Nonlinear Vibrations in an Elastic Structure Subjected to Vertical Excitation and Coupled With Liquid Sloshing in a Rectangular Tank

1997 ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequency ◽  
Liquid Surface ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Liquid Sloshing ◽  
Elastic Structure ◽  
Vertical Excitation ◽  
Rectangular Tank ◽  
Resonance Curves

Abstract The nonlinear coupled vibrations of an elastic structure and liquid sloshing in a rectangular tank, partially filled with liquid, are investigated. The structure containing the tank is vertically subjected to a sinusoidal excitation. In the theoretical analysis, the resonance curves for the responses of the structure and liquid surface are presented by the harmonic balance method, when the natural frequency of the structure is equal to twice the natural frequency of one of the sloshing modes. From the theoretical analysis, the following predictions have been obtained: (a) Due to the nonlinearity of the fluid force, harmonic oscillations appear in the structure, while subharmonic oscillations occur on the liquid surface, (b) the shapes of the resonance curves markedly change depending on the liquid depth, and (c) when the detuning condition is slightly deviated, almost periodic oscillations and chaotic oscillations appear at certain intervals of the excitation frequency. These were qualitatively in good agreement with the experimental results.

Nonlinear Vibrations of an Elastic Structure Subjected to Vertical Excitation and Coupled With Liquid Sloshing in a Cylindrical Tank: Resonance With an Axisymmetric Mode

1999 ◽  
Author(s):  
Takashi Ikeda ◽  
Shin Murakami
Keyword(s):  
Natural Frequency ◽  
Resonance Curve ◽  
Liquid Sloshing ◽  
Elastic Structure ◽  
Cylindrical Tank ◽  
Axisymmetric Mode ◽  
Vertical Excitation ◽  
Structure Changes ◽  
Flat Shape ◽  
Resonance Curves

Abstract The nonlinear coupled vibrations of an elastic structure and liquid sloshing in a cylindrical tank are investigated. When the structure is vertically subjected to a sinusoidal excitation, and when the natural frequency of the structure is equal to twice the natural frequency of the first axisymmetric mode of sloshing, modal equations governing the coupled motions are derived. Then, the theoretical resonance curves are presented by using the method of harmonic balance and an FFT analysis. As a result, it is demonstrated that the resonance curve for the structure changes from a shape with a peak to a flat shape as the liquid level decreases. It is also clarified that amplitude-modulated motions appear when the tuning condition is deviated. In experiments, theoretical resonance curves were qualitatively in good agreement with the experimental results.

Nonlinear Parametric Vibrations of an Elastic Structure With a Cylindrical Liquid Container (in the Case of an Anti-Symmetric Sloshing Mode)

2001 ◽  
Author(s):  
Takashi Ikeda ◽  
Shin Murakami
Keyword(s):  
Natural Frequency ◽  
Harmonic Balance ◽  
Small Deviation ◽  
Harmonic Balance Method ◽  
Mathieu Equation ◽  
Elastic Structure ◽  
Coupled Vibration ◽  
Sloshing Mode ◽  
Resonance Curves ◽  
Fft Analysis

Abstract The nonlinear-coupled vibrations of an elastic structure and liquid sloshing in a cylindrical container are investigated. Since the structure is vertically subjected to a sinusoidal excitation, the behavior of the liquid surface is governed by a kind of the Mathieu equation. Modal equations governing the coupled motions are derived, when the natural frequency of the structure is equal to twice the natural frequency of an anti-symmetric mode of sloshing. The theoretical resonance curves are also presented by using an FFT analysis and the improved harmonic balance method. The influences of a liquid level and a detuning parameter on the theoretical resonance curves are shown. A small deviation of the tuning condition can cause amplitude-modulated motions and separate the occurrence region of the coupled vibration into two regions. In the experiments, the theoretical resonance curves were qualitatively in agreement with the experimental data. In addition, amplitude-modulated motions were observed.

Nonlinear Vibrations in a Parametrically Excited Fluid-Structure Interaction System With One-to-One Internal Resonance

2003 ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Natural Frequency ◽  
Internal Resonance ◽  
Fluid Structure Interaction ◽  
Liquid Sloshing ◽  
Fluid Structure ◽  
Inertia Effects ◽  
Structure Interaction ◽  
Interaction System ◽  
Resonance Curves ◽  
One To One

Theoretical resonance curves prove that a structure’s resonance can facilitate liquid sloshing even when the internal resonance ratio is one-to-one. An investigation of nonlinear sloshing liquid vibrations in a rectangular tank supported by an elastic structure that is subjected to a vertical and sinusoidal excitation reveals that liquid sloshing occurs when the structure’s natural frequency is approximately equal to the natural frequency of sloshing, that is, in the state of one-to-one internal resonance, and that amplitude-modulated motions appear when the condition of the internal resonance deviates to some extent. A special consideration of the nonlinear inertia effects of liquid force and the use of Galerkin’s method help derive the differential (modal) equations governing the dynamic behaviors of the fluid-structure interaction system, while van der Pol’s method helps express the theoretical resonance curves. These theoretical results are in quantitative agreement with the experimental data.

