• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.5
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• pp.966-972
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• 2007

This paper presents position control of nonlinear three-dimensional crane systems using neural network approach. Such crane system generally includes very complicated characteristic dynamics and mechanical framework such that its mathematical model is expressed by strong nonlinearity. This leads difficulty in control design for the systems. We linearize the nonlinear system model to construct PID control applying well-known linear control theory and then neural network is utilized to compensate system perturbation due to linearization. Thus, control input of the crane system is composed of nominal PID and neural output signals respectively. Our method illustrates simple design procedure, but system perturbation and modelling error are overcome through a neural compensator. As well. adaptive neural control is constructed from online learning. Computer simulation demonstrates our control approach is superior to the classic control systems.

• Structural Engineering and Mechanics
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• v.54 no.5
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• pp.987-998
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• 2015

In this paper, free vibrations of a clamped-clamped double-walled carbon nanotube (DWNT) under axial force is studied. By utilizing Euler-Bernoulli beam theory, each layer of DWNT is modeled as a beam. In this analysis, nonlinear form of interlayer van der Waals (vdW) forces and nonlinearities aroused from mid-plane stretching are also considered in the equations of motion. Further, direct application of multiple scales perturbation method is utilized to solve the obtained equations and to analyze free vibrations of the DWNT. Therefore, analytical expressions are found for vibrations of each layer. Linear and nonlinear natural frequencies of the system and vibration amplitude ratios of inner to outer layers are also obtained. Finally, the results are compared with the results obtained by Galerkin method.

• Bulletin of the Korean Chemical Society
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• v.12 no.4
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• pp.383-387
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• 1991

A new perturbation theory called as star expansion method is used to obtain the nonlinear retarded solution of the Schlogl models with some kinds of external input. The approximate nonlinear solutions are compared with the exact solution, linear solutions, and those obtained by the Feynman method.

• Computational Structural Engineering
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• v.10 no.3
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• pp.125-131
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• 1997

Most dynamic systems have are known to various random properties in excitation and system parameters. In this paper, a procedure for response analysis is proposed for the linear dynamic system with random properties in both excitation and system parameters. The system parameters and responses with random properties are modeled by perturbation technique, and then response analysis is formulated by probabilistic and vibration theories. And probabilistic FEM is also used for the calculation of mean response which is difficult by the proposed response model. As an applicative example, the transient response is considered for systems of single degree of freedom with random mass and spring constant subjected to stationary white-noise excitation and the results are compared to those of numerical simulation.

• Smart Structures and Systems
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• v.25 no.6
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• pp.693-705
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• 2020

In the current investigation, large amplitude free vibration behavior of shallow curved pipes (tubes) made of functionally graded materials is investigated. Properties of the tube are distributed across the radius of the tube and are obtained by means of a power law function. It is also assumed that all thermo-mechanical properties are temperature dependent. The governing equations of the tube are obtained using a higher order shear deformation tube theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large displacements and small strains. Uniform temperature elevation of the tube is also included into the formulation. For the case of tubes which are simply supported in flexure and axially immovable, the governing equations are solved using the two-step perturbation technique. Closed form expressions are provided to obtain the small and large amplitude fundamental natural frequencies of the FGM shallow curved tubes in thermal environment. Numerical results are given to explore the effects of thermal environment, radius ratio, and length to thickness ratio of the tube on the fundamental linear and non-linear frequencies.

• Steel and Composite Structures
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• v.44 no.3
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• pp.371-388
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• 2022

The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1995.04a
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• pp.110-115
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• 1995

In this paper, the problem of non-linear torsional oscillation of a system incorporating a Hooke's joint is studied. Classical perturbation methods including higher order averaging and bifurcation theory are adopted for analysis. The equation of motion derived by Porter[1] is presented and the type of the system is identified. It has been found that two important cases deserve extensive study. Method of higher order averaging which is a main research tool in this study is introduced briefly. The averaged equations are studied analyticallyand numerically and the method of averaging has been found to be effective to study complex non-linear system.

• Journal of Advanced Research in Ocean Engineering
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• v.2 no.1
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• pp.12-21
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• 2016

In this paper, the $2^{nd}$ order hydrodynamic force effect of heaving submerged circular cylinder is considered, with the linear potential theory. Boundary value problem (BVP) is expanded up to the $2^{nd}$ order by using of the perturbation method and the $2^{nd}$ order velocity potential is calculated by means of integral equation technique using the classical Green's function expressed in cylindrical coordinates. The method of solving BVP is based on eigenfunction expansions. With different cylinder heights and heaving frequencies, graphical results are presented. As a result of the study, the cause of oscillatory force pattern is analyzed with the occurrence of negative added mass when a top of the cylinder gets closer to the free surface.

• Journal of Ocean Engineering and Technology
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• v.13 no.2 s.32
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• pp.129-137
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• 1999

The time of the onset of double-diffusive convection in time-dependent, nonlinear concentration fields is investigated theoretically. The initially quiescent horizontal fluid layer with a uniform temperature gradient experiences a sudden concentration change from below, but its stable thermal stratification affects concentration effects in such way to invoke convective motion. The related stability analysis, including Soret effect, is conducted on the basis of the propagation theory. Under the linear stability theory the concentration penetration depth is used as a length scaling factor, and the similarity transform for the linearized perturbation equations. The newlly obtained stability equations are solved numerically. The resulting critical time to mark the onset of regular cells are obtained as a function of the thermal Rayleigh number, the solute Rayleigh number, and the Soret effect coefficient. For a certain value of the Soret effect coefficient, the stable thermal gradient promote double-diffusive convective motion.

• Structural Engineering and Mechanics
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• v.70 no.2
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• pp.179-197
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• 2019

In this article, the effect of different geometrical, materials and load parameters on the transient response of axisymmetric viscoelastic functionally graded annular plates with different boundary conditions are studied. The behavior of the plate is assumed the elastic in bulk and viscoelastic in shear with the standard linear solid model. Also, the graded properties vary through the thickness according to a power law function. Three types of mostly applied transient loading, i.e., step, impulse, and harmonic with different load distribution respect to radius coordinate are examined. The motion equations and the corresponding boundary conditions are extracted by applying the first order shear deformation theory which are three coupled partial differential equations with variable coefficients. The resulting motion equations are solved analytically using the perturbation technique and the generalized Fourier series. The sensitivity of the response to the graded indexes, different transverse loads, aspect ratios, boundary conditions and the material properties are investigated too. The results are compared with the finite element analysis.