• Structural Engineering and Mechanics
• /
• v.41 no.5
• /
• pp.617-632
• /
• 2012

An isogeometric approach is presented for static analysis of thin plate problems of various geometries. Non-Uniform Rational B-Splines (NURBS) basis function is applied for approximation of the thin plate deflection, as for description of the geometry. The governing equation based on Kirchhoff plate theory, is discretized using the standard Galerkin method. The essential boundary conditions are enforced by the Lagrange multiplier method. Several typical examples of thin plate and thin plate on elastic foundation are solved and compared with the theoretical solutions and other numerical methods. The numerical results show the robustness and efficiency of the proposed approach.

• Structural Engineering and Mechanics
• /
• v.32 no.4
• /
• pp.501-516
• /
• 2009

This paper aims to study the large deflections of variable-arc-length elastica subjected to the terminal forces (e.g., axial force and torque). Based on Kirchhoff's rod theory and with help of Euler parameters, the set of nonlinear governing differential equations which free from the effect of singularity are established together with boundary conditions. The system of nonlinear differential equations is solved by using the shooting method with high accuracy integrator, seventh-eighth order Runge-Kutta with adaptive step-size scheme. The error norm of end conditions is minimized within the prescribed tolerance ($10^{-5}$). The behavior of VAL elastica is studied by two processes. One is obtained by applying slackening first. After that keeping the slackening as a constant and then the twist angle is varied in subsequent order. The other process is performed by reversing the sequence of loading in the first process. The results are interpreted by observing the load-deflection diagram and the stability properties are predicted via fold rule. From the results, there are many interesting aspects such as snap-through phenomenon, secondary bifurcation point, loop formation, equilibrium configurations and effect of variable-arc-length to behavior of elastica.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.31 no.3 s.258
• /
• pp.365-372
• /
• 2007

Revisited in this paper are Green's functions for unit concentrated forces in an infinite orthotropic Kirchhoff plate. Instead of obtaining Green's functions expressed in explicit forms in terms of Barnett-Lothe tensors and their associated tensors in cylindrical or dual coordinates systems, presented here are Green's functions expressed in two quasi-harmonic functions in a Cartesian coordinates system. These functions could be applied to thin plate problems regardless of whether the plate is homogeneous or inhomogeneous in the thickness direction. With a composite variable defined as $z=x_1+ipx_2$ which is adopted under the necessity of expressing the Green's functions in terms of two quasi-harmonic functions in a Cartesian coordinates system Stroh-like formalism for orthotropic Kirchhoffplates is evolved. Using some identities of logarithmic and arctangent functions given in this paper, the Green's functions are presented in terms of two quasi-harmonic functions. These forms of Green's functions are favorable to obtain the Newtonian potentials associated with defect problems. Thus, the defects in the orthotropic plate may be easily analyzed by way of the Green's function method.

• The KSFM Journal of Fluid Machinery
• /
• v.3 no.2 s.7
• /
• pp.15-23
• /
• 2000

The present work describes the prediction method for the unsteady flow field and the acoustic pressure field of a ducted axial fan. The prediction method is comprised of time-marching free-wake method, acoustic analogy, and the Kirchhoff-Helmholtz BEM. The predicted sound signal of a rotor is similar to the experiment one. We assume that the rotor rotates with a constant angular velocity and the flow field around the rotor is incompressible and inviscid. Then, a time-marching free-wake method is used to model the fan and to calculate the flow field. The force of each element on the blade is calculated by the unsteady Bernoulli equation. Lowson's method is used to predict the acoustic source. The newly developed Helmholtz-Kirchhoff BEM lot thin body is used to calculate tile sound field of the ducted fan. The ducted fan with 6 blades is analysed and the sound field around the duct is calculated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2000.11a
• /
• pp.100-105
• /
• 2000

The present work describes the prediction method for the unsteady flow field and the acoustic pressure field of a ducted axial fan. The prediction method is comprised of time-marching free-wake method, acoustic analogy. and the Helmholtz-Kirchhoff BEM. The predicted sound signal of a rotor is similar to the experiment one. We assume that the rotor rotates with a constant angular velocity and the flow field around the rotor is incompressible and inviscid. Then, a time-marching free-wake method is used to model the fan and to calculate the flow field. The force of each element on the blade is calculated by the unsteady Bernoulli equation. Lawson's method is used to predict the acoustic source. The newly developed Helmholtz-Kirchhoff BEM for thin body is used to calculate the sound field of the ducted fan. The ducted fan with 6 blades is analysed and the sound field around the duct is calculated.

