• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.1
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• pp.175-185
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• 2014

This study presents the prediction of propagated wave profiles using the wave information at a fixed point. The fixed points can be fixed in either space or time. Wave information based on the linear wave theory can be expressed by Fredholm integral equation of the first kinds. The discretized matrix equation is usually an ill-conditioned system. Tikhonov regularization was applied to the ill-conditioned system to overcome instability of the system. The regularization parameter is calculated by using the L-curve method. The numerical results are compared with the experimental results. The analysis of the numerical computation shows that the Tikhonov regularization method is useful.

• Advances in Computational Design
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• v.7 no.3
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• pp.211-227
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• 2022

In this research, the size-dependent impact of an embedded piezoelectric nanoplate subjected to in-plane loading on free vibration characteristic is studied. The foundation is two-parameter viscoelastic. The nonlocal elasticity is employed in order to capture the influence of size of the plate. By utilizing Hamilton's principle as well as the first- order shear deformation theory, the governing equation and boundary conditions are achieved. Then, using Navier method the equations associated with the free vibration of a plate constructed piezoelectric material under in-plane loads are solved analytically. The presented formulation and solution procedure are validated using other papers. Also, the impacts of nonlocal parameter, mode number, constant of spring, electric potential, and geometry of the nanoplate on the vibrational frequency are examined. As this paper is the first research in which the vibration associated with piezoelectric nanoplate on the basis of FSDT and nonlocal elasticity is investigated analytically, this results can be used in future investigation in this area.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.11-31
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• 2023

The paper presents a critical analysis of selected topics related to the modeling of interacting species in which prey has nonlinear reproduction, which is in competition with predator. The mathematical model's stochastic stability is investigated. The method of designing appropriate Lyapunov functions is used to identify permanence conditions among the parameters of the model and conditions for the structure to no longer be extinct. The system's two-dimensional diffusive stability is regarded and studied. The system experiences the process of saddle-node bifurcation by varying the death rate of predator parameter. Further effects of parameters that undergo inherent oscillations are numerically investigated, revealing that as the intensity of predation parameter b is increased, the device encounters non-periodic and damped oscillations.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.312-317
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• 2005

Fluid-elastic instability and turbulence excitation for an under developing steam generator are investigated numerically. The stability ratio and the amplitude of turbulence excitation are obtained by using the PIAT (Program for Integrity Assessment of Steam Generator Tube) code from the information on the thermal-hydraulic data of the steam generator. The aspect ratio, the ratio between the height of U-tube from the upper most tube support plate (h) and the width of two vertical portion of U-tube (w), is defined for geometric parameter study. Several aspect ratios with relocation of tube support plates are adopted to study the effects on the mode shapes and characteristics of flow-induced vibration. When the aspect ratio exceeds value of 1, most of the mode shapes at low frequency are generated at the top of U-tube. It makes very high value of the stability ratio and the amplitude of turbulent excitation as well. We can consider that the local mode shape at the upper side of U-tube will develop the wear phenomena between the tube and the anti-vibration bars such as vertical, horizontal, and diagonal strips. It turns out that the aspect ratio reveals very important parameter for the design stage of the steam generator. The appropriate value of the aspect ratio should be specified and applied.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.8
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• pp.698-707
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• 2011

This paper is to analyze the stability of the thick plate on inhomogeneous Pasternak foundation, with linearly varying thickness and concentrated mass by finite element method. To verify this finite element method, the results of natural frequencies and buckling stresses by the proposed method are compared with the existing solutions. The dynamic instability regions are decided by the dynamic stability analysis of the thick plate on inhomogeneous Pasternak foundation, with linearly varying thickness and concentrated mass. The non-dimensional Winkler foundation parameter is applied as 100, 1000 and non-dimensional shear foundation parameter is applied as 5. The tapered ratios are applied as 0.25 and 1.0, the ratios of concentrated mass to plate mass as 0.25 and 1.0, and the ratio of in-plane force to critical load as 0.4. As the result of numerical analysis of the thick plate on inhomogeneous Pasternak foundation for $u{\times}v=300cm{\times}300cm$ and $a{\times}b=600cm{\times}600cm$, instability areas of the thick plate which has the larger rigidity of inner area are farther from ${\beta}$-axis and narrower than those which has the larger rigidity of outer area.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.9 s.102
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• pp.1009-1015
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• 2005

Fluid-elastic instability and turbulence excitation for an under developing steam generator are investigated numerically. The stability ratio and the amplitude of turbulence excitation are obtained by using the $PIAT^{(R)}$ (program for integrity assessment of steam generator tube) code from the information on the thermal-hydraulic data of the steam generator. The aspect ratio, the ratio between the height of U-tube from the upper most tube support Plate (h) and the width of two vertical portion of U-tube (w), is defined for geometric parameter study. Several aspect ratios with relocation of tube support plates are adopted to study the effects on the mode shapes and characteristics of flow-induced vibration. When the aspect ratio exceeds value of 1, most of the mode shapes at low frequency are generated at the top of U-tube. It makes very high value of the stability ratio and the amplitude of turbulent excitation as well. We can consider that the local mode shape at the upper side of U-tube will develop the wear phenomena between the tube and the anti-nitration bars such as vortical, horizontal, and diagonal strips. It turns out that the aspect ratio reveals very important parameter for the design stage of the steam generator. The appropriate value of the aspect ratio should be specified and applied.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.489-505
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• 2016

