scholarly journals Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Raouf A. Ibrahim
Keyword(s):  
Parametric Excitation ◽  
Breaking Waves ◽  
Spectral Density Function ◽  
Faraday Waves ◽  
Analytical Treatment ◽  
Weakly Nonlinear ◽  
Sloshing Dynamics ◽  
Numerical Tools ◽  
Wave Competition ◽  
The Stability

Liquid parametric sloshing, known also as Faraday waves, has been a long standing subject of interest. The development of the theory of Faraday waves has witnessed a number of controversies regarding the analytical treatment of sloshing modal equations and modes competition. One of the significant contributions is that the energy is transferred from lower to higher harmonics and the nonlinear coupling generated static components in the temporal Fourier spectrum, leading to a contribution of a nonoscillating permanent sinusoidal deformed surface state. This article presents an overview of different problems of Faraday waves. These include the boundary value problem of liquid parametric sloshing, the influence of damping and surfactants on the stability and response of the free surface, the weakly nonlinear parametric and autoparametric sloshing dynamics, and breaking waves under high parametric excitation level. An overview of the physics of Faraday wave competition together with pattern formation under single-, two-, three-, and multifrequency parametric excitation will be presented. Significant effort was made in order to understand and predict the pattern selection using analytical and numerical tools. Mechanisms for selecting the main frequency responses that are different from the first subharmonic one were identified in the literature. Nontraditional sources of parametric excitation and Faraday waves of ferromagnetic films and ferrofluids will be briefly discussed. Under random parametric excitation and g-jitter, the behavior of Faraday waves is described in terms of stochastic stability modes and spectral density function.

New Methodology for the Determination of the Vertical Center of Gravity of In-Service Semisubmersibles: Proposal and Numerical Assessment

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Ivan N. Porciuncula ◽  
Claudio A. Rodríguez ◽  
Paulo T. T. Esperança
Keyword(s):  
Accurate Determination ◽  
Center Of Gravity ◽  
Practical Implementation ◽  
Numerical Assessment ◽  
Neutral Equilibrium ◽  
Inclination Angles ◽  
Numerical Tools ◽  
The Stability ◽  
Metacentric Height

Along its lifetime, an offshore unit is subjected to several equipment interventions. These modifications may include large conversions in loco that usually are not adequately documented. Hence, the accurate determination of the platform's center of gravity (KG) is not possible. For vessels with low metacentric height (GM), such as semisubmersibles, Classification Societies penalize the platform's KG, inhibiting the installation of new equipment until an accurate measurement of KG is provided, i.e., until an updated inclining test is performed. For an operating semisubmersible, the execution of this type of test is not an alternative because it implies in removing the vessel from its in-service location to sheltered waters. Relatively recently, some methods have been proposed for the estimation of KG for in-service vessels. However, as all of the methods depend on accurate measurements of inclination angles and, eventually, on numerical tools for the simulation of vessel dynamics onboard, they are not straightforward for practical implementation. The objective of the paper is to present a practical methodology for the experimental determination of KG, without the need of accurate measurements of inclinations and/or complex numerical simulations, but based on actual operations that can be performed onboard. Indeed, the proposed methodology relies on the search, identification, and execution of a neutral equilibrium condition where, for instance, KG = KM. The method is exemplified using actual data of a typical semisubmersible. The paper also numerically explores and discusses the stability of the platform under various conditions with unstable initial GM, as well as the effect of mooring and risers.

scholarly journals Spectral analysis of vibration in weakly non-linear systems

2000 ◽  
Vol 22 (3) ◽  
pp. 181-192
Author(s):  
Nguyen Tien Khiem
Keyword(s):  
Nonlinear Systems ◽  
Spectral Density ◽  
Density Function ◽  
Asymptotic Methods ◽  
Random Excitation ◽  
Spectral Density Function ◽  
Kolmogorov Equation ◽  
Spectral Structure ◽  
Random Load ◽  
Weakly Nonlinear