• Ocean and Polar Research
• /
• v.37 no.4
• /
• pp.333-340
• /
• 2015

The contrast (fish body to medium ratio) of density and sound speed were measured to estimate acoustic scattering from small juvenile cod (Gadus macrocephalus) with the Kirchhoff-Ray Mode backscatter model. The density contrast was measured by the density-bottle method and the sound speed contrast was estimated by the time of flight method. The results revealed that the measured density contrasts of juvenile cod varied between 1.003 and 1.029 (mean = 1.014, S.D. = 0.01). On the other hand, sound speed contrasts varied between 1.039 and 1.041 (mean = 1.041, S.D. = 0.001). The relationship between averaged target strength (TS) and total length (TL) established by the model were <$TS_{38kHz}$> = 20log(TL) - 68.8 and <$TS_{38kHz}$> = 20log(TL) - 69.4, respectively.

• International Journal of Ocean System Engineering
• /
• v.3 no.1
• /
• pp.22-32
• /
• 2013

A heuristic physical theory of diffraction (PTD) for an acoustic impedance wedge is proposed. This method is based on Ufimtsev's three-dimensional PTD, which is derived for an acoustic soft or hard wedge. We modify the original PTD according to the process of physical optics (or the Kirchhoff approximation) to obtain a 3D heuristic diffraction model for an impedance wedge. In principle, our result is equivalent to Luebbers' model presented in electromagnetism. Moreover, our approach provides a useful insight into the theoretical basis of the existing heuristic diffraction methods. The derived heuristic PTD is applied to an arbitrary impedance polygon, and a simple PTD formula is derived as a supplement to the physical optics formula.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.05a
• /
• pp.1010-1015
• /
• 2002

Over the last few decades, noise has played a major role in the development of aircraft engines. The dominant noise is generated by the wake interactions of fan and downstream stator. Engine inlet and exhaust ducts are being fitted with liner materials that aid in damping fan related noise. In this paper, the radiation of duct internal noise from duct open ends with liners is studies via numerical methods. The linearized Euler's equations in generalized curvilinear coordinates are solved by the DRP scheme. The far field sound pressure levels are computed by the Kirchhoff integration method. Through comparison of sound directivity from bell-mouth duct with and without liners, it is shown that radiation from engine inlet is affected by liner effects or a soft wall boundary condition.

• Proceedings of the Acoustical Society of Korea Conference
• /
• spring
• /
• pp.171-174
• /
• 2004

표적강도는 수중 산란체의 능동 탐지 확률을 좌우하는 중요한 변수중 하나이며 산란체의 기하학적 형상에 의해 결정이 되기 때문에 수치해석을 통한 해석 및 예측이 가능하다. 수치해석 기법은 현재 여러 가지가 알려져 있으며, 그중 Kirchhoff approximation이 다른 해석 기법에 비해 거울면 반사특성의 산란해석에 적합하며, 프로그램으로의 적용이 용이하다는 장점으로 인해 많이 사용되고 있다. 본 연구에서는 이러한 장점에 의거하여 Kirchhoff approximation을 이용하여 표적강도 수치해석 프로그램을 개발 및 검증하였다. 프로그램의 성능 검증은 원통형 산란체에 대한 이론해 검증과 원통형 실험 산란체를 통한 실험 검증을 수행하였다.

• International Journal of Aeronautical and Space Sciences
• /
• v.17 no.4
• /
• pp.476-490
• /
• 2016

This paper defines mode shape function of a composite solar panel assumed as Kirchhoff-Love plate for considering a torsional mode of composite solar panel. It then goes on to define dynamic model of a high-agility satellite considering the flexibility of composite solar panel as well as stiffness of a solar panel's hinge using Lagrange's theorem, Ritz method and the mode shape function. Furthermore, this paper verifies the validity of dynamic model by comparing numerical results from the finite element analysis. In addition, this paper performs a dynamic response analysis of a rigid satellite which includes only natural modes for solar panel's hinges and a flexible satellite which includes not only natural modes of solar panel's hinges, but also structural modes of composite solar panels. According to the results, we confirm that the torsional mode of solar panel should be considered for the structural design of high-agility satellite. Finally, we performed optimization of high-agility satellite for minimizing mass with solar panel's area limit using the defined dynamic model. Consequently, we observed that the defined dynamic model for a high-agility satellite and result of the optimal design are very useful not only because of their optimal structural design but also because of the dynamic analysis of the satellite.