating the dynamic response of the laminated composite plate subjected to the blast loading. Then, the problem is solved without considering the in-plane deformations. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates and transverse shear stresses are ignored for both cases. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The effects of the magnitude of the blast load, the thickness of the plate and boundary conditions on the in-plane deformations are investigated.