• Journal of applied mathematics & informatics
• /
• v.42 no.1
• /
• pp.49-64
• /
• 2024

When setting up a structure with an embedded shallow arch, there is a phenomenon where the end of the arch moves. To study the so-called moving domain problem, one try to transform a considered noncylindrical domain into the cylindrical domain using the transform operator, as well as utilizing the method of penalty and other approaches. However, challenges arise when calculating time derivatives of solutions in a domain depending on time, or when extending the initial conditions from the non-cylindrical domain to the cylindrical domain. In this paper, we employ the transform operator to prove the existence and uniqueness of weak solutions of the shallow arch equation on the moving domain as clarifying the time derivatives of solutions in the moving domain.

• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.565-572
• /
• 2019

In this paper, we consider a Korteweg-de Vries equation in noncylindrical domain. This work is devoted to prove existence and uniqueness of global solutions employing Faedo-Galerkin's approximation and transformation of the noncylindrical domain with moving boundary into cylindrical one. Moreover, we estimate the exponential decay of solutions in the asymptotically cylindrical domain.

• Journal of Korean Association for Spatial Structures
• /
• v.22 no.2
• /
• pp.57-64
• /
• 2022

In this paper, the physical model and governing equations of a shallow arch with a moving boundary were studied. A model with a moving boundary can be easily found in a long span retractable roof, and it corresponds to a problem of a non-cylindrical domain in which the boundary moves with time. In particular, a motion equation of a shallow arch having a moving boundary is expressed in the form of an integral-differential equation. This is expressed by the time-varying integration interval of the integral coefficient term in the arch equation with an un-movable boundary. Also, the change in internal force due to the moving boundary is also considered. Therefore, in this study, the governing equation was derived by transforming the equation of the non-cylindrical domain into the cylindrical domain to solve this problem. A governing equation for vertical vibration was derived from the transformed equation, where a sinusoidal function was used as the orthonormal basis. Terms that consider the effect of the moving boundary over time in the original equation were added in the equation of the transformed cylindrical problem. In addition, a solution was obtained using a numerical analysis technique in a symmetric mode arch system, and the result effectively reflected the effect of the moving boundary.

• Structural Engineering and Mechanics
• /
• v.19 no.1
• /
• pp.43-53
• /
• 2005

The linearized buckling problem is considered for an isotropic clamped-clamped cylindrical shell with an oblique end. A theoretical solution based on the Budiansky shell theory is developed, and numerical results are determined using the differential quadrature method. In formulating the solutions, the surface of the shell is developed onto a plane, and the resulting irregular domain is then mapped, using blending functions, onto a square parent domain. The analysis is carried out in the parent domain. Convergence, validation, and parametric studies are conducted for a uniform external pressure loading. Results determined are compared with finite element results. The paper ends with an appropriate set of conclusions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11b
• /
• pp.459-463
• /
• 2002

ER mount can be used instead of rubber mount in cylindrical shell to improve the vibration and noise performance. The noise radiated by cylindrical shell will be reduced by reducing the force transmitted to the cylindrical shell through ER mount. In this paper LQ control theory is used to reduce the transmitted force to the cylindrical shell. The finite element method of cylindrical shell is formulated by NASTRAN and its vibrating shape is calculated in frequency domain. The noise radiated from the cylindrical shell is calculated by the use of SYSNOISE, the boundary element CAE tool. The vibration of the cylindrical shell and radiated acoustic pressure is compared in case of both controlled and uncontrolled ER mount.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11a
• /
• pp.348.2-348
• /
• 2002

ER mount is often used instead of rubber mount in cylindrical shell to improve the vibration and noise performanec. The noise radiated by cylindrical shell will be reduced by reducing the force transmitted to the cylindrical shell through ER mount. In this paper, LQ control theory is used to reduce the transmitted force to the cylindrical shell. The finite element method of cylindrical shell is formulated by NASTRAN and its vibrating shape is calculated in frequency domain. (omitted)

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.45 no.8
• /
• pp.121-127
• /
• 2008

This paper presents an electric field distribution in a reverberation chamber using cylindrical diffuser. The characteristics of electric field distributions are compared with QRD(Quadratic Residue Diffuser) and cylindrical diffuser for $1{\sim}3$ GHz frequency band. The FDTD(Finite-Difference Time-Domain) method is used to analyze the field characteristics, and the field uniformity. At 2 GHz, the standard deviation and the tolerance of test volume in the reverberation chamber are improved by 0.11 dB, 0.43 dB for the case of cylindrical diffuser. The field strength is increased by 43.2 dBmV/m vs QRD's of 36.6 dBmV/m. Comparing with QRD's, the characteristic of polarization is also improved. These results show that reverberation chamber using cylindrical diffuser can be used alternative facility for measurement of electromagnetic interference and immunity.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.13 no.10
• /
• pp.751-759
• /
• 2003

The theoretical method is developed to investigate the vibration characteristics of the sloshing and bulging mode for the circular cylindrical storage tank with an annular plate on free surface. The cylindrical tank is filled with an inviscid and incompressible liquid. The liquid domain is limited by a rigid cylindrical surface and a rigid flat bottom. As the effect of free surface waves Is taken into account in the analysis, the bulging and sloshing modes are studied. The solution for the velocity potential of liquid movement is assumed as a suitable harmonic function that satisfies Laplace equation and the relevant boundary conditions. The Rayleigh-Ritz method is used to derive the frequency equation of the cylindrical tank. The effect of Inner-to-outer radius ratio and thickness of annular plate and liquid volume on vibration characteristics of storage tank is studied. The finite element analysis is performed to demonstrate the validity of present theoretical method.

• Steel and Composite Structures
• /
• v.32 no.5
• /
• pp.687-699
• /
• 2019

In this paper, free and force vibration behaviors of graphene-reinforced composite functionally graded (GRC-FG) cylindrical shells in thermal environments are investigated based on Reddy's third-order shear deformation theory (HSDT). The GRC-FG cylindrical shells are composed of piece-wise pattern graphene-reinforced layers which have different volume fraction. Based on the extended Halpin-Tsai micromechanical model, the effective material properties of the resulting nanocomposites are evaluated. Using the Hamilton's principle and the assumed mode method, the motion equation of the GRC-FG cylindrical shells is formulated. Using the time- and frequency-domain methods, free and force vibration properties of the GRC-FG cylindrical shell are analyzed. Numerical cases are provided to study the effects of distribution of graphene, shell radius-to-thickness ratio and temperature changes on the free and force vibration responses of GRC-FG cylindrical shells.

• Journal of Ocean Engineering and Technology
• /
• v.18 no.5
• /
• pp.7-14
• /
• 2004

The interaction of incident manochromatic waves with an array of N surface-piercing porous dual cylindrical structures is investigated in the frame of three-dimensional linear potential theory. The dual cylindrical structure is camposed of concentric two cylinders. The exterior cylinder is porous and the interior cylinder is impermeable. The fluid domain is divided into N+1 regions i.e. a single exterior region and N interior regions. The diffraction potentials in each region representing the scattering of incident waves by an array of porous cylindrical structures are expressed by the Fourier Bessel series. The unknown coefficients in each region are determined by applying the porous boundary condition and continuity of mass flux at the matching boundary. It is found that an array of porous cylindrical structures reduces both the wave forces and the wave run-up, and shows the excellent performance of wave blocking. The results show that various types of breakwater exchanging seawater are prospective by controlling the porosity and the configuration of cylindrical structures.