Random Excitation of a Structure Interacting With Liquid Sloshing Dynamics

2002 ◽  
Author(s):  
Takashi Ikeda ◽  
Raouf A. Ibrahim
Keyword(s):  
Free Surface ◽  
Natural Frequency ◽  
Internal Resonance ◽  
Gaussian White Noise ◽  
Liquid Sloshing ◽  
Elastic Structure ◽  
Center Frequency ◽  
System Response ◽  
Liquid Free Surface ◽  
Sloshing Dynamics

The nonlinear random interaction of an elastic structure with liquid sloshing dynamics in a cylindrical tank is investigated in the neighborhood of 1:2 internal resonance. Such internal resonance takes place when the natural frequency of the elastic structure is close to twice the natural frequency of the antisymmetric sloshing mode (1,1). The excitation is generated from the response of a linear shaping filter subjected to a Gaussian white noise. The analytical model involves three sloshing modes; (1,1), (0,1) and (2,1). The system response statistics and stability boundaries are numerically estimated using Monte Carlo simulation. The influence of the excitation center frequency, its bandwidth, and the liquid level on the system responses is studied. It is found that there is an irregular energy exchange between the structure and the liquid free surface motion when the center frequency is close to the structure natural frequency. Depending on the excitation power spectral density, the liquid free surface experiences zero motion, uncertain motion (intermittency), partially developed motion, and fully developed random motion. The structure response probability density function is almost Gaussian, while the liquid elevation deviates from normality. The unstable region, where the liquid motion occurs, becomes wider as the excitation intensity increases or as the bandwidth decreases. As the liquid depth decreases, the region of nonlinear interaction shrinks which is associated with a shift of the peak of the structure mean square response toward the left side of the frequency axis.

Study of Hydrostatic Pump Created Under Liquid Sloshing in a Rectangular Tank Subjected to External Excitation

2016 ◽  
Vol 08 (01) ◽  
pp. 1650004 ◽  
Author(s):  
Abdallah Bouabidi ◽  
Zied Driss ◽  
Mohamed Salah Abid
Keyword(s):  
Numerical Simulation ◽  
Excitation Frequency ◽  
Liquid Sloshing ◽  
Experimental Results ◽  
Experimental Setup ◽  
Liquid Motion ◽  
External Excitation ◽  
Sinusoidal Movement ◽  
Rectangular Tank ◽  
External Excitation Frequency

The aim of this work is to study the hydrostatic pump created under liquid sloshing in a rectangular tank partially filled with liquid. A numerical simulation was performed to predict the liquid motion in the tank. The apparition of the compression and the depression zones due to the liquid motion was presented and analyzed. An experimental setup with sinusoidal movement was developed to study the hydrostatic pump. The hydrostatic pump is created using a mixing element. The experimental results show that the compression and the depression zones can create the hydrostatic pump. The effect of the connecting chamber value was studied for different values of external excitation frequency. The pump depends considerably on the dimension of the connecting zone between the two volumes. For the different connecting chamber values, the pumped quantity increase with the increase of the frequency.

An Investigation on Two-Dimensional Nonlinear Sloshing in Rectangular Tank

2015 ◽  
Author(s):  
Dongya Zhao ◽  
Zhiqiang Hu ◽  
Gang Chen
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Liquid Surface ◽  
Surface Condition ◽  
Excitation Frequency ◽  
Surface Elevation ◽  
Two Dimensional ◽  
Free Surface Condition ◽  
Rectangular Tank ◽  
Oscillation Movement

