• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.1
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• pp.174-194
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• 2015

In this paper, an Energy Flow Analysis (EFA) for coplanar coupled Mindlin plates was performed to estimate their dynamic responses at high frequencies. Mindlin plate theory can consider the effects of shear distortion and rotatory inertia, which are very important at high frequencies. For EFA for coplanar coupled Mindlin plates, the wave transmission and reflection relationship for progressing out-of-plane waves (out-of-plane shear wave, bending dominant flexural wave, and shear dominant flexural wave) in coplanar coupled Mindlin plates was newly derived. To verify the validity of the EFA results, numerical analyses were performed for various cases where coplanar coupled Mindlin plates are excited by a harmonic point force, and the energy flow solutions for coplanar coupled Mindlin plates were compared with the classical solutions in the various conditions.

• Advances in aircraft and spacecraft science
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• v.2 no.3
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• pp.233-248
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• 2015

Frame structures have been traditionally represented as an assembling of components, these last described within the beam theory framework. In the case of frames involving complex components in which classical beam theory could fail, 3D descriptions seem the only valid route for performing accurate enough analyses. In this work we propose a framework for frame structure analyses that proceeds by assembling the condensed parametric rigidity matrices associated with the elementary beams composing the beams involved in the frame structure. This approach allows a macroscopic analysis in which only the condensed degrees of freedom at the elementary beams interfaces are considered, while fine 3D parametric descriptions are retained for local analyses.

• Structural Engineering and Mechanics
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• v.36 no.6
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• pp.669-678
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• 2010

In general means, the stress concentration problem of elastic plate with a rectangular hole can be investigated by numerical methods, and only approximative results are derived. This paper deduces an analytical study of the stress concentration due to a rectangular hole in an elastic plate under bending loads. Base on classical elasticity theory and FEM applying the U-transformation technique, the uncoupled governing equations with 3-DOF are established, and the analytical displacement solutions of the finite element equations are derived in series form or double integral form. Therefore, the stress concentration factor can then be discussed easily and conveniently. For the plate subjected to unidirectional bending loads, the non-conforming plate bending element with four nodes and 12-DOF is taken as examples to demonstrate the application of the proposed method. The inner force distribution is obtained. The solutions are adequate for the condition when the hole is far away from the edges and the thin plate subjected to any transverse loadings.

• International Journal of Computer Science & Network Security
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• v.21 no.12
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• pp.223-227
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• 2021

A treatment based on the algebraic operations on fuzzy numbers is used to replace the fuzzy problem into an equivalent crisp one. The finite difference technique is used to replace the continuous boundary value problem (BVP) of arbitrary order 1<α≤2, with fuzzy boundary parameters into an equivalent crisp (algebraic or differential) system. Three numerical examples with different behaviors are considered to illustrate the treatment of the singular perturbed case with different fractional orders of the BVP (α=1.8, α=1.9) as well as the classical second order (α=2). The calculated fuzzy solutions are compared with the crisp solutions of the singular perturbed BVP using triangular membership function (r-cut representation in parametric form) for different values of the singular perturbed parameter (ε=0.8, ε=0.9, ε=1.0). Results are illustrated graphically for the different values of the included parameters.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.419-431
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• 2021

In this paper we discuss the classical problem of finding conditions on the entire coefficients A(z) and B(z) guaranteeing that all nontrivial solutions of f" + A(z)f' + B(z)f = 0 are of infinite order. We assume A(z) is an entire function of completely regular growth and B(z) satisfies three different conditions, then we obtain three results respectively. The three conditions are (1) B(z) has a dynamical property with a multiply connected Fatou component, (2) B(z) satisfies T(r, B) ~ log M(r, B) outside a set of finite logarithmic measure, (3) B(z) is extremal for Denjoy's conjecture.

• Journal of the Korean Chemical Society
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• v.22 no.4
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• pp.202-220
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• 1978

Uniform semiclassical (WKB) solutions are obtained for nonseparable systems without using a close coupling formalism and are given explicitly in terms of well known analytic functions for various physically interesting and realistic cases. They do not become singular at turning points or surfaces and when taken in their asymptotic forms, they reduce to the usual WKB solutions that could be obtained if the Stokes phenomenon was properly taken care of for solutions. In obtaining such uniform solutions, the Schroedinger equations for nonseparable systems are suitably "renormalized" to solvable "normal" forms through certain transformations. Ehrenfest's adiabatic principle plays an important guiding role for obtaining such "renormalized" uniform solutions for nonseparable systems. The eigenvalues of the Hamiltonian can be calculated from the extended Bohr-Sommerfeld quantization rules when appropriate classical trajectories are obtained. An application is made to many-electron systems and for one of the simplest examples to show the utility of the method the approximate wavefunction is calculated of the ground state helium atom.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.9 no.4
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• pp.1043-1049
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• 2008

In this paper, we investigate the static response. natural frequencies and buckling loads of functionally graded material (FGM) plates, using a Navier method. The eigenvalues of the FGM plates and shells are calculated by varying the volume fraction of the ceramic and metallic constituents using a sigmoid function, but their Poisson's ratios of the FGM plates and shells are assumed to be constant. The expressions of the membrane. bending and shear stiffness of FGM plates art more complicated combination of material properties than a homogeneous element. In order to validate the present solutions, the reference solutions of rectangular plates based on the classical theory are used. The various examples of composite and FGM structures are presented. The present results are in good agreement with the reference solutions.

• The Journal of the Acoustical Society of Korea
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• v.22 no.4E
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• pp.155-160
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• 2003

Both ultrasonic velocity at 3 MHz and absorption coefficient for the frequency range of 0.2-2 MHz were measured in an aqueous solution of polyacrylamide for the concentration range of 0.5% to 2.5% by weight. Pulse echo overlap method was taken for measuring the ultrasonic velocity over the temperature range of 10-90℃ and the high-Q ultrasonic resonator method was used for the absorption coefficient at 30℃. The velocity exhibited a maximum value at approximately 70℃, 71℃, 72℃, 73℃ and 74℃ in 2.5%, 2.0%, 1.5%, 1.0%, and 0.5% solutions, respectively. The velocity increased with the concentration at a given temperature. The ultrasonic absorption (a/f²) at a given temperature increased linearly with the concentration for the concentration below 1.5%, but suddenly increased for the concentration above 1.5% concentration. The value of a/f² at 1MHz was entirely due to the classical Stoke's viscous effect. The ultrasonic relaxation in polyacrylamide aqueous solutions, which may be the result of structural fluctuations of polymer molecules such as the segmental motion of the polymer chains, was observed, and at 2.5%, the value of a/f² was found to suddenly increase as frequency decreased.

• Advances in aircraft and spacecraft science
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• v.11 no.1
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Journal of the Korean Society for Nondestructive Testing
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• v.21 no.2
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• pp.177-181
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• 2001

Nondestructive testing(NDT) is one of the fundamental tools to improve the quality of commercial and industrial products. NDT is potentially a major application of interferometry. Interferometry(ESPI, Shearography, ect) has successfully been applied in various industrial environments such as high performance aircraft, home appliance, automotive, and laminates on engine structures, etc. Today's industry demands high performance components with toughest mechanical features and ultimate safety standards. Especially in automotive and aircraft industry the development process focuses on tailor-made design and solutions to meet customer specifications. To reconcile economy, ligh-weight construction has become a key issue. Many companies are looking for new advanced NDT techniques to archive cost efficiency over the limitations of classical methods. ESPI and shearography allow a rapid, full field and 3D-measurement without contact. In this paper recent applications of ESPI and shearography for NDT are described. Advanced features of classical techniques are specified and new applications in material and component testing are presented.