• International Journal of Naval Architecture and Ocean Engineering
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• v.3 no.1
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• pp.53-64
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• 2011

The present study considers multi-level approach for the analysis of parametric roll phenomena. Three kinds of computation method, GM variation, impulse response function (IRF), and Rankine panel method, are applied for the multi-level approach. IRF and Rankine panel method are based on the weakly nonlinear formulation which includes nonlinear Froude-Krylov and restoring forces. In the computation result of parametric roll occurrence test in regular waves, IRF and Rankine panel method show similar tendency. Although the GM variation approach predicts the occurrence of parametric roll at twice roll natural frequency, its frequency criteria shows a little difference. Nonlinear roll motion in bichromatic wave is also considered in this study. To prove the unstable roll motion in bichromatic waves, theoretical and numerical approaches are applied. The occurrence of parametric roll is theoretically examined by introducing the quasi-periodic Mathieu equation. Instability criteria are well predicted from stability analysis in theoretical approach. From the Fourier analysis, it has been verified that difference-frequency effects create the unstable roll motion. The occurrence of unstable roll motion in bichromatic wave is also observed in the experiment.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.23 no.4
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• pp.30-35
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• 2015

In this paper, a theoretical study of low frequency non acoustic instability, the $L^*$ instability, of a solid rocket motor is investigated. The $L^*$ stability criterion is determined by analysing the $L^*$ stability curves of two very distinct propellants for five different geometrical combustors. The $L^*$ instability of two extreme fuels showed totally different behavior in terms of operating pressure of the combustor. A parametric study on the stability for different chamber volume and different throat area keeping constant $L^*$ is conducted and analyzed. It was found that one of the main parameters, the non-dimensional critical characteristic time, requires an enough margin from the critical $L^*$ stability curve.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.1
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• pp.19-29
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• 2013

This paper deals with the study of buckling, vibration, and parametric instability characteristics in a damaged cross-ply and angle-ply laminated plate like beam under in-plane harmonic loading, using the finite element approach. Damage is modelled using an anisotropic damage formulation, based on the concept of reduction in stiffness. The effect of damage on free vibration and buckling characteristics of a thin plate like beam has been studied. It has been observed that damage shows a strong orthogonality and in general deteriorates the static and dynamic characteristics. For the harmonic type of loading, analysis was carried out on a thin plate like beam by solving the governing differential equation which is of Mathieu-Hill type, using the method of multiple scales (MMS). The effects of damage and its location on dynamic stability characteristics have been presented. The results indicate that, compared to the undamaged plate like beam, heavily damaged beams show steeper deviations in simple and combination resonance characteristics.

• Structural Engineering and Mechanics
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• v.37 no.4
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• pp.401-413
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• 2011

The aerodynamic stability of orthotropic tensioned membrane structures with rectangular plane is theoretically studied under the uniform ideal potential flow. The aerodynamic force acting on the membrane surface is determined by the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics. Then, based on the large amplitude theory and the D'Alembert's principle, the interaction governing equation of wind-structure is established. Under the circumstances of single mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction equation into a system of second order nonlinear differential equation with constant coefficients. Through judging the stability of the system characteristic equation, the critical divergence instability wind velocity is determined. Finally, from different parametric analysis, we can conclude that it has positive significance to consider the characteristics of orthotropic and large amplitude for preventing the instability destruction of structures.

• ETRI Journal
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• v.16 no.4
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• pp.13-25
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• 1995

We have derived a nonlinear spatiotemporal differential equation for space-charge fields from Kukhtarev’s material equations in a moving coordinate system and obtained the spatial subharmonic instability boundaries by using linear stability analysis. It is also found that there is an analogy between the temporal subharmonic and the spatial subharmonc instabilities in the sense that the governing differential equations describing the instability boundaries are formally identical. The experiments for generating spatial subharmonic waves are performed in a photorefractive $Bi_{12}SiO_{20}$ crystal by using conventional moving grating technique. The threshold detunings are experimentally determined and the results are compared with the theory.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.119.2-119.2
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• 2012

Charged particle energization is an outstanding problem in space physics. This paper investigates the nonlinear dynamics of Alfve'n-cyclotron waves accompanying particle heating processes and the drift Alfv'en-cyclotron (or EMIC) instability associated with a current disruption event on 29 January 2008 observed with THEMIS satellite by means of a particle-in-cell simulation. The simulation shows that the drift Alfv'en-cyclotron instabilities are excited in two regimes, a relatively low frequency mode propagating in a quasi-perpendicular direction while the second high-frequency branch propagating in a predominantly parallel propagation direction, which is consistent with observation as well as earlier theories. It is shown that parametric decay processes lead to an inverse cascade of Alfv'en-cyclotron waves and the generation of ion-acoustic waves by decay instability. It is also shown that the nonlinear decay processes are accompanied by small perpendicular heating and parallel cooling of the protons, and a pronounced parallel heating of the electrons.

• Coupled systems mechanics
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• v.2 no.3
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• pp.215-230
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• 2013

This paper investigates the pull-in instability of functionally graded poly-SiGe micro-beams under the combined electrostatic and intermolecular forces and temperature change. The exponential distribution model and Voigt model are used to analyze the functionally graded materials (FGMs). Principle of virtual work is used to derive the nonlinear governing differential equation which is then solved using differential quadrature method (DQM). A parametric study is conducted to show the significant effects of material composition, geometric nonlinearity, temperature change and intermolecular Casimir force.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.435-459
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• 2015

Parametric resonance of shear deformable composite skew plates subjected to non-uniform (parabolic) and linearly varying periodic edge loading is studied for different boundary conditions. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is solved using Rayleigh-Ritz method in conjunction with boundary characteristics orthonormal polynomials (BCOPs) functions. The orthonormal polynomials are generated for unit square domain using Gram-Schmidt orthogonalization process. Bolotin method is followed to obtain the boundaries of parametric resonance region with higher order approximation. These boundaries are traced by the periodic solution of Mathieu-Hill equations with period T and 2T. Effect of various parameters like skew angle, span-to-thickness ratio, aspect ratio, boundary conditions, static load factor on parametric resonance of skew plate have been investigated. The investigation also includes influence of different types of linearly varying loading and parabolically varying bi-axial loading.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 1997.04a
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• pp.247-256
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• 1997

A nonlinear mathematical model of longitudinal combustion instability appropriate for ramjets and augmentors was developed based on modal analysis. The model was limited to a two-mode formulation. The associated differential equations were solved both analytically and numerically and used to perform parametric studies.

• Ocean Systems Engineering
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• v.4 no.2
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• pp.117-136
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• 2014

The increased interest in the design of energy efficient ships post IMO regulation on enforcing EEDI has encouraged researchers to reevaluate the numerical methods in predicting important hull design parameters. The prediction of added resistance and stability of ships in the rough sea environment dictates selection of ship hulls. A 3D panel method based on Green function is developed for vessel motion prediction. The effects of parametric instability are also investigated using the Volterra series approach to model the hydrostatic variation due to ship motions. The added resistance is calculated using the near field pressure integration method.