• Structural Engineering and Mechanics
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• v.67 no.6
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• pp.565-578
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• 2018

This research article reported the nonlinear finite solutions of the nonlinear flexural strength and stress behaviour of nano sandwich graded structural shell panel under the combined thermomechanical loading. The nanotube sandwich structural model is derived mathematically using the higher-order displacement polynomial including the full geometrical nonlinear strain-displacement equations via Green-Lagrange relations. The face sheets of the sandwich panel are assumed to be carbon nanotube-reinforced polymer composite with temperature dependent material properties. Additionally, the numerical model included different types of nanotube distribution patterns for the sandwich face sheets for the sake of variable strength. The required equilibrium equation of the graded carbon nanotube sandwich structural panel is derived by minimizing the total potential energy expression. The energy expression is further solved to obtain the deflection values (linear and nonlinear) via the direct iterative method in conjunction with finite element steps. A computer code is prepared (MATLAB environment) based on the current higher-order nonlinear model for the numerical analysis purpose. The stability of the numerical solution and the validity are verified by comparing the published deflection and stress values. Finally, the nonlinear model is utilized to explore the deflection and the stresses of the nanotube-reinforced (volume fraction and distribution patterns of carbon nanotube) sandwich structure (different core to face thickness ratios) for the variable type of structural parameter (thickness ratio, aspect ratio, geometrical configurations, constraints at the edges and curvature ratio) and unlike temperature loading.

• Journal of IKEEE
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• v.11 no.1 s.20
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• pp.1-14
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• 2007

In this paper, a design of an integral augmented nonlinear optimal variable structure system(INOVSS) is presented for the prescribed output control of uncertain MIMO systems under persistent disturbances. This algorithm basically concerns removing the problems of the reaching phase and combining with the nonlinear optimal control theory. By means of an integral nonlinear sliding surface, the reaching phase is completely removed. The ideal sliding dynamics of the integral nonlinear sliding surface is obtained in the form of the nonlinear state equation and is designed by using the nonlinear optimal control theory, which means the design of the integral nonlinear sliding surface and equivalent control input. The homogeneous $2{\upsilon}(\kappa)$ form is defined in order to easily select the $2{\upsilon}$ or even $(\kappa)-form$ higher order nonlinear terms in the suggested sliding surface. The corresponding nonlinear control input is designed in order to generate the sliding mode on the predetermined transformed new surface by means of diagonalization method. As a result, the whole sliding output from a given initial state to origin is completely guaranteed against persistent disturbances. The prediction/predetermination of output is enable. Moreover, the better performance by the nonlinear sliding surface than that of the linear sliding surface can be obtained. Through an illustrative example, the usefulness of the algorithm is shown.

• Journal of the Korean Society for Nondestructive Testing
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• v.18 no.5
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• pp.365-372
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• 1998

The method of measuring the nonlinear effect of ultrasonic waves is suggested as a new approach for the effective evaluation of material degradation. In sonic wave propagation, the existence of nonlinear effect can be demonstrated by the generation of higher order harmonic waves. So, at first, the mechanism of generating higher order harmonic components due to nonlinear effect was explained by using nonlinear elasticity. Next, we attempted to measure how much of the higher order harmonic component was generated in the degraded material. For this purpose, a measurement system mainly based on a high-powered nonlinear ultrasonic signal analysis system was constructed, and SS41 and SS45 specimen intentionally degraded by tensile load and fatigue load were tested. From the results, we confirmed that the measurement of nonlinear acoustic effect may be useful for the evaluation of material degradation.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.127-144
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• 2005

In this paper, we consider the higher order nonlinear neutral delay difference equation of the form $\Delta^{\gamma}(x_{n}+px_{n-\gamma})+f(n, x_{n-\sigma_1(n)}, x_{n-\sigma_2(n)}, \ldots, x_{n-\sigma{_m}(n)})=0$. We give an integrated classification of nonoscillatory solutions of the above equation according to their asymptotic behaviours. Necessary and sufficient conditions for the existence of nonoscillatory solutions with designated asymptotic properties are also established.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.78-83
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• 2003

In this paper, it is dealt with a controller design problem for nonlinear systems with higher order relative degree. A robust adaptive control for uncertain nonlinear systems with stable zero dynamics will be proposed based on the high-gain adaptive output feedback and backstepping strategies. The proposed method is useful in the case where only the output signal is available.

