Autoparametric Resonances of Elastic Structures Coupled With Two Sloshing Modes in a Square Liquid Tank

2011 ◽  
Author(s):  
Takashi Ikeda ◽  
Masaki Takashima ◽  
Yuji Harata
Keyword(s):  
Vibration Suppression ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Liquid Level ◽  
Tuned Liquid Damper ◽  
Response Curves ◽  
Small Deviations ◽  
Sloshing Mode ◽  
Linear Damping ◽  
Good Agreement

Nonlinear vibrations of an elastic structure coupled with liquid sloshing in a square tank subjected to vertical sinusoidal excitation are investigated. Previous studies examined the vibrations of a structure coupled with only one sloshing mode in a rectangular tank. However, square tanks are expected to work more efficiently as a vibration suppression device (Tuned Liquid Damper, TLD) because two sloshing modes, (1,0) and (0,1) modes, simultaneously appear when the internal resonance ratio 2:1:1 is satisfied. In reality, it is impossible to build a perfectly square tank. Therefore, a nearly square liquid tank is also considered when the tuning condition is slightly deviated. In the theoretical analysis, the fluid in the tank is assumed to be perfect. The modal equations of motion for seven sloshing modes are derived using Galerkin’s method, considering the nonlinear terms. The linear damping terms are then incorporated into the modal equations to consider the damping effect of sloshing. The frequency response curves are determined using van der Pol’s method (based on the harmonic balance method). From these response curves, the influences of the liquid level, the aspect ratio of the tank cross section, and the deviation of the tuning condition are investigated. For a square tank it is found that (1,0) and (0,1) modes are nonlinearly coupled. When the liquid level is high, there are three patterns for sloshing: (I) both (1,0) and (0,1) sloshing modes appear at identical amplitudes; (II) these two modes appear at different amplitudes; and (III) either (1,0) or (0,1) mode appears. Compared with the performance of a rectangular TLD, a square TLD works more efficiently when the liquid level is low. Small deviations of the tuning condition may cause amplitude modulated motion to appear. Bifurcation sets are also calculated to illustrate the influence of the system parameters on the performance of the TLD. Experiments were also conducted in order to confirm the validity of the theoretical results. These results were in good agreement with the experimental data.

Autoparametric Resonances of Elastic Structures Coupled With Two Sloshing Modes in a Square Liquid Tank

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Takashi Ikeda ◽  
Masaki Takashima ◽  
Yuji Harata
Keyword(s):  
Equations Of Motion ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Liquid Level ◽  
Response Curves ◽  
Small Deviations ◽  
Tuned Liquid Dampers ◽  
Linear Damping ◽  
Liquid Dampers ◽  
Good Agreement

Nonlinear vibrations of an elastic structure coupled with liquid sloshing in a square tank subjected to vertical sinusoidal excitation are investigated. In the theoretical analysis, the ratios of the natural frequencies of the structure and two sloshing modes satisfy 2:1:1. The equations of motion for the structure and seven sloshing modes are derived using Galerkin’s method while considering the nonlinearity of sloshing. The linear damping terms are then incorporated into the modal equations to consider the damping effect of sloshing. The frequency response curves are determined using van der Pol’s method. The influences of the liquid level, the aspect ratio of the tank cross-section, the deviation of the tuning condition, and the excitation amplitude are investigated. When the liquid level is high, and depending on the excitation frequency, there are three patterns of sloshing: (i) both (1,0) and (0,1) sloshing modes appear at identical amplitudes; (ii) these two modes appear at different amplitudes; and (iii) either (1,0) or (0,1) mode appears. Small deviations of the tuning condition may cause Hopf bifurcations to occur followed by amplitude modulated motion including chaotic vibrations. Bifurcation sets are also calculated to illustrate the influence of the system parameters on the response of the system. It is found that for low liquid levels, square tuned liquid dampers (TLDs) work more effectively than rectangular TLDs. Experiments were also conducted in order to confirm the validity of the theoretical results and were in good agreement with the experimental data.