The weakly nonlinear systems subjected to deterministic excitations have been fully and deeply studied by use of the well developed asymptotic methods [1-4]. The systems excited by a random load have been investigated mostly using the Fokker-Plank-Kolmogorov equation technique combined with the asymptotic methods [5-8]. However, the last approach in most successful cases allows to obtain only a stationary single point probability density function, that contains no information about the correlation nor' consequently, the spectral structure of the response. The linearization technique [9, 10] in general permits the spectral density of the response to be determined, but the spectral function obtained by this method because of the linearization eliminates the effect of the nonlinearity. Thus, spectral structure of response of weakly nonlinear systems to random excitation, to the author's knowledge, has not been studied enough. This paper deals with the above mentioned problem. The main idea of this work is the use of an analytical simulation of random excitation given by its spectral density function and afterward application of the well known procedure of the asymptotic method to obtain an asymptotic expression of the response spectral density function. The obtained spectral relationship covers the linear system case and especially emphasizes the nonlinear effect on the spectral density of response. The theory will be illustrated by an example and at the end of this paper there will be a discussion about the obtained results.  

Finite-amplitude internal wavepacket dispersion and breaking

2001 ◽  
Vol 429 ◽  
pp. 343-380 ◽  
Author(s):  
BRUCE R. SUTHERLAND
Keyword(s):  
Numerical Simulations ◽  
Internal Waves ◽  
Large Amplitude ◽  
Finite Amplitude ◽  
Critical Amplitude ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
The Stability ◽  
The Waves ◽  
Horizontal Wavelength

The evolution and stability of two-dimensional, large-amplitude, non-hydrostatic internal wavepackets are examined analytically and by numerical simulations. The weakly nonlinear dispersion relation for horizontally periodic, vertically compact internal waves is derived and the results are applied to assess the stability of weakly nonlinear wavepackets to vertical modulations. In terms of Θ, the angle that lines of constant phase make with the vertical, the wavepackets are predicted to be unstable if [mid ]Θ[mid ] < Θc, where Θc = cos−1 (2/3)1/2 ≃ 35.3° is the angle corresponding to internal waves with the fastest vertical group velocity. Fully nonlinear numerical simulations of finite-amplitude wavepackets confirm this prediction: the amplitude of wavepackets with [mid ]Θ[mid ] > Θc decreases over time; the amplitude of wavepackets with [mid ]Θ[mid ] < Θc increases initially, but then decreases as the wavepacket subdivides into a wave train, following the well-known Fermi–Pasta–Ulam recurrence phenomenon.If the initial wavepacket is of sufficiently large amplitude, it becomes unstable in the sense that eventually it convectively overturns. Two new analytic conditions for the stability of quasi-plane large-amplitude internal waves are proposed. These are qualitatively and quantitatively different from the parametric instability of plane periodic internal waves. The ‘breaking condition’ requires not only that the wave is statically unstable but that the convective instability growth rate is greater than the frequency of the waves. The critical amplitude for breaking to occur is found to be ACV = cot Θ (1 + cos2 Θ)/2π, where ACV is the ratio of the maximum vertical displacement of the wave to its horizontal wavelength. A second instability condition proposes that a statically stable wavepacket may evolve so that it becomes convectively unstable due to resonant interactions between the waves and the wave-induced mean flow. This hypothesis is based on the assumption that the resonant long wave–short wave interaction, which Grimshaw (1977) has shown amplifies the waves linearly in time, continues to amplify the waves in the fully nonlinear regime. Using linear theory estimates, the critical amplitude for instability is ASA = sin 2Θ/(8π2)1/2. The results of numerical simulations of horizontally periodic, vertically compact wavepackets show excellent agreement with this latter stability condition. However, for wavepackets with horizontal extent comparable with the horizontal wavelength, the wavepacket is found to be stable at larger amplitudes than predicted if Θ [lsim ] 45°. It is proposed that these results may explain why internal waves generated by turbulence in laboratory experiments are often observed to be excited within a narrow frequency band corresponding to Θ less than approximately 45°.

scholarly journals Effect of Rotational Speed Modulation on the Weakly Nonlinear Heat Transfer in Walter-B Viscoelastic Fluid in the Highly Permeable Porous Medium

