• Geomechanics and Engineering
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• v.2 no.1
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• pp.45-56
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• 2010

The current study presents a mathematical model and numerical method for free vibration of tapered piles embedded in two-parameter elastic foundations. The method of Discrete Singular Convolution (DSC) is used for numerical simulation. Bernoulli-Euler beam theory is considered. Various numerical applications demonstrate the validity and applicability of the proposed method for free vibration analysis. The results prove that the proposed method is quite easy to implement, accurate and highly efficient for free vibration analysis of tapered beam-columns embedded in Winkler- Pasternak elastic foundations.

• Journal of Auto-vehicle Safety Association
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• v.6 no.1
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• pp.10-15
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• 2014

Motion Analysis of pedestrian headform was first applied in this paper for the purpose of determining the relationship between stiffness of hood and HIC. Since the analysis of headform movement involves rotation, it has been problematic if analysis of the headform movement is made in local coordinate system only. Correlation of test and simulation is expected to be enhanced through the development of New type of Head Movement Analysis Method.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.31 no.6_2
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• pp.577-583
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• 2013

Recently, massive archives of ground information imagery from new sensors have become available. To establish a functional relationship between the image and the ground space, sensor models are required. The rational functional model (RFM), which is used as an alternative to the rigorous sensor model, is an attractive option owing to its generality and simplicity. To determine the rational polynomial coefficients (RPC) in RFM, however, we encounter the problem of obtaining a stable solution. The design matrix for solutions is usually ill-conditioned in the experiments. To solve this unstable solution problem, regularization techniques are generally used. In this paper, we describe the effective determination of the optimal regularization parameter in the regularization technique during RPC derivation. A brief mathematical background of RFM is presented, followed by numerical approaches for effective determination of the optimal regularization parameter using the Euler Method. Experiments are performed assuming that a tilted aerial image is taken with a known rigorous sensor. To show the effectiveness, calculation time and RMSE between L-curve method and proposed method is compared.

• Advances in nano research
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• v.6 no.3
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• pp.201-217
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• 2018

In the present research, wave propagation characteristics of a rotating FG nanobeam undergoing rotation is studied based on nonlocal strain gradient theory. Material properties of nanobeam are assumed to change gradually across the thickness of nanobeam according to Mori-Tanaka distribution model. The governing partial differential equations are derived for the rotating FG nanobeam by applying the Hamilton's principle in the framework of Euler-Bernoulli beam model. An analytical solution is applied to obtain wave frequencies, phase velocities and escape frequencies. It is observed that wave dispersion characteristics of rotating FG nanobeams are extremely influenced by angular velocity, wave number, nonlocal parameter, length scale parameter, temperature change and material graduation.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.2
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• pp.237-247
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• 1999

Flight parameters of a light aircraft in normal category named ChangGong-91 we identified from flight tests. Modified Maximum Likelihood Estimation (MMLE) is used to produce aerodynamic coefficients, stability and control derivatives. A Flight Training Device (FTD) has been developed based on the identified flight parameters. Flat earth, rigid body, and standard atmosphere are assumed in the FTD model. Euler angles are adapted for rotational state variables to reduce computational load. Variations in flight Mach number and Reynolds number are assumed to be negligible. Body, stability and inertial axes allow 6 second-order linear differential equations for translational and rotational motions. The equations of motion are integrated with respect to time, resulting in good agreements with flight tests.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.802-807
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• 2003

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and tip masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the translational spring parameter, the rotational spring parameter, the mass ratio and the dimensionless mass moment of inertia.

• Steel and Composite Structures
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• v.33 no.1
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• pp.133-142
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• 2019

In the present study, microstructure-dependent static stability analysis of inhomogeneous tapered micro-columns is performed. It is considered that the micro column is made of functionally graded materials and has a variable cross-section. The material and geometrical properties of micro column vary continuously throughout the axial direction. Euler-Bernoulli beam and modified couple stress theories are used to model the nonhomogeneous micro column with variable cross section. Rayleigh-Ritz solution method is implemented to obtain the critical buckling loads for various parameters. A detailed parametric study is performed to examine the influences of taper ratio, material gradation, length scale parameter, and boundary conditions. The validity of the present results is demonstrated by comparing them with some related results available in the literature. It can be emphasized that the size-dependency on the critical buckling loads is more prominent for bigger length scale parameter-to-thickness ratio and changes in the material gradation and taper ratio affect significantly the values of critical buckling loads.

• Steel and Composite Structures
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• v.47 no.6
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• pp.795-811
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• 2023

When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.

• Structural Engineering and Mechanics
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• v.88 no.4
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• pp.355-368
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• 2023

Employing the non-local strain gradient theory (NSGT), this paper investigates the nonlinear resonance characteristics of functionally graded material (FGM) nanoshells with initial geometric imperfection for the first time. The effective material properties of the porous FGM nanoshells with even distribution of porosities are estimated by a modified power-law model. With the guidance of Love's thin shell theory and considering initial geometric imperfection, the strain equations of the shells are obtained. In order to characterize the small-scale effect of the nanoshells, the nonlocal parameter and strain gradient parameter are introduced. Subsequently, the Euler-Lagrange principle was used to derive the motion equations. Considering three boundary conditions, the Galerkin principle combined with the modified Lindstedt Poincare (MLP) method are employed to discretize and solve the motion equations. Finally, the effects of initial geometric imperfection, functional gradient index, strain gradient parameters, non-local parameters and porosity volume fraction on the nonlinear resonance of the porous FGM nanoshells are examined.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.9
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• pp.3841-3857
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• 2020

RSA is one of the best well-known public key cryptosystems. This methodology is widely used at present because there is not any algorithm which can break this system that has all strong parameters within polynomial time. However, it may be easily broken when at least one parameter is weak. In fact, many weak parameters are already found and are solved by some algorithms. Some examples of weak parameters consist of a small private key, a large private key, a small prime factor and a small result of the difference between two prime factors. In this paper, the new weakness of RSA is proposed. Assuming Euler's totient value, Φ (n), can be rewritten as Φ (n) = ad + b, where d is the private key and a, b ∈ ℤ, if a divides both of Φ (n) and b and the new exponent for the decryption equation is a small integer, this condition is assigned as the new weakness for breaking RSA. Firstly, the specific algorithm which is created for this weakness directly is proposed. Secondly, two equations are presented to find a, b and d. In fact, one of two equations must be implemented to find a and b at first. After that, the other equation is chosen to find d. The experimental results show that if this weakness has happened and the new exponent is small, original plaintext, m, will be recovered very fast. Furthermore, number of steps to recover d are very small when a is large. However, if a is too large, d may not be recovered because m which must be always written as m = h^a is higher than modulus.