Vibration Suppression of Flexible Structures Utilizing Internal Resonance of Liquid Sloshing in a Nearly Square Tank

2010 ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Flexible Structures ◽  
Harmonic Excitation ◽  
Liquid Sloshing ◽  
Maximum Efficiency ◽  
Tuned Liquid Damper ◽  
Response Curves

This paper proposes a new idea to utilize the internal resonance of two different sloshing modes in a nearly square tank when used as a tuned liquid damper (TLD). This idea results in achieving higher efficiency of vibration suppression for flexible structures subjected to horizontal harmonic excitation. Namely, the two sloshing modes (1, 0) and (0, 1) in a nearly square tank are degenerated and hence their natural frequencies are nearly equal with each other. Because the two predominant sloshing modes are nonlinearly coupled, internal resonance is expected to occur. Galerkin’s method is used to determine the modal equations of motion for liquid sloshing. Then, van der Pol’s method is used to determine the expressions of the frequency response curves. Frequency response curves and bifurcation sets are numerically calculated. From these results, the optimal values of the size and instillation angle of the tank can be determined in order to achieve maximum efficiency of vibration suppression in a flexible structure. Experiments confirmed the validity of the theoretical analysis.

On the Nonlinear Vibration Analysis of a Hand-Held Impact Machine

2020 ◽  
Author(s):  
Oreoluwa Alabi ◽  
Oumar Barry
Keyword(s):  
Analytical Solution ◽  
Prolonged Exposure ◽  
Vibration Suppression ◽  
Single Point ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Design Parameters ◽  
Nonlinear Stiffness ◽  
Impact Machine ◽  
Direct Numerical Integration

Abstract Prolonged exposure of the human arm to vibrations from hand-held impact (HIM) tools can be hazardous as such, it is important that the level of vibration suppression in HIMs is improved. This paper sought to address this issue by studying a model of the hand-arm system (HAS) coupled to a HIM which is also coupled to a nonlinear tuned vibration absorber inerter (NVAI). The HAS is modelled as a 2-DOF system coupled to the HIM at a single point. The HIM is modelled as an oscillator with linear damping, and both linear and nonlinear stiffnesses. The nonlinear stiffness of the HIM is introduced to represent the nonlinearities introduced by the vibro-impact dynamics of the HIM. After obtaining the equations of motion for the system, an analytical solution is obtained using the harmonic balance method. The analytical solution is validated using direct numerical integration and the results show very good agreement. The performance of the NVAI is compared to those of the classical nonlinear and linear vibration absorbers. Parametric study is carried out to examine the role of key design parameters, such as the damping of the absorber, nonlinear stiffness of the HIM and inertance of the NVAI, on the performance of the NVAI.

Blade Vibration Suppression Using Friction Elements in Shrouding

2011 ◽  
Author(s):  
Michal Hajzˇman ◽  
Miroslav Byrtus ◽  
Vladimi´r Zeman
Keyword(s):  
Numerical Integration ◽  
Nonlinear Equations ◽  
Harmonic Balance ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Blade Vibration ◽  
Friction Element ◽  
Nonlinear Equations Of Motion

The problem of two blades with a friction element is studied in order to analyze the effects of the friction on the undesirable vibration suppression. The simplified contact model between friction planes of the blade shrouding and the friction element is derived to be a fast computational tool comparing with a time-consuming finite element solution. The harmonic balance method is suitable for the linearization of originally nonlinear equations of motion under certain assumptions given on the excitation of the system and on its dynamic response. On the other hand the nonlinear equations of motion can be solved directly by their numerical integration, which is more time-consuming but it is not limited by given assumptions. The comparison of results of the harmonic balance method and of the numerical integration of motion equations is given in the paper.

