• Title/Summary/Keyword: Parametric instability

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Parametric pitch instability investigation of Deep Draft Semi-submersible platform in irregular waves

  • Mao, Huan;Yang, Hezhen
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.8 no.1
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    • pp.13-21
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    • 2016
  • Parametric pitch instability of a Deep Draft Semi-submersible platform (DDS) is investigated in irregular waves. Parametric pitch is a form of parametric instability, which occurs when parameters of a system vary with time and the variation satisfies a certain condition. In previous studies, analyzing of parametric instability is mainly limited to regular waves, whereas the realistic sea conditions are irregular waves. Besides, parametric instability also occurs in irregular waves in some experiments. This study predicts parametric pitch of a Deep Draft Semi-submersible platform in irregular waves. Heave motion of DDS is simulated by wave spectrum and response amplitude operator (RAO). Then Hill equation for DDS pitch motion in irregular waves is derived based on linear-wave theory. By using Bubnov-Galerkin approach to solve Hill equation, the corresponding stability chart is obtained. The differences between regular-waves stability chart and irregular-waves stability chart are compared. Then the sensitivity of wave parameters on DDS parametric pitch in irregular waves is discussed. Based on the discussion, some suggestions for the DDS design are proposed to avoid parametric pitch by choosing appropriate parameters. The results indicate that it's important and necessary to predict DDS parametric pitch in irregular waves during design process.

Dynamic Stability of Liquid in a Spherical Tank Covered with Membrane under Vertical Harmonic Excitation

  • Chiba, Masakatsu;Murase, Ryo;Nambu, Yohsuke;Komatsu, Keiji
    • International Journal of Aerospace System Engineering
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    • v.2 no.2
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    • pp.34-39
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    • 2015
  • Experimental studies were conducted on the liquid sloshing characteristics in a spherical tank covered with a flexible membrane. A spherical acrylic tank with 145.2 mm in radius was used as a test tank, and it was half-filled with water. Silicon membranes with 0.2 mm thickness were used as a test membrane with plane or hemispherical types. The test tank was harmonically excited in a vertical direction by an electro-dynamic exciter. In this case, a parametric instability vibration comes up when the excitation frequency is twice the natural frequency. Parametric instability regions of natural modes were measured for three cases, i.e. liquid surface is free, covered with plane membrane and hemi-spherical membrane.

On the parametric instability of multilayered conical shells using the FOSDT

  • Lair, John;Hui, David;Sofiyev, Abdullah H.;Gribniak, Viktor;Turan, Ferruh
    • Steel and Composite Structures
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    • v.31 no.3
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    • pp.277-290
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    • 2019
  • This paper investigates the parametric instability (PI) of multilayered composite conical shells (MLCCSs) under axial load periodically varying the time, using the first order shear deformation theory (FOSDT). The basic equations for the MLCCSs are derived and then the Galerkin method is used to obtain the ordinary differential equation of the motion. The equation of motion converted to the Mathieu-Hill type differential equation, in which the DI is examined employing the Bolotin's method. The expressions for left and right limits of dimensionless parametric instability regions (PIRs) of MLCCSs based on the FOSDT are obtained. Finally, the influence of various parameters; lay-up, shear deformations (SDs), aspect ratio, as well as loading factors on the borders of the PIRs are examined.

Effects of damping on the parametric instability behaviour of plates under localized edge loading (compression or tension)

  • Deolasi, P.J.;Datta, P.K.
    • Structural Engineering and Mechanics
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    • v.3 no.3
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    • pp.229-244
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    • 1995
  • The parametric instability behaviour of a plate subjected to localized in-plane compressive or tensile periodic edge loading is studied, considering the effects of damping into the system. Different edge loading cases have been considered. Damping has been introduced in the form of proportional damping. Dynamic instability behaviour under compressive or tensile periodic edge loading shows that the instability regions are influenced by the load band width and its location on the edge. The effects of damping on the instability regions show that there is a critical value of dynamic load factor beyond which the plate becomes dynamically unstable. The critical dynamic load factor increases as damping increases. Damping generally reduces the widths of the instability regions.