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1448
Author(s):  
Anand Kumar ◽  
Vinod K. Gupta ◽  
Neetu Meena ◽  
Ishak Hashim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Prandtl Number ◽  
Heat Transport ◽  
Viscoelastic Fluid ◽  
Rotational Speed ◽  
Weakly Nonlinear ◽  
Speed Modulation ◽  
The Stability ◽  
The Impact

In this article, a study on the stability of Walter-B viscoelastic fluid in the highly permeable porous medium under the rotational speed modulation is presented. The impact of rotational modulation on heat transport is performed through a weakly nonlinear analysis. A perturbation procedure based on the small amplitude of the perturbing parameter is used to study the combined effect of rotation and permeability on the stability through a porous medium. Rayleigh–Bénard convection with the Coriolis expression has been examined to explain the impact of rotation on the convective flow. The graphical result of different parameters like modified Prandtl number, Darcy number, Rayleigh number, and Taylor number on heat transfer have discussed. Furthermore, it is found that the modified Prandtl number decelerates the heat transport which may be due to the combined effect of elastic parameter and Taylor number.

scholarly journals The Energy Compensation of the HRG Based on the Double-Frequency Parametric Excitation of the Discrete Electrode

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3549
Author(s):  
Wanliang Zhao ◽  
Hao Yang ◽  
Fucheng Liu ◽  
Yan Su ◽  
Lijun Song
Keyword(s):  
Parametric Excitation ◽  
Dynamical Equation ◽  
Dynamic Performance ◽  
Free Precession ◽  
Double Frequency ◽  
Energy Compensation ◽  
Hemispherical Resonator ◽  
The Stability ◽  
Resonator Vibration ◽  
Excitation Parameters

In this study, for energy compensation in the whole-angle control of Hemispherical Resonator Gyro (HRG), the dynamical equation of the resonator, which is excited by parametric excitation of the discrete electrode, is established, the stability conditions are analyzed, and the method of the double-frequency parametric excitation by the discrete electrode is derived. To obtain the optimal parametric excitation of the resonator, the total energy stability of the resonator is simulated for the evolution of the resonator vibration with different excitation parameters and the free precession of the standing wave by the parametric excitation. In addition, the whole-angle control of the HRG is designed, and the energy compensation of parametric excitation is proven by the experiments. The results of the experiments show that the energy compensation of the HRG in the whole-angle control can be realized using discrete electrodes with double-frequency parametric excitation, which significantly improves the dynamic performance of the whole-angle control compared to the force-to-rebalance.

Analytical Treatment of In-Plane Parametrically Excited Undamped Vibrations of Simply Supported Parabolic Arches

2003 ◽  
Vol 125 (1) ◽  
pp. 73-79 ◽  
Author(s):  
Dimitris S. Sophianopoulos ◽  
George T. Michaltsos
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Dynamic Stability ◽  
Parametric Excitation ◽  
Stability Problem ◽  
Axial Loading ◽  
Time Dependent ◽  
Analytical Treatment ◽  
Simply Supported ◽  
Forced Motion

The present work offers a simple and efficient analytical treatment of the in-plane undamped vibrations of simply supported parabolic arches under parametric excitation. After thoroughly dealing with the free vibration characteristics of the structure dealt with, the differential equations of the forced motion caused by a time dependent axial loading of the form P=P0+Pt cos θt are reduced to a set of Mathieu-Hill type equations. These may be thereafter tackled and the dynamic stability problem comprehensively discussed. An illustrative example based on Bolotin’s approach produces results validating the proposed method.

