• Structural Engineering and Mechanics
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• 제40권4호
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• pp.583-594
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• 2011

In the present study, free vibration of an axially functionally graded (AFG) pile embedded in Winkler-Pasternak elastic foundation is analyzed within the framework of the Euler-Bernoulli beam theory. The material properties of the pile vary continuously in the axial direction according to the power-law form. The frequency equation is obtained by using Lagrange's equations. The unknown functions denoting the transverse deflections of the AFG pile is expressed in modal form. In this study, the effects of material variations, the parameters of the elastic foundation on the fundamental frequencies are examined. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• International Journal of Aeronautical and Space Sciences
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• 제18권2호
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• pp.300-314
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• 2017

This paper examines finite rotation angle (FRA) applications for spacecraft attitude control. The coordinate transformation matrix and the attitude kinematics represented by FRAs are introduced. The interpolation techniques for the angular orientations are thoroughly investigated using the FRAs and the results are compared to those using traditional methods. The paper proposes trajectory description techniques by using extremely smooth polynomial functions of time, which can describe point-to-point attitude maneuvers in a realizable and accurate manner with the help of unique FRA features. In addition, new controller design techniques using the FRAs are developed by combining the proposed interpolation techniques with a model predictive control framework. The proposed techniques are validated through their attitude control applications for an aggressive point-to-point maneuver. Conclusively, the FRAs provide much more flexibility than quaternions and Euler angles when describing kinematics, generating trajectories, and designing attitude controllers for spacecraft.

• 대한조선학회지
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• 제24권3호
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• pp.35-42
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• 1987

For the analysis of natural vibrations of a rectangular stiffened plate with inner cutouts, an application of the Rayleigh-Ritz method is investigated. In construction of the trial function for the Rayleigh quotient, only the outer boundary conditions are satisfied with combination of Euler beam functions. As to the modeling of stiffened plates for the energy calculations, a lumping stiffener-effects method and the orthotropic plate analogy are considered for the purpose of comparison. Some numerical results obtained by the Rayleigh-Ritz method are compared with results by experiments and the finite element method. The following are major conclusions; (1) With the lumping stiffener-effects modeling the Rayleigh-Ritz method gives good results of both natural frequencies and mode shapes. The orthotropic plate analogy in cases of regularly stiffened plates is of restrictive use i.e. acceptable for a small cutout. (2) The natural frequency of a stiffened plate with inner cutouts between stiffeners is higher than that of without cutouts and increase as the hole area ratio increases as long as there are no discontinuous stiffeners due to the cutout.

• 호남수학학술지
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• 제35권4호
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• pp.701-706
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• 2013

Summation theorems for hypergeometric series $_2F_1$ and generalized hypergeometric series $_pF_q$ play important roles in themselves and their diverse applications. Some summation theorems for $_2F_1$ and $_pF_q$ have been established in several or many ways. Here we give a proof of Watson's classical summation theorem for the series $_3F_2$(1) by following the same lines used by Rakha [7] except for the last step in which we applied an integral formula introduced by Choi et al. [3].

• Structural Engineering and Mechanics
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• 제2권3호
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• pp.285-294
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• 1994

Based on a fast and accurate method for the stationary random seismic response analysis for discretized structures(Lin 1992, Lin et al. 1992), a Ritz method for dealing with such responses of continuous systems in developed. This method is studied quantitatively, using cantilever shear beams for simplicity and clarity. The process can be naturally extended to deal with various boundary conditions as well as non-uniform Bernoulli-Euler beams, or even Timoshenko beams. Algorithms for both proportionally and non-proportionally damped responses are described. For all of such damping cases, it is not necessary to solve for the natural vibrations of the beams. The solution procedure is very simple, and equally efficient for a white or a non-white ground excitation spectrum. Two examples are given where various power spectral density functions, variances, covariances and second spectral moments of displacement, internal force response, and their derivatives are calculated and analyses. Some Ritz solutions are compared with "exact" CQC solutions.

• International Journal of Aeronautical and Space Sciences
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• 제8권1호
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• pp.66-78
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• 2007

A multi-point aerodynamic shape optimization technique has been developed for helicopter rotor blades in hover based on a continuous adjoint method on unstructured meshes. The Euler flow solver and the continuous adjoint sensitivity analysis were formulated on the rotating frame of reference. The 'objective function and the sensitivity were obtained as a weighted sum of the values at each design point. The blade section contour was modified by using the Hicks-Henne shape functions. The mesh movement due to the blade geometry change was achieved by using a spring analogy. In order to handle the repeated evaluation of the design cycle efficiently, the flow and adjoint solvers were parallelized based on a domain decomposition strategy. A solution-adaptive mesh refinement technique was adopted for the accurate capturing of the wake. Applications were made to the aerodynamic shape optimization of the Caradonna-Tung rotor blades and the UH-60 rotor blades in hover.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 춘계학술대회 논문집
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• pp.9-13
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• 1997

This parer is a study on the inverse dynamics of a one-link flexible robot arm which is controlled by translational base motion. The system is composed of a flexible arm, a base for driving arm, a DC servomotor, and a computer. The arm base is moved so that the arm tip follows a desired function. The governing equations are based on the Bernoullie-Euler beam theory and solved by applying the Laplace transform method and then the numerical inversion method. Moter voltage is obtained by simulation for tip trajectory functions i. e. Bang-Bang, Cosine and Gauss Function. And, the tip motion is measured while simulation results are applying. Then the results are investigated to select most proper input and to compare their chateristics. Experimental results show the Cosine function is most proper with respect to low maximum voltage and steady state error.

• Structural Engineering and Mechanics
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• 제61권3호
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• pp.335-345
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• 2017

Free vibration analysis for continuous bridge under any number of vehicles is conducted in this paper. Calculation strategy for natural frequency and mode shape is proposed based on Euler-Bernoulli beam theory and numerical assembly method. Firstly, a half-car planar model is adopted; equations of motion and displacement functions for bridge and vehicle are established, respectively. Secondly, the undermined coefficient matrices for wheels, vehicles, intermediate support, left-end support and right-end support are derived. Then, the numerical assembly technique for conventional finite element method is adopted to construct the overall matrix of coefficients for whole system. Finally, natural frequencies and corresponding mode shapes are determined based on iterative method and overall matrix solution. Numerical simulation is presented to verify the effectiveness of the proposed method. The results reveal that the solutions of present method are exact ones. Natural frequencies and associate modal shapes of continuous bridge under different conditions of vehicles are investigated. The influences of vehicle parameters on natural frequencies are also demonstrated.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.949-954
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• 2006

The purpose of this paper is to investigate the stability of tapered columns with clamped one end and carrying a tip mass of rotatory inertia with translational elastic support at the other end. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck columns is derived using the Bernoulli-Euler beam theory. Both the divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter, mass ratio and spring stiffness.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2000년도 추계학술대회 논문집
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• pp.506-513
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• 2000

The tunnel booming noise generated by a train moving into a tunnel has been one of the most serious constraints in the development of the high-speed trains. It is well known that the nose shape of the train has the significant influence on the intensity of the booming noise. In this study, the nose shape has been optimized by using the response surface methodology and the axi-symmetric compressible Euler equations. The parametric studies are also performed with respect to the slenderness ratio, the blockage ratio and the train speed to investigate their sensitivities to the optimization results. The results show that it is possible to define more general design space by introducing the Hicks-Henne shape functions, resulting in the more effective nose shape than that of Maeda. The mechanism and the aspects of the train-tunnel interaction were also investigated from the results of the parametric study.