• Structural Engineering and Mechanics
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• v.60 no.2
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• pp.271-299
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• 2016

In this article, based on the higher-order shear deformation plate theory, buckling analysis of a rectangular plate made of functionally graded piezoelectric materials and its effective parameters are investigated. Assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for the buckling analysis of an FGP rectangular plate are established. In addition to the Maxwell equation, all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. Considering double sine solution (Navier solution) for displacement field and electric potential, an analytical solution is obtained for full simply supported boundary conditions. The accurate buckling load of FGP plate is presented for both open and closed circuit conditions. It is found that the critical buckling load for open circuit is more than that of closed circuit in all loading conditions. Furthermore, it is observed that the influence of dielectric constants on the critical buckling load is more than those of others.

• Structural Engineering and Mechanics
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• v.30 no.4
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• pp.427-444
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• 2008

A mathematical model for the nonlinear dynamics of a rotating beam with flexible root attached to a rotating hub with elastic foundation is developed. The model is developed based on the large planar and flexural deformation theory and the potential energy method to account for axial shortening due to bending deformation. In addition the exact nonlinear curvature is used in the system potential energy. The Lagrangian dynamics and the assumed mode method is used to derive the nonlinear coupled equations of motion hub rotation, beam tip deflection and hub horizontal and vertical displacements. The derived nonlinear model is simulated numerically and the results are presented and discussed for the effect of root flexibility, hub stiffness, torque type, torque period and excitation frequency and amplitude on the dynamic behavior of the rotating beam-hub and on its stability.

• Bulletin of the Society of Naval Architects of Korea
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• v.20 no.4
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• pp.33-40
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• 1983

The drift force acting on a freely-floating sphere in water of finite depth is studied within the framework of a linear potential theory. A velocity potential describing fluid motion is determined by distribution pulsating sources and dipoles on the immersed surface of the sphere. Upon knowing values of the potential, hydrodynamic forces are evaluated by integrating pressures over the immersed surface of the sphere. The motion response of the sphere in water of finite depth is obtained by solving the equation of motion. From these results, the drift force on the sphere is evaluated by the momentum theorem, in which a far-field velocity potential is utilized in forms of Kochin function. The drift force coefficient Cdr of a fixed sphere increases monotononically with non-dimensional wave frequency ${\sigma}a$. On the other hand, in freely-floating case, the Cdr has a peak value at ${\sigma}a$ of heave resonance. The magnitude of the drift force coefficient Cdr in the case of finite depth is different form that for deep water, but the general tendency seems to be similar in both cases. It is to note that Cdr is greater than 1.0 when non-dimensional water depth d/a is 1.5 in the case of freely-floating sphere.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.34 no.3
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• pp.58-71
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• 2022

Analytical solutions for two-dimensional velocities of regular waves generated by bottom wave makers in a flume were derived in this study. Triangular and rectangular bottom wave makers were adopted. The velocity potential was derived based on the linear wave theory with the bottom moving boundary condition, kinematic and dynamic free surface boundary conditions. Then, analytical solutions of two-dimensional particle velocities were derived from the velocity potential. The velocity potential and two-dimensional particle velocities which were derived as complex integral equations were numerically calculated. The solutions showed physically valid results as velocities of regular waves generated by bottom wave makers in a flume.

• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.391-402
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• 2017

In this paper, a new nonlocal trigonometric shear deformation theory is proposed for thermal buckling response of nanosize functionally graded (FG) nano-plates resting on two-parameter elastic foundation under various types of thermal environments. This theory uses for the first time, undetermined integral variables and it contains only four unknowns, that is even less than the first shear deformation theory (FSDT). It is considered that the FG nano-plate is exposed to uniform, linear and sinusoidal temperature rises. Mori-Tanaka model is utilized to define the gradually variation of material properties along the plate thickness. Nonlocal elasticity theory of Eringen is employed to capture the size influences. Through the stationary potential energy the governing equations are derived for a refined nonlocal four-variable shear deformation plate theory and then solved analytically. A variety of examples is proposed to demonstrate the importance of elastic foundation parameters, various temperature fields, nonlocality, material composition, aspect and side-to-thickness ratios on critical stability temperatures of FG nano-plate.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.8 no.2
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• pp.155-166
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• 1988

