• Structural Engineering and Mechanics
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• v.68 no.2
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• pp.203-213
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• 2018

This paper presents a study of geometric nonlinear forced vibration of carbon nano-tubes (CNTs) reinforcement composite plates on nonlinear elastic foundations. The plate is bonded with piezoelectric layers. The von Karman geometric nonlinearity assumptions with classical plate theory are employed to obtain the governing equations. The Galerkin and homotopy perturbation method (HPM) are utilized to investigate the effect of carbon nano-tubes volume fractions, large amplitude vibrations, elastic foundation parameters, piezoelectric applied voltage on frequency ratio and primary resonance. The results indicate that the carbon nano-tube volume fraction, applied voltage and elastic foundation parameters have significant effect on the hardening response of carbon nanotubes reinforced composite (CNTRC) plates.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.157-160
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• 1998

The analysis of a coaxial cable with periodic slots as a leaky-wave antenna is considered. The mode matching method and method of moments with Galerkin testing procedure is then used to obtain the determinantal equation for the unknown leaky-wave propagating constant. Both technigues allow the fields to be obtained in any region, and the radiation characteristics of the structure. By resorting to a suitable numerical techniques, it is possible to calculate the leaky-wave propagating constants and the radiation patterns. Numerical results demonstrate the validity of the technique.

• Korean Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.107-121
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• 1996

An optimization procedure is proposed to determine the optimal stacking sequence on the buckling of laminated composite plates with midplane symmetry under various loading conditions. Classical lamination theory is used for the determination of the critical buckling load of simply supported angle-ply laminates. Analysis is performed by the Galerkin method and Rayleigh-Ritz method. The approximate solution of buckling is replaced by the algorithms that produce generalized eigenvalue problem. Direct search technique is employed to solve the optimization problem effectively. A series of computations is carried out for plates having different aspect ratios, different load ratios and different number of lay-ups.

• Structural Engineering and Mechanics
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• v.10 no.3
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• pp.277-288
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• 2000

The present paper, deals with the dynamic analysis of a thin-walled tower with varying cross-section and additional masses. It, especially, deals with the effect of the rotary inertia of those masses, which have been neglected up to now. Using Galerkin's method, we can find the spectrum of the eigenfrequencies and, also, the shape functions. Finally, we can solve the equations of the problem of the forced vibrations, by using Carson-Laplace's transformation. Applying this method on a tall mast with 2 concentrated masses, we can examine the effect of the rotary inertia and the diaphragmatic operation of the above masses, on the 3 first eigenfrequencies.

• Structural Engineering and Mechanics
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• v.4 no.4
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• pp.383-396
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• 1996

In this paper, the behavior of plates partially restrained against rotation under stress gradient is investigated. As a first stage, an energy formulation is presented to model this boundary condition and a general expression is derived for the prediction of the elastic buckling of the plate under this general loading condition. The accuracy of the derived expression is compared numerically using the Galerkin method with other available data for the two limiting conditions of rotationally free and clamped boundaries. Results show that the prediction is within a 5% difference. The influence of rotational restraint and stress gradient upon the buckling load and the associated buckling mode is investigated. Numerical results show sensitivity of the buckling mode to the degree of rotational restraint and the variation of the buckling load with the stress gradient.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.97.2-97
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• 2002

A method for the non-destructive detection of damage using parameterized partial differential equations and Galerkin approximation techniques is presented. This method provides the theoretical and experimental verification of a nondestructive time domain approach to examine structural damage in smart structure. The time histories of the vibration response of structure were used to identify the presence of damage. Damage in a structure causes changes in the physical coefficients of mass density, elastic modulus and damping coefficient. This paper examines the beam-like structures with PVDF sensor and PZT actuator to perform identification of those physical parameters and to detect the...

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.17-30
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• 1997

In this work we approximate the solution of initialboun-dary value problem using a Galerkin-finite element method for the spatial discretization and Implicit Runge-Kutta method for the spatial discretization and implicit Runge-Kutta methods for the time stepping. To deal with the nonlinear term f(x, t, u), we introduce the well-known extrapolation sheme which was used widely to prove the convergence in $L_2$-norm. We present computational results showing that the optimal order of convergence arising under $L_2$-norm will be preserved in $L_{\infty}$-norm.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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• pp.2042-2049
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• 2000

This paper is concerned with the comparison of forging characteristics between forward and backward processes, through the three-dimensional finite element simulation, for the aluminum powder forging of engine pistons. Starting from the theoretical formulation of velocity and temperature fields in the sintered preform during the process, we examine the comparative distributions of relative density, effective stress and temperature as well as the variations of total forging load and total volume reduction. Through the comparative results, we find out that the forward method provides better forging characteristics than the backward method.

• Interaction and multiscale mechanics
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• v.2 no.3
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• pp.263-276
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• 2009

This paper is intended to investigate interaction response of a train running over a suspension bridge undergoing support settlements. The suspension bridge is modeled as a single-span suspended beam with hinged ends and the train as successive moving oscillators with identical properties. To conduct this dynamic problem with non-homogeneous boundary conditions, this study first divides the total response of the suspended beam into two parts: the static and dynamic responses. Then, the coupled equations of motion for the suspended beam carrying multiple moving oscillators are transformed into a set of nonlinearly coupled generalized equations by Galerkin's method, and solved using the Newmark method with an incremental-iterative procedure including the three phases: predictor, corrector, and equilibrium-checking. Numerical investigations demonstrate that the present iterative technique is available in dealing with the dynamic interaction problem of vehicle/bridge coupling system and that the differential movements of bridge supports will significantly affect the dynamic response of the running vehicles but insignificant influence on the bridge response.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.320-325
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• 2004

The paper deals with the dynamic response of a cantilevered beam under a travelling mass with constant acceleration. Governing equations of motion taking into account all inertia effects of the travelling mass are derived by Galerkin's mode summation method, and Runge-Kutta integration method is applied to solve the differential equations. The effects of the speed, acceleration and the magnitude of the travelling mass on the response of the beam are fully investigated. A variety of numerical results allows us to draw important conclusions for structural design purposes.