• Coupled systems mechanics
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• v.8 no.1
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• pp.71-93
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• 2019

Finite element simulations of solid mechanics problems often involve the use of Non-Confirming Meshes (NCM) to increase accuracy in capturing nonlinear behavior, including damage and plasticity, in part of a solid domain without an undue increase in computational costs. In the presence of material nonlinearity and plasticity, higher-order variables are often needed to capture nonlinear behavior and material history on non-conforming interfaces. The most popular formulations for coupling non-conforming meshes are dual methods that involve the interpolation of a traction field on the interface. These methods are subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) stability condition, and are therefore limited in their implementation with the higher-order elements needed to capture nonlinear material behavior. Alternatively, the enriched discontinuous Galerkin approach (EDGA) (Haikal and Hjelmstad 2010) is a primal method that provides higher order kinematic fields on the interface, and in which interface tractions are computed from local finite element estimates, therefore facilitating its implementation with nonlinear material models. The inclusion of higher-order interface variables, however, presents the issue of preserving material history at integration points when a increase in integration order is needed. In this study, the enriched discontinuous Galerkin approach (EDGA) is extended to the case of small-deformation plasticity. An interface-driven Gauss-Kronrod integration rule is proposed to enable adaptive enrichment on the interface while preserving history-dependent material data at existing integration points. The method is implemented using classical J2 plasticity theory as well as the pressure-dependent Drucker-Prager material model. We show that an efficient treatment of interface variables can improve algorithmic performance and provide a consistent approach for coupling non-conforming meshes in inelasticity.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.49-62
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• 2007

In this paper, the oscillation and existence of nonoscillatory solutions of odd order difference equations with nonlinear neutral terms are studied respectively. Some new criteria are established. Furthermore, some examples are given to illustrate the advance of our results.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.601-621
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• 2019

This study presents a comprehensive nonlinear dynamic approach to investigate the linear and nonlinear vibration of sandwich plates fabricated from functionally graded materials (FGMs) resting on an elastic foundation. Higher-order shear deformation theory and Hamilton's principle are employed to obtain governing equations. The Runge-Kutta method is employed together with the commercially available mathematical software MAPLE 14 to solve the set of nonlinear dynamic governing equations. Method validity is evaluated by comparing the results of this study and those of previous research. Good agreement is achieved. The effects of temperature change on frequencies are investigated considering various temperatures and various volume fraction index values, N. As the temperature increased, the plate frequency decreased, whereas with increasing N, the plate frequency increased. The effects of the side-to-thickness ratio, c/h, on natural frequencies were investigated. With increasing c/h, the frequencies increased nonlinearly. The effects of foundation stiffness on nonlinear vibration of the sandwich plate were also studied. Backbone curves presenting the variation of maximum displacement with respect to plate frequency are presented to provide insight into the nonlinear vibration and dynamic behavior of FGM sandwich plates.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.3
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• pp.175-180
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• 2012

A nonlinear navigation filter for biomimetic robot using analytic approximation of mean and covariance of state variable is proposed. The approximations are performed at the time update step in the filter structure. The mean is approximated to the 3rd order of Taylor's series expansion of true mean and the covariance is approximated to the 3rd order either. The famous EKF is a nonlinear filtering method approximating the mean to 1st order and the covariance to the 3rd order. The UKF approximate them to the higher orders by numerical method. The proposed method derived a analytical approximation of them for navigation system and therefore don't need so called sigma point transformation in UKF. The simulation results show that the proposed method can be a good alternative of UKF in the systems which require less computational burden.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.137-140
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• 1999

A lot of researcher have proposed a method of kernel identifying nonlinear system by use of Wiener kernels[6-7] or Volterra kernel[5] and so on. In this research, the authors proposed a method of identifying Volterra kernels for nonlinear system by use of pseudorandom M-sequence in which a crosscorrelation function between input and output of a nonlinear system is taken[4]. we can be applied to an MISO nonlinear system or a system which depends on its input amplitude[2]. But, there exist many systems in which it is difficult to determine a Volterra kernel having the same time coordinate on the crosscorrelation function. In those cases, we have to estimate Volterra kernel by using its neighboring points[4]. In this paper, we propose a new method for not estimating but obtaining Volterra kernel having the same time coordinate using calculation between the neighboring points. Some numerical simulations show that this method is effective for obtaining higher order Volterra kernel of nonlinear control systems.