Dynamic Stability of a Free-Free Beam with a Tip Rigid Body under a Controlled Pulsating Thrust (끝단 강체를 갖고 맥동 제어추력을 받는 양단 자유보의 동적 안정성)

  • Ryu, Bong-Jo;Lee, Gyu-Seop;Seong, Yun-Gyeong;Choe, Bong-Mun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.1
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    • pp.232-239
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    • 2000
  • The paper describes the parametric instability of free-free beams subjected to a controlled pulsating follower force. The beam has a tip rigid body not a mass point, and the direction of pulsating follower force is controlled by the direction control sensor. Equations of motion are derived by Hamilton's principle and the instability regions are obtained by finite element formulation. The effects of magnitude, rotary inertia, the distance between free end of the beam and the center of gravity of the rigid body on the instability types and regions are investigated by the change of the constant and periodic part of the follower force.

Parametric instability of the nonconservative elastic system (비보존 탄성계의 파라미터 불안정)

  • 박영필;노광춘
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.11 no.1
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    • pp.124-131
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    • 1987
  • The parameteric instability of the cantilever beam carrying two concentrated masses subjected to a periodic follower force is investigated theoretically and experimentally. The effects of the constant follower force and the periodic follower force the mass ratio and the location of the concentrated mass on the parametric instability of the system are discussed. In experiment, the nonconservative follower force is produced by the magnetic force of the electromagnet. The theoretical and the experimental results on the parameteric instability are in good agreement each other.

Parametric Instability of Cylinderical Panels (주기적(週基的)인 압축하중을 받는 원통(円筒) Panel의 동적(動的) 불안정(不安定) 특성(特性)에 관한 연구)

  • Park, Sung Jin;Mikami, Takashi
    • Journal of Korean Society of Steel Construction
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    • v.12 no.6
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    • pp.737-748
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    • 2000
  • This paper presents a numerical analysis procedure and a characteristics for dynamic of cylindrical panels. The panels with simply-simply or simply-clamped edge supports are subjectes to circumferential compressive or flexural stresses. The differential equations governing vibration and dynamic for these panels are derived by using the fundamental differential equation of the Love-Timoshenko and are solved numerically by the Galerkin method. The panel with simply-clamped edge supports is used a trigonometric function or an eigen function of a beam as a trial function and the effects of trial functions on numerical solutions are displayed. Numerical results are presented to demonstrate the effects of the flexural parameters in natural frequencies and coefficients of critical buckling, and some typical mode shapes of vibration and buckling are also presented.

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Auto-parametric resonance of framed structures under periodic excitations

  • Li, Yuchun;Gou, Hongliang;Zhang, Long;Chang, Chenyu
    • Structural Engineering and Mechanics
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    • v.61 no.4
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    • pp.497-510
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    • 2017
  • A framed structure may be composed of two sub-structures, which are linked by a hinged joint. One sub-structure is the primary system and the other is the secondary system. The primary system, which is subjected to the periodic external load, can give rise to an auto-parametric resonance of the second system. Considering the geometric-stiffness effect produced by the axially internal force, the element equation of motion is derived by the extended Hamilton's principle. The element equations are then assembled into the global non-homogeneous Mathieu-Hill equations. The Newmark's method is introduced to solve the time-history responses of the non-homogeneous Mathieu-Hill equations. The energy-growth exponent/coefficient (EGE/EGC) and a finite-time Lyapunov exponent (FLE) are proposed for determining the auto-parametric instability boundaries of the structural system. The auto-parametric instabilities are numerically analyzed for the two frames. The influence of relative stiffness between the primary and secondary systems on the auto-parametric instability boundaries is investigated. A phenomenon of the "auto-parametric internal resonance" (the auto-parametric resonance of the second system induced by a normal resonance of the primary system) is predicted through the two numerical examples. The risk of auto-parametric internal resonance is emphasized. An auto-parametric resonance experiment of a ${\Gamma}$-shaped frame is conducted for verifying the theoretical predictions and present calculation method.

Static and Dynamic Instability Characteristics of Thin Plate like Beam with Internal Flaw Subjected to In-plane Harmonic Load

  • R, Rahul.;Datta, P.K.
    • 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.

Parametric Instability Boundaries for Spatial Subharmonics in Photorefractive Moving Gratings: Theory and Experiments

  • Kwak, Chong-Hoon;Lee, El-Hang
    • 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.

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