• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.501-515
• /
• 2009

A second order nonlinear ordinary differential equation is obtained by solving the initial-boundary value problem of a class of elas-todynamics equations, which models the radially symmetric motion of a incompressible hyper-elastic solid sphere under a suddenly applied surface tensile load. Some new conclusions are presented. All existence conditions of nonzero solutions of the ordinary differential equation, which describes cavity formation and motion in the interior of the sphere, are presented. It is proved that the differential equation has singular periodic solutions only when the surface tensile load exceeds a critical value, in this case, a cavity would form in the interior of the sphere and the motion of the cavity with time would present a class of singular periodic oscillations, otherwise, the sphere remains a solid one. To better understand the results obtained in this paper, the modified Varga material is considered simultaneously as an example, and numerical simulations are given.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.7 no.2
• /
• pp.346-363
• /
• 2015

We have performed integrated dynamics modeling for a supercavitating vehicle. A 6-DOF equation of motion was constructed by defining the forces and moments acting on the supercavitating body surface that contacted water. The wetted area was obtained by calculating the cavity size and axis. Cavity dynamics were determined to obtain the cavity profile for calculating the wetted area. Subsequently, the forces and moments acting on each wetted part-the cavitator, fins, and vehicle body-were obtained by physical modeling. The planing force-the interaction force between the vehicle transom and cavity wall-was calculated using the apparent mass of the immersed vehicle transom. We integrated each model and constructed an equation of motion for the supercavitating system. We performed numerical simulations using the integrated dynamics model to analyze the characteristics of the supercavitating system and validate the modeling completeness. Our research enables the design of high-quality controllers and optimal supercavitating systems.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 1997.04a
• /
• pp.128-135
• /
• 1997

The indirect boundary integral equation is formulated to analyze the behavior of a cavity in a multilayered half-plane subjected to earthquake waves. This formulation uses the fundamental solutions that are numerically calculated by the generalized transmission and reflection coefficient method. The free surface of the cavity without external excitation influences the behavior of the half-plane. Consequently this analysis adds the consideration of scattering-field into the analysis and the total motion field of the cavity is decomposed into the free-field and scattering-field motions. The free-field motion is obtained from the modification of the transmission and reflection coefficient method. The scattering-field motion is calculated is calculated by the indirect boundary value problem which has the ficticious boundaries and sources. In this study, P wave, SV wave, SH wave, and Rayleigh wave are analyzed respectively.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.12 no.1
• /
• pp.479-490
• /
• 2020

The hydrodynamic characteristic of transonic motion projectiles with different head diameters are investigated by numerical simulation. Compressibility effect in liquid-phase water are modeled using the Tait state equation. The result shows that with increasing of velocity the compression waves transfer to shock waves, which cause the significant increasing of pressure and decreasing the dimensions of supercavities. While the increasing of head diameter, the thickness, the vapor volume fraction and the drag coefficient of supercavities are all enhanced, which is conducive to the stability of transonic-speed projectiles. The cavity dynamics of the different head projectiles are compared, and the results shows when Mach number is in high region, the truncated cone head projectile is enveloped by a cavity which results in less drag and better stability.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.14 no.3
• /
• pp.997-1002
• /
• 2013

The article is aiming to investigate the thermal-fluidic characteristics of magnetic fluid in a cavity using GSMAC (generalized-simplified marker and cell method). The transport equations of the magnetic fluid are including the continuity equation, momentum equation and energy equation for natural convection and Maxwell equation and magnetization equation of magnetite nano-sized particles motion. In addition, the heat transfer characteristics such as temperatures and Nusselt numbers and flow characteristics such as streamlines and isotherms of the magnetic fluid were analyzed with the intensity and direction of the magnetic fields. As a result, the thermal-fluidic characteristics of the magnetic fluid in a cavity were could be controlled by the intensity and direction of the magnetic fields.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2000.06a
• /
• pp.785-790
• /
• 2000

The resonant frequency of a gas-filled cylindrical Helmholtz resonator in a liquid is obtained analytically. The equation of motion of the resonator is derived by using the condition of equilibrium of forces acting on the mass in the neck of the resonator. The reaction force on the upper side of the cylinder due to the acceleration of external fluid and sound radiation is obtained by using the analytical results for the baffled circular-piston problem. From the frequency response function of the resonator, a formula to predict the resonant frequency of the resonator is derived. It is shown that the resonant frequency of the Helmholtz resonator significantly decreases due to the cushioning effect of gas inside the cavity. Therefore, when a pressure transducer is to be installed in a pin-hole type mounting method, much care should be paid to remove the gas from the cavity.