Simultaneous Resonance and Anti-Resonance in Dynamical Systems Under Asynchronous Parametric Excitation

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Artem Karev ◽  
Peter Hagedorn
Keyword(s):  
Dynamical Systems ◽  
Parametric Excitation ◽  
Analytical Method ◽  
Normal Forms ◽  
High Sensitivity ◽  
Combination Resonance ◽  
Concurrent Study ◽  
The Stability ◽  
Analytical Expressions ◽  
Special Case

Abstract Since the discovery of parametric anti-resonance, parametric excitation has also become more prominent for its stabilizing properties. While resonance and anti-resonance are mostly studied individually, there are systems where both effects appear simultaneously at each combination resonance frequency. With a steep transition between them and a high sensitivity of their relative positions, there is a need for a concurrent study of resonance and anti-resonance. The semi-analytical method of normal forms is used to derive approximate analytical expressions describing the magnitude of the stability impact as well as the precise locations of stabilized and destabilized areas. The results reveal that the separate appearance of resonance and anti-resonance is only a special case occurring for synchronous parametric excitation. In particular, in circulatory systems the simultaneous appearance is expected to be much more common.

scholarly journals STABILITY OF A SAND BED UNDER BREAKING WAVES

1974 ◽  
Vol 1 (14) ◽  
pp. 45 ◽  
Author(s):  
Ole Secher Madsen
Keyword(s):  
Pressure Gradient ◽  
Surf Zone ◽  
Breaking Waves ◽  
Breaking Wave ◽  
Light Weight ◽  
Loss Of Stability ◽  
Vertical Flow ◽  
Sufficient Magnitude ◽  
The Stability ◽  
Bed Material

The possible effect on the stability of a porous sand bed of the flow induced within the bed during the passage of near-breaking or breaking waves is considered. It is found that the horizontal flow rather than the vertical flow within the bed may affect its stability. An approximate analysis, used in geotechnical computations of slope stability, indicates that a momentary bed failure is likely to occur during the passage of the steep front slope of a near-breaking wave. Experimental results for the pressure gradient along the bottom under near-breaking waves are presented. These results indicate that the pressure gradient is indeed of sufficient magnitude to cause the momentary failure suggested by the theoretical analysis. The loss of stability of the bed material due to the flow induced within the bed itself may affect the amount of material set in motion during the passage of a near-breaking or breaking wave, in particular, in model tests employing light weight bed material. The failure mechanism considered here is also used as the basis for a hypothesis for the depth of disturbance of the bed in the surf zone. The flow induced in a porous bed is concluded to be an important mechanism which should be considered when dealing with the wave-sediment interaction in the surf zone.

Dynamic analysis of a microelectromechanical systems resonant gyroscope excited using combination parametric resonance

2006 ◽  
Vol 220 (9) ◽  
pp. 1463-1479 ◽  
Author(s):  
B J Gallacher ◽  
J S Burdess
Keyword(s):  
Perturbation Analysis ◽  
Parametric Excitation ◽  
Microelectromechanical Systems ◽  
Equations Of Motion ◽  
Multiple Time ◽  
Excitation Scheme ◽  
Electrostatically Actuated ◽  
Modes Of Vibration ◽  
The Stability ◽  
Electrostatic Coupling

This paper investigates the application of parametric excitation to a resonant microelectromechanical systems (MEMS) gyroscope. The modal equations of motion of an electrostatically actuated ring are derived and shown to be coupled via the electrostatic stiffness. Such electrostatic coupling between in-plane modes of vibration permits parametric instabilities that may be exploited in a novel excitation scheme. A multiple time scale perturbation method is used to analyse the response of the ring gyroscope to the combination parametric excitations with the principal objective of separating the drive and response frequencies of the ring gyroscope. As pairs of flexural modes of the perfect ring are degenerate, the combination excitation between distinct modes demand the ring to be analysed as a four degree of freedom system. Slight mis-tuning between the otherwise degenerate modes is incorporated in the perturbation analysis. The results of the perturbation analysis are subsequently used to determine the stability boundaries for a typical ring gyroscope when excited using a sum combination resonance between the flexural modes of order 2 and 5. In this case, the ratio of the drive and response frequencies is approximately 10:1. Drive and sense configurations that enable effective parametric excitation of a desired mode are investigated. Simulation of the oscillator scheme is achieved using MATLAB Simulink and this validates the perturbation analysis. Agreement between the models within 10 per cent is demonstrated.

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