Vibration Control of 2DOF Structures Utilizing Sloshing in Square Tanks

2012 ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Shota Ninomiya
Keyword(s):  
Aspect Ratio ◽  
Vibration Control ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Tuned Liquid Damper ◽  
Response Curves ◽  
Chaotic Motions ◽  
Installation Angle ◽  
Theoretical Results

This paper investigates the vibration control of a tower-like structure utilizing a square tuned liquid damper (TLD) when the structure is subjected to horizontal, harmonic excitation. In the theoretical analysis, when the tuning condition, 1:1:1:1, is satisfied, the natural frequencies of the 2DOF structure and two predominate sloshing modes are nearly equal. Galerkin’s method is used to derive the modal equations of motion for sloshing. The nonlinearity of the hydrodynamic force due to sloshing is considered in the equations of motion for the 2DOF structure. Linear viscous damping terms are incorporated into the modal equations to consider the damping effect of sloshing. Van der Pol’s method is employed to determine the frequency response curves which are compared to the numerical simulation. The influences of the excitation frequency, the tank installation angle, and the aspect ratio of the tank cross-section on the response curves are examined. The theoretical results show that whirling motions and amplitude modulated motions (AMMs) including chaotic motions may occur in the structure because swirl motions and Hopf bifurcations followed by AMMs appear in the tank. It is also found that square TLDs work more efficiently than conventional rectangular TLDs, and its performance is further improved when the aspect ratio is slightly increased and the installation angle is equal to zero. Experiments were conducted in order to confirm the validity of the theoretical results.

scholarly journals Multipoint Wave Measurement in Tuned Liquid Damper Using Laser Doppler Vibrometer and Stepwise Rotating Galvanometer Scanner

Sensors ◽  
2021 ◽  
Vol 21 (24) ◽  
pp. 8211
Author(s):  
Yoon-Soo Shin ◽  
Junhee Kim
Keyword(s):  
Natural Frequency ◽  
Vibration Suppression ◽  
Laser Doppler Vibrometer ◽  
Laser Doppler ◽  
Liquid Level ◽  
Tuned Liquid Damper ◽  
Tuned Liquid Dampers ◽  
Liquid Dampers ◽  
Tuning Frequency ◽  
Galvanometer Scanner

Liquid dampers, such as tuned liquid dampers (TLDs), are employed to improve serviceability by reducing wind-affected building vibrations. In order to maximize the vibration suppression efficiency of the liquid damper, the tuning frequency of the liquid damper should match the natural frequency of the building. Experimental evaluation of the tuning frequency of a liquid damper performed in a factory prior to installation in a building is a critical task to ensure correct performance, and for this, multipoint measurement of the TLD is required. In this study, a novel liquid level measurement system combining Laser Doppler Vibrometer (LDV) and a stepwise rotating galvanometer scanner was developed to observe liquid sloshing in TLD. The proposed system can measure the liquid level at multiple points simultaneously with a single laser point. In the experimental phase, the liquid damper’s natural frequency and mode shape are experimentally evaluated utilizing the developed system. The performance of the proposed system was verified by comparison with the video sensing system.

Nonlinear liquid sloshing in a square tank subjected to obliquely horizontal excitation

2012 ◽  
Vol 700 ◽  
pp. 304-328 ◽  
Author(s):  
Takashi Ikeda ◽  
Raouf A. Ibrahim ◽  
Yuji Harata ◽  
Tasuku Kuriyama
Keyword(s):  
Theoretical Analysis ◽  
Frequency Response ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Frequency Range ◽  
Response Curves ◽  
Chaotic Motions ◽  
Nonlinear Responses ◽  
Good Agreement

