• Honam Mathematical Journal
• /
• v.35 no.4
• /
• pp.683-699
• /
• 2013

In this paper, an improved ($\frac{G^{\prime}}{G}$)-expansion method is proposed for obtaining travelling wave solutions of nonlinear evolution equations. The proposed technique called ($\frac{F}{G}$)-expansion method is more powerful than the method ($\frac{G^{\prime}}{G}$)-expansion method. The efficiency of the method is demonstrated on a variety of nonlinear partial differential equations such as KdV equation, mKd equation and Boussinesq equations. As a result, more travelling wave solutions are obtained including not only all the known solutions but also the computation burden is greatly decreased compared with the existing method. The travelling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. The result reveals that the proposed method is simple and effective, and can be used for many other nonlinear evolutions equations arising in mathematical physics.

• Smart Structures and Systems
• /
• v.22 no.1
• /
• pp.105-120
• /
• 2018

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin's decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.

• 제어로봇시스템학회:학술대회논문집
• /
• 1999.10a
• /
• pp.145-148
• /
• 1999

It is known that Volterra kernel models can represent a wide variety of nonlinear chemical processes. Also, it is necessary for Volterra model identification to excite the process to be identified with a signal having wide range of frequency spectrum and high enough amplitude of input signals. Kashiwagi[4 ∼ 7] has recently shown a method for measuring Volterra kernels up to third order using pseudorandom M-sequence signals. However, in practice, since it is not always possible to apply such input sequences to the actual chemical plants. Even when we can apply such a pseudorandom signal to the process, it takes much time to obtain higher order Volterra kernels. Considering these problems, the authors propose here a new method for practical identification of Volterra kernels by use of approximate open differential equation (ODE) model and simple plant test. Simulation results are shown for verifying the usefulness of our method of identification of nonlinear chemical processes.

• Steel and Composite Structures
• /
• v.17 no.5
• /
• pp.753-776
• /
• 2014

In this paper, nonlinear vibration and post-buckling analysis of beams made of functionally graded materials (FGMs) resting on nonlinear elastic foundation subjected to thermo-mechanical loading are studied. The thermo-mechanical material properties of the beams are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and to be temperature-dependent. The assumption of a small strain, moderate deformation is used. Based on Euler-Bernoulli beam theory and von-Karman geometric nonlinearity, the integral partial differential equation of motion is derived. Then this PDE problem which has quadratic and cubic nonlinearities is simplified into an ODE problem by using the Galerkin method. Finally, the governing equation is solved analytically using the variational iteration method (VIM). Some new results for the nonlinear natural frequencies and buckling load of the FG beams such as the influences of thermal effect, the effect of vibration amplitude, elastic coefficients of foundation, axial force, end supports and material inhomogenity are presented for future references. Results show that the thermal loading has a significant effect on the vibration and post-buckling response of FG beams.

• 제어로봇시스템학회:학술대회논문집
• /
• 1995.10a
• /
• pp.26-30
• /
• 1995

In this study, the fuzzy approximator and sliding mode control (SMC) scheme are considered. An adaptive sliding mode control is proposed based on the SMC theory. This proposed control scheme is that a adaptive law is utilized to approximate the unknown function f by fuzzy logic system in designing the sliding mode controller for the nonlinear system. In order to reduce the approximation errors, the differences of nonlinear function and fuzzy approximator, an adaptive law is also intoduced and the stability of proposed control scheme are proven with simple adaptive law and roburst adaptive law. This proposed control scheme is applied to a single link robot arm.

• Journal of the Society of Naval Architects of Korea
• /
• v.57 no.4
• /
• pp.198-206
• /
• 2020

In this study, the dynamic structural behavior of pressure vessels due to pressure pulse initiated by implosion of neighbouring airbacked equipments including Unmanned Underwater Vehicles (UUV), sensor system, and so on were dealt with for the structural design and safety assessment of pressure hulls of submarine. The dynamic buckling and collapse responses of pressure vessel in deep sea were investigated considering the effects of initial hydrostatic pressure and fluid-structure interactions. The governing equations for circular cylindrical shells were formulated theoretically assuming a relatively simple displacement fields and the derived nonlinear simultaneous ordinary differential equations were analysed by developed numerical solution algorithm. Finally, the introduced safety assessment procedures for the dynamic buckling behaviors of pressure hulls due to implosion pressure pulse were validated by comparing the theoretical analysis results with those of experiments for examples of simple cylinders.

• Advances in concrete construction
• /
• v.10 no.4
• /
• pp.357-367
• /
• 2020

The impulse of this paper is to examine the influence of unsteady flow comprising of Eyring-Powell nanofluid over a stretched surface. This work aims to explore efficient transfer of heat in Eyring-Powell nanofluid with bio-convection. Nanofluids possess significant features that have aroused various investigators because of their utilization in industrial and nanotechnology. The influence of including motile microorganism is to stabilize the nanoparticle suspensions develop by the mixed influence of magnetic field and buoyancy force. This research paper reveals the detailed information about the linearly compressed Magnetohydrodynamics boundary layer flux of two dimensional Eyring-Powell nanofluid through disposed surface area due to the existence of microorganism with inclusion the influence of non- linear thermal radiation, energy activation and bio-convection. The liquid is likely to allow conduction and thickness of the liquid is supposed to show variation exponentially. By using appropriate similarity type transforms, the nonlinear PDE's are converted into dimensionless ODE's. The results of ODE's are finally concluded by employing (HAM) Homotopy Analysis approach. The influence of relevant parameters on concentration, temperature, velocity and motile microorganism density are studied by the use of graphs and tables. We acquire skin friction, local Nusselt and motil microorganism number for various parameters.