• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.175-180
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• 1993

A new method for the vibration analysis of arbitrarily-shaped beams is proposed on the assumption of imaginary seperation of the beams into prismatic beams and the remaining portions. The stiffness and mass of the beams are devided into two portions according to the seperation. Applying the mode shapes of prismatic beams and Lagrange's equations give new characteristics equation. This equation has a low dimension of matrix with the coupling terms showing the effect of remaining portions on the vibration of arbitrarily-shaped beams

• International Journal of Naval Architecture and Ocean Engineering
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• v.4 no.3
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• pp.267-280
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• 2012

An approximate method based on an assumed mode method has been presented for the free vibration analysis of a rectangular plate with arbitrary edge constraints. In the presented method, natural frequencies and their mode shapes of the plate are calculated by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. Characteristic orthogonal polynomials having the property of Timoshenko beam functions which satisfies edge constraints corresponding to those of the objective plate are used. In order to examine the accuracy of the proposed method, numerical examples of the rectangular plates with various thicknesses and edge constraints have been presented. The results have shown good agreement with those of other methods such as an analytic solution, an approximate solution, and a finite element analysis.

• Advances in aircraft and spacecraft science
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• v.5 no.1
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• pp.21-49
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• 2018

In this paper, geometric nonlinear bending characteristics of single wall carbon nanotube reinforced composite (SWCNTRC) doubly curved shell panels subjected to uniform transversely loadings are investigated. The nonlinear mathematical model is developed for doubly curved SWCNTRC shell panel on the basis of higher-order shear deformation theory and Green- Lagrange nonlinearity. All nonlinear higher order terms are included in the mathematical model. The effective material properties of SWCNTRC are estimated by using Eshelby-Mori-Tanaka micromechanical approach. The governing equation of the shell panel is obtained using the total potential energy principle and a Newton-Raphson iterative method is employed to compute the nonlinear displacement and stresses. The present results are compared with published literature. The effect of SWCNT volume fraction, width-to-thickness ratio, radius-to-width ratio (R/a), boundary condition, linear and nonlinear deflection, stresses and different types of shell geometry on nonlinear bending response is investigated.

• Transactions of Materials Processing
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• v.11 no.4
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• pp.355-362
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• 2002

In this study, an axi-symmetric finite element program for elastic analysis of the die set shrink fitted in cold extrusion was developed. The geometrical constraint according to shrink fit was enforced by employing the Lagrange multiplier method. The numerical results for strain and stress distributions in the die set including single and multi stress rings assembled by shrink fit were compared well with the Lame's equation for thick-walled solution available in the literature. To extend the applicability of the analysis program developed, various cases without or with stress ring and with pre-stress applied on stress ring were numerically investigated as well. This numerical approach enables the optimization study to determine optimal dimensions of die set to improve tool life for practical use in industry.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1212-1217
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• 2007

ATM(automated teller machine) is a machine which can deposit and withdraw money directly. For effective transfer of bills in the machine, crown belts are used. In this paper, the transverse vibration of crown belt is investigated. The equation of motion of the belt is derived using Lagrange's equation. Galerkin's method is applied to convert the partial differential equation to the ordinary differential equations. Experimental investigations are performed on the belt system with the variation of pulley type, eccentricity, and tension. The results of numerical analysis show in good agreement with the experimental results.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.603-613
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• 2023

In this paper, the concept of geodesic centered tractography is explored for diffusion tensor imaging (DTI). In DTI, where geodesics has been tracked and the inverse of the fourth-order diffusion tensor is inured to determine the diversity. Specifically, we investigated geodesic tractography technique for High Angular Resolution Diffusion Imaging (HARDI). Riemannian geometry can be extended to a direction-dependent metric using Finsler geometry. Euler Lagrange geodesic calculations have been derived by Finsler geometry, which is expressed as HARDI in sixth order tensor.

• The Journal of the Korea Contents Association
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• v.7 no.4
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• pp.234-240
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• 2007

The purpose of this paper was to architecture optimal model of the scooped swing in high bar. The scooped swing was modeled to the double pendulum and was simulated with the Lagrange's equation of motion. Lagrange's method based on a energy approaching method was implemented as a equation of motion. The subject was a national man-gymnast(age 18yrs, height 153 cut mass 48 kg) and the high bar of SPIETH company was used to measure the scooped swing. Qualisys system(six MCU-240 cameras, QTM software)was used to capture data for imaging analysis. The solution of a model and data processing were solved in Mathematica5.0. The results were as follows: First model value of maximum bar displacement was longer than experimental value, that is, 0.02 m. Second, both angular pattern of segment1(HAT) had a increasing curve but curve patterns had a different concave and convex me. Third the experimental value of maximum angular angle of segment2(total leg) had larger than model value, that is, $4^{\circ}$. Conclusively, model parameters were quasi-optimized to obtain a quasi-match between simulated and actual performances. It hopes to simulate a human model by means of integrating musculoskeletal and neuromuscular system in the future study.

• Smart Structures and Systems
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• v.16 no.5
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• pp.853-872
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• 2015

Numerical analysis of large amplitude free vibration behaviour of laminated composite spherical shell panel embedded with the piezoelectric layer is presented in this article. For the investigation purpose, a general nonlinear mathematical model has been developed using higher order shear deformation mid-plane kinematics and Green-Lagrange nonlinearity. In addition, all the nonlinear higher order terms are included in the present mathematical model to achieve any general case. The nonlinear governing equation of freely vibrated shell panel is obtained using Hamilton's principle and discretised using isoparametric finite element steps. The desired nonlinear solutions are computed numerically through a direct iterative method. The validity of present nonlinear model has been checked by comparing the responses to those available published literature. In order to examine the efficacy and applicability of the present developed model, few numerical examples are solved for different geometrical parameters (fibre orientation, thickness ratio, aspect ratio, curvature ratio, support conditions and amplitude ratio) with and/or without piezo embedded layers and discussed in details.

• Journal of the Korean Vacuum Society
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• v.12 no.S1
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• pp.33-35
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• 2003

The electrooptic properties of the reflected light in a reflective mode, $45^{\circ}C$twisted nematic liquid crystal (TNLC) cell were investigated in the voltage regions near and away from the Freedericksz transition threshold. The measured reflectivity away from the threshold voltage ($V_th$) could not be described by the model which assurnes a constant tilt angle as well as a linearized distribution of twist angle across the cell, although the data are well fitted near $V_th$. We found that in the voltage region away from $V_th$, the model considering the distributions of the tilt angle and the twist angle should be applied for the calculation of the reflectivity. The director-axis distributions were obtained from the numerical integration of the Euler-Lagrange equation.

• Steel and Composite Structures
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• v.18 no.3
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• pp.693-709
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• 2015

In this article, nonlinear free vibration behaviour of functionally graded spherical panel is analysed. A nonlinear mathematical model is developed based on higher order shear deformation theory for shallow shell by taking Green-Lagrange type of nonlinear kinematics. The material properties of functionally graded material are assumed to be varying continuously in transverse direction and evaluated using Voigt micromechanical model in conjunction with power-law distribution. The governing equation of the shell panel is obtained using Hamilton's principle and discretised with the help of nonlinear finite element method. The desired responses are evaluated through a direct iterative method. The present model has been validated by comparing the frequency ratio (nonlinear frequency to linear frequency) with those available published literatures. Finally, the effect of geometrical parameters (curvature ratio, thickness ratio, aspect ratio and support condition), power law indices and amplitude of vibration on the frequency ratios of spherical panel have been discussed through numerical experimentations.