AbstractNonlinear responses of surface waves in rigid square and nearly square tanks partially filled with liquid subjected to obliquely horizontal, sinusoidal excitation are investigated theoretically and experimentally. Two predominant modes of sloshing are significantly coupled nonlinearly because their natural frequencies are nearly identical resulting in 1:1 internal resonance. Therefore, if only one of these modes is directly excited, the other mode is indirectly excited due to the nonlinear coupling. In the nonlinear theoretical analysis, the modal equations of motion are derived for the two predominant sloshing modes as well as five higher sloshing modes. The linear viscous terms are incorporated in order to consider the damping effect of sloshing. The expressions for the frequency response curves are determined using van der Pol’s method. The influences of the excitation direction and the aspect ratio of the tank cross-section on the frequency response curves are numerically examined. Planar and swirl motions of sloshing, and Hopf bifurcations followed by amplitude modulated motions including chaotic motions, are predicted when the excitation frequency is close to one of the natural frequencies of the two predominant sloshing modes. Lyapunov exponents are calculated and reveal the excitation frequency range over which liquid chaotic motions occur. In addition, bifurcation sets are shown to clarify the influences of the parameters on the change in the structural stability. The theoretically predicted results are in good agreement with the measured data, thus the theoretical analysis was experimentally validated.

Response of an Annular Tuned Liquid Damper Equipped With Damping Screens

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
K. P. McNamara ◽  
J. S. Love ◽  
M. J. Tait ◽  
T. C. Haskett
Keyword(s):  
Wind Turbine ◽  
Mechanical Model ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Tuned Liquid Damper ◽  
Equivalent Mechanical Model ◽  
Sloshing Mode ◽  
Force Excitation ◽  
Mode Response ◽  
Good Agreement

Abstract Annular tuned liquid dampers (TLDs) may be installed in slender structures with limited floor space, in which people and utilities must pass through the core, such as a wind turbine or observation tower. This study investigates an annular-shaped TLD equipped with damping screens. A linearized equivalent mechanical model capable of capturing the fundamental sloshing mode response of an annular TLD is presented. An experimental shake table testing program is completed to assess the performance of the model. Thirty-six frequency sweep tests consisting of various TLD configurations, excitation amplitudes, and excitation directions are completed. Good agreement is observed between the linearized equivalent mechanical model and experimental wave heights, sloshing forces, and energy dissipated per cycle that have been filtered to include only the fundamental sloshing mode response. The model is also observed to be in good agreement with experimental data for different excitation directions. The model is coupled to a generalized structure to investigate the response of a structure equipped with an annular TLD. The annular TLD is found to reduce the response of a generalized offshore wind turbine structure undergoing harmonic force excitation. The annular TLD provides performance comparable to an optimal linear tuned mass damper (TMD) with the same properties for a range of force excitation amplitudes.

scholarly journals Displacement Transmissibility Characteristics of Harmonically Base Excited Damper Isolators with Mixed Viscous Damping

2013 ◽  
Vol 20 (5) ◽  
pp. 921-931 ◽  
Author(s):  
Xiaojuan Sun ◽  
Jianrun Zhang
Keyword(s):  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Viscous Damping ◽  
Damping Force ◽  
Response Characteristics ◽  
Damping Characteristics ◽  
Linear Damping ◽  
Frequency Ratios ◽  
Good Agreement

The viscous damping force in the mixed form asfd(x˙)=c1x˙+c2|x˙|x˙can well describe damping characteristics of isolators and dampers in many cases. In this paper, performance characteristics of single-degree-of-freedom (SDOF) linear-stiffness isolators with mixed and piecewise mixed viscous damping are analytically examined under harmonic base excitation. Based on the first-order harmonic balance method (HBM), both relative and absolute displacement transmissibility expressions with the equivalent linear damping coefficient (ELDC) are given. And the analytical calculations show good agreement with the numerical results. Also, the influence of nonlinear damping on the response characteristics is investigated by comparing the transmissibility of linear and nonlinear systems. The resonant frequency always shifts to a lower value as the nonlinear damping component of the forcefd(x˙)=c1x˙+c2|x˙|x˙becomes stronger, and when the damping ratio in the corresponding linear model is relatively high, the relative transmissibility decreases at frequencies higher than the resonance frequency of the corresponding linear damping system and the absolute one increases for the frequency ratios above2. Finally, the displacement transmissibility of a nonlinear isolator with piecewise mixed viscous damping is discussed and the process shows research similarity with the non-piecewise case.

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Primary System ◽  
Lumped Mass ◽  
Response Curves ◽  
Internal Resonances ◽  
The One

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

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