An "equivalent homogeneous, orthotropic" model that includes edge effects and an accompanying finite element analysis is presented for elastomeric bearings. The model is developed for two-dimensional configurations with horizontal layers, and for linear, elastic, small deformation conditions. The equivalent homogeneous theory, in addition to capturing the overall response characteristics of the layered elastomeric bearing system, approximately models the important edge effects, which occur at and near boundaries that cut the layers, and the stress concentrations at layer interfaces. The primary dependent variables for the theory have been selected such that the highest derivatives appearing in the strain energy function are first-order, thus requiring only $C_0$ continuity of the finite element approximations. As a result, the finite element analysis is simple and computationally efficient. Numerical examples are presented to verify the theory and to illustrate potential applications of the analysis.

• Ocean Systems Engineering
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• v.3 no.3
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• pp.219-236
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• 2013

The accurate prediction of motion in waves of a marine vehicle is essential to assess the maximum sea state vs. operational requirements. This is particularly true for small crafts, such as Autonomous Surface Vessels (ASV). Two different numerical methods to predict motions of a SWATH-ASV are considered: an inviscid strip theory initially developed at MIT for catamarans and then adapted for SWATHs and new a hybrid strip theory, based on the numerical solution of the radiation forces by an unsteady viscous, non-linear free surface flow solver. Motion predictions obtained by the viscous flow method are critically discussed against those obtained by potential flow strip theory. Effects of viscosity are analyzed by comparison of sectional added mass and damping calculated at different frequencies and for different sections, RAOs and motions response in irregular waves at zero speed. Some relevant conclusions can be drawn from this study: influence of viscosity is definitely non negligible for SWATH vessels like the one presented: amplitude of the pitch and heave motions predicted at the resonance frequency differ of 20% respectively and 50%; in this respect, the hybrid method with fully non-linear, viscous free surface calculation of the radiation forces turns out to be a very valuable tool to improve the accuracy of traditional strip theories, without the burden of long computational times requested by fully viscous time domain three dimensional simulations.

• Journal of Ocean Engineering and Technology
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• v.31 no.5
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• pp.371-377
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• 2017

This paper introduces a simulation-based determination method for hydrodynamic derivatives and 6DOF (degrees-offreedom) motion analysis for an underwater vehicle. Hydrodynamic derivatives were derived from second-order modulus expansion and composed of the added mass, and linear and nonlinear damping coefficients. The added mass coefficients were analytically obtained using the potential theory. All of the linear and nonlinear damping coefficients were determined using CFD simulation, which were performed for various cases based on the actual operating condition. Then, the linear and nonlinear damping coefficients were determined by fitting the CFD results, which referred to 6DOF forces and moments acting on an underwater vehicle, with the least square method. To demonstrate the applicability of the current study, 6DOF simulations for three different scenarios (L-, U-, and S-turn) were carried out, and the results were validated on the basis of physical plausibility.

• Advances in Computational Design
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• v.5 no.4
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.12 no.3
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• pp.116-129
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• 2000

The interaction of incident monochromatic waves with a tensioned, flexible, circular membrane submerged horizontally below free surface is investigated in the frame of three-dimensional linear hydro-elastic theory. The velocity potential is split into two parts i.e. the diffraction potential representing the scattering of incident waves by a rigid circular disk and the radiation potential describing motion induced waves by elastic responses of flexible membrane. The fluid domain is divided into three regions, and the diffraction and radiation potentials in each region are expressed by the Fourier Bessel series. The displacement of circular membrane is expanded with a set of natural functions, which satisfy the membrane equation of motion and boundary conditions. The unknown coefficients in each region are determined by applying the continuity of pressure and normal velocity at the matching boundaries. The results show that various types of wave focusing are possible by controlling the size, submergence depth, and tension of membrane.