• Journal of Astronomy and Space Sciences
• /
• v.15 no.1
• /
• pp.209-220
• /
• 1998

The stability problem of steady motion of a rigid body with multi-elastic appendages and multi-liquid-filled cavities, in the presence of no external forces or torque, is considered in this paper. The flexible appendages are modeled as the clamped -free-free-free rectangular plates, or/and as the discrete mass- spring sub-system. The motion of liquid in every single ellipsoidal cavity is modeled as the uniform vortex motion with a finite number of degrees of freedom. Assuming that stationary holonomic constraints imposed on the body allow its rotation about a spatially fixed axis, the equation of motion for such a systematic configuration can be very complex. It consists of a set of ordinary differential equations for the motion of the rigid body, the uniform rotation of the contained liquids, the motion of discrete elastic parts, and a set of partial differential equations for the elastic appendages supplemented by appropriate initial and boundary conditions. In addition, for such a hybrid system, under suitable assumptions, their equations of motion have four types of first integrals, i.e., energy and area, Helmholtz' constancy of liquid - vortexes, and the constant of the Poisson equation of motion. Chetaev's effective method for constructing Liapunov functions in the form of a set of first integrals of the equations of the perturbed motion is employed to investigate the sufficient stability conditions of steady motions of the complete system in the sense of Liapunov, i.e., with respect to the variables determining the motion of the solid body and to some quantities which define integrally the motion of flexible appendages. These sufficient conditions take into account the vortexes of the contained liquids, the vibration of the flexible components, and coupling among the liquid-elasticity solid.

• Journal of computational fluids engineering
• /
• v.9 no.1
• /
• pp.18-24
• /
• 2004

The unified simulation for the multiphase flow by predictor-corrector scheme based on CIP method is introduced. In this algorithm, the interface between different phases is identified by a density function and tracked by solving an advection equation. Solid body motion is modeled by the translation and angular motion. The mathematical formulation and numerical results are also described. To verify the efficiency, accuracy and capability of proposed algorithm, two dimensional incompressible cavity flow, the motion of a floating ball into water and a single rising bubble by buoyancy force are numerically simulated by the present scheme. As results, it is confirmed that the present scheme gives an efficient, stable and reasonable solution in the multiphase flow problem.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
• /
• v.14 no.2
• /
• pp.118-124
• /
• 1985

The motion of a fluid in the closed annular cavity formed by two concentric vertical cylinders with externally finned tube has been analysed by a numerical solutions of the equation of momentum and energy. For the calculation procedure, the fluid is assumed to have constant thermo-dynamic and transporties except for the density, which is temperature-dependent in the buoyancy term of the vertical momentum equation (Boussinesq approximation). The govern ins equations for velocity and temperature are solved by a finite difference technique which incoorporates a scheme for treating the coupled variables. Results are presented for a range of the Rayleigh number and for various values of the fin height and the number of fins.

• Structural Engineering and Mechanics
• /
• v.89 no.4
• /
• pp.383-397
• /
• 2024

To improve the vibration control performance and applicability of traditional particle tuned mass damper (PTMD) and realize the significant characteristic of lightweight design, this study proposes a novel particle tuned mass inerter system (PTMIS) by introducing inerter system (IS) to the PTMD. In the study, the motion equation of single degree of freedom (SDOF) structure attached with PTMIS is established first, then the variation law of the system's vibration reduction performance (VRP) is discussed through parameter analysis, and it is compared with the PTMD to analyze its VRP advantages. Finally, its vibration reduction (VR) mechanism from the perspective of core control force and energy analysis is explored, and its cavity relative displacement from the application perspective is analyzed. The results show that the PTMIS can remarkably improve the vibration control effectiveness of the PTMD. The reason is that the inerter can store energy and transfer the energy to the cavity and particles, which further stimulates the interaction between the two parts, thereby improving the nonlinear energy consumption effectiveness. Also, the IS can amplify the damping element's energy dissipation efficiency. In addition, the PTMIS can effectively reduce the working stroke of the PTMD, and through the analysis of the lightweight characteristics of the PTMIS, it is found that its lightweight advantage can reach nearly 100%.