Sinusoidal shear deformation theory (SSDT) is developed here for dynamic buckling of functionally graded (FG) nano-plates. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. In order to present a realistic model, the structural damping of nano-structure is considered using Kelvin-Voigt model. The surrounding elastic medium is modeled with a novel foundation namely as orthotropic visco-Pasternak medium. Size effects are incorporated based on Eringen'n nonlocal theory. Equations of motion are derived from the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is applied for obtaining the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, orthotropic visco-Pasternak foundation, power index of FG plate, structural damping and boundary conditions on the dynamic instability of system. The results are compared with those of first order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the dynamic buckling responses of system.

• Journal of The Korean Astronomical Society
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• v.28 no.1
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• pp.97-107
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• 1995

The stability of the geometrically thin, two-temperature hot accretion disk is studied. The general criterion for thermal instability is derived from the linear local analyses, allowing for advective cooling and dynamics in the vertical direction. Specifically, classic unsaturated Comptonization disk is analysed in detail. We find five eigen-modes: (1) Heating mode grows in thermal time scale, $(5/3)({\alpha}{\omega})^{-1}$, where alpha is the viscosity parameter and w the Keplerian frequency. (2) Cooling mode decays in time scale, $(2/5)(T_e/T_i)({\alpha}{\omega})^{-1}$, where $T_e\;and\;T_i$ are the electron and ion temperatures, respectively. (3) Lightman-Eardley viscous mode decays in time scale, $(4/3)(\Lambda/H)^2({\alpha}{\omega})^{-1}$, where $\Lambda$ is the wavelength of the perturbation and H the unperturbed disk height. (4) Two vertically oscillating modes oscillate in Keplerian time scale, $(3/8)^{1/2}\omega^{-1}$ with growth rate $\propto\;(H/\Lambda)^2$. The inclusion of dynamics in the vertical direction does not affect the thermal instability, adding only the oscillatory modes which gradually grow for short wavelength modes. Also, the advective cooling is not strong enough to suppress the growth of heating modes, at least for geometrically thin disk. Non-linear development of the perturbation is followed for simple unsaturated Compton disk: depending on the initial proton temperature perturbation, the disk can evolve to decoupled state with hot protons and cool electrons, or to one-temperature state with very cool protons and electrons.

• Geomechanics and Engineering
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• v.20 no.4
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• pp.287-297
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• 2020

This paper investigates the stability of a three-dimensional (3D) wedge under the pseudo-static action of an earthquake based on the nonlinear Barton-Bandis (B-B) failure criterion. The influences of the mechanical parameters of the discontinuity surface, the geometric parameters of the wedge and the pseudo-static parameters of the earthquake on the stability of the wedge are analyzed, as well as the sensitivity of these parameters. Moreover, a stereographic projection is used to evaluate the influence of pseudo-static direction on instability mode. The parametric analyses show that the stability coefficient and the instability mode of the wedge depend on the mechanical parameter of the rock mass, the geometric form of the wedge and the pseudo-static state of the earthquake. The friction angle of the rock φ_b, the roughness coefficient of the structure surface JRC and the two angles related to strikes of the joints θ₁ and θ₂ are sensitive to stability. Furthermore, the sensitivity of wedge height h, the compressive strength of the rock at the fracture surface JCS and the slope angle α to the stability are insignificant.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.2
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• pp.77.1-77.1
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• 2014

Galactic spiral arms are abundant with interesting gaseous substructures. It has been suggested that arm substructures arise from the wiggle instability (WI) of spiral shocks. While the nature of the WI remained elusive, our recent work without considering magnetic fields shows that the WI is physically originated from the accumulation of potential vorticity (PV) generated by deformed shock fronts. To elucidate the characteristics of the WI in more realistic galactic situations, we extend our previous linear stability analysis of spiral shocks by including magnetic fields. We find that magnetic fields reduce the amount of density compression at shocks, making the shock fronts to move toward the upstream direction. Magnetic tension forces from bent field lines stabilize the WI by prevent the generation of PV. When the spiral-arm forcing is F=5% of the centrifugal force of galaxy rotation, the maximum growth rate of the WI is found to be about 1.0, 0.4, and 0.2 times the orbital angular frequency for the plasma parameter ${\beta}=100$, 10, and 5, respectively. Shocks with ${\beta}=1$ are stable to the WI for F=5%, while becoming still unstable when F=10%.