Two-dimensional liquid sloshing in rectangular tank of FLNG system is investigated both numerically and experimentally. In numerical simulation, a time-domain scheme has been developed based on potential flow theory in boundary element method. Tank movement is defined by wall boundary condition to produce a reciprocating oscillation. Nonlinear free surface condition is adopted to capture free surface elevation. Energy dissipation caused by viscous effects is considered by applying artificial damping term to the dynamic free surface condition, which is also vital to achieve a steady-state solution. For comparison, experiments of a rectangular tank filled with water subjected to specified oscillation are carried out. As coupling effects between sloshing and tank motion is not included in this research, the testing apparatus is required to produce consistent oscillation movement and not affected by the change of filling condition and sloshing load. Liquid surface elevations in several typical places of the tank were measured. Sloshing related parameters including oscillation amplitude, frequency and filling level are analyzed systematically. It’s found that numerical simulation results have good agreement with phenomenon observed under small amplitude excitation, and this nonlinear analysis method is proved to be effective in capturing liquid surface elevation. It is found that sloshing in tank is sensitive to filling level as well as excitation frequency, especially in the crucial combination cases of them. For given filling level, sloshing tends to be violent near corresponding natural frequencies, and viscous damping has limited contribution to sloshing amplitude when resonance occurs. This fundamental investigation also paves path for the study of more complicated sloshing problems.

Localization Phenomena in Pendulum Arrays Subjected to Vertical Excitation

2014 ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Chongyue Shi ◽  
Keisuke Nishimura
Keyword(s):  
Experimental Data ◽  
Theoretical Analysis ◽  
Frequency Response ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Response Curves ◽  
Chaotic Motions ◽  
Vertical Excitation ◽  
Parametric Resonances ◽  
Spring Constants

Localization phenomena, also referred to as intrinsic localized modes (ILMs), are investigated in an N-pendulum array subjected to vertical harmonic excitation. The pendula behave nonlinearly and are connected with each other by weak linear springs. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for frequency response curves for the principal parametric resonances, considering the nonlinear restoring moment of the pendula. In the numerical results, frequency response curves for N=2 and 3 are shown to examine the patterns of ILMs, and the influences of the connecting spring constants and the imperfections of the pendula. Bifurcation sets are also calculated to show the excitation frequency range and the conditions for the occurrence of ILMs. Increasing the connecting spring constant results in the appearance of Hopf bifurcation. The numerical simulations reveal the occurrence of ILMs with amplitude modulated motions (AMMs) including chaotic motions. ILMs were observed in experiments, and the experimental data were compared with the theoretical results. The validity of the theoretical analysis was confirmed by the experimental data.

Experimental and Numerical Study on Liquid Sloshing Dynamics with Single Vertical Porous Baffle in a Sway Excited Ship Tank

2020 ◽  
Author(s):  
Sahaj k v ◽  
Nasar Thuvanismail
Keyword(s):  
Free Surface ◽  
Boundary Element ◽  
Numerical Study ◽  
Excitation Frequency ◽  
Boundary Element Methods ◽  
Liquid Sloshing ◽  
Shake Table ◽  
Natural Period ◽  
Rectangular Tank ◽  
Porous Screen

<p>Liquid motion in partially filled tanks may cause large structural loads if the period of tank motion is close to the natural period of fluid inside the tank. This phenomenon is called sloshing. Sloshing means any motion of a free liquid surface inside a container. The effect of severe sloshing motion on global seagoing vessels is an important factor in safety design of such containers. In order to examine the sloshing effects, a shake table experiments were conducted for different water fill depth of aspect ratio 0.163, 0.325 and 0.488. The parametric studies were carried out to show the liquid sloshing effects in terms of slosh frequencies, maximum free surface elevation and hydrodynamic forces acting on the tank wall. Sloshing oscillation for the excitation frequency f<sub>1</sub>, f<sub>2</sub>, f<sub>3</sub>, f<sub>4 </sub>and f<sub>5</sub> are observed and analysed. The excitation frequencies is varied between 0.4566 Hz to 1.9757 Hz and constant amplitudes of 7.5mm was adopted. The movement of fluid in a rectangular tank has been studied using experimental approach and different baffle configurations were adopted for analysing the sloshing oscillation, natural frequencies and variation in wave deflection. The adopted porosities in the present study is 15% – 25 %. Porous screen is placed inside the tank at L/2 location and study is extended for single porous screen for better wave energy absorption. Capacitance wave probes have been placed at tank ends to record the free surface water elevation. Load cells are used to measure the sloshing force inside the tank. Linear variable displacement transducers is used to measure the displacement of shake table. In the present study single porous screen under the action of wave were analysed to understand the wave control performance due to porosity parameters. A boundary element model is developed to calculate problems of wave interaction with a porous screen structure. The numerical results from the present boundary element methods (BEM) are compared with series of experiments conducted in a rectangular tank with various baffle porosities and submerged depths.</p><p> </p>

Sign in / Sign up

Export Citation Format

Share Document