Pendulum as Vibration Absorber for Flexible Structures: Experiments and Theory

1996 ◽  
Vol 118 (4) ◽  
pp. 558-566 ◽  
Author(s):  
O. Cuvalci ◽  
A. Ertas
Keyword(s):  
Energy Transfer ◽  
Coupling Effect ◽  
Equations Of Motion ◽  
Flexible Structures ◽  
Experimental Results ◽  
Vibration Absorber ◽  
Pendulum System ◽  
Nonlinear Equations Of Motion ◽  
Tip Mass ◽  
Sinusoidal Excitation

The dynamic response of a beam-tip mass-pendulum system subjected to a sinusoidal excitation is investigated. A simple pendulum mounted to a tip mass of a beam is used as a vibration absorber. The nonlinear equations of motion are developed to investigate the autoparametric interaction between the first two modes of the system. The nonlinear terms appear due to the curvature of the beam and the coupling effect between the beam and pendulum. Complete energy transfer between modes is shown to occur when the beam frequency is twice the pendulum frequency. Experimental results are compared with a theoretical solution obtained using numerical integration. The experimental results are in qualitative agreement with the theory.

On the Parametric Excitation of Pendulum-Type Vibration Absorber

1961 ◽  
Vol 28 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Energy Transfer ◽  
Numerical Solution ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Absorber ◽  
Single Cycle ◽  
Linearized System ◽  
Nonlinear Equations Of Motion ◽  
Beam Oscillation ◽  
Energy Interchange

The free motion of an undamped pendulum-type vibration absorber is studied on the basis of approximate nonlinear equations of motion. It is shown that this type of mechanical system exhibits the phenomenon of auto parametric excitation; a type of “instability” which cannot be accounted for on the basis of the linearized system. Complete energy transfer between modes is shown to occur when the beam frequency is twice the simple pendulum frequency. On the basis of a numerical solution, approximately 150 cycles of the beam oscillation take place during a single cycle of energy interchange.

The Gyroscopic Vibration Absorber

1967 ◽  
Vol 89 (4) ◽  
pp. 706-712
Author(s):  
Robert Jones
Keyword(s):  
Linear Function ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Vibration Absorber ◽  
Variable Frequency ◽  
Equivalent Weight ◽  
Support Structure ◽  
Linearized Equations ◽  
Vibration Excitation ◽  
Analytical Results

The linearized equations of motion of the gyroscopic vibration absorber are derived showing that the antiresonant frequency is a linear function of the speed of the gyroscopic disk; thus the gyroscopic vibration absorber (GVA) can be easily synchronized and therefore applied to vehicles and machinery having variable frequency vibration excitation. The effects on the antiresonant frequency from elastic restraint about the pivots and flexibility in the support structure are also examined. The bandwidth of the GVA is compared to a Frahm absorber of equivalent weight. Experimental results confirm the analytical results and show the feasibility of the GVA as a synchronous absorber.

Formulation of a Basic Building Block Model for Interaction of High Speed Vehicles on Flexible Structures

1989 ◽  
Vol 56 (2) ◽  
pp. 451-458 ◽  
Author(s):  
L. Vu-Quoc ◽  
M. Olsson
Keyword(s):  
Nonlinear Equations ◽  
Building Block ◽  
High Speed ◽  
Traditional Approach ◽  
Equations Of Motion ◽  
A Priori ◽  
Flexible Structures ◽  
Structural Deformation ◽  
Block Model ◽  
Nonlinear Equations Of Motion

In traditional analyses of vehicle/structure interaction, especially when there are constraints between vehicle masses and the structure, vehicle nominal motion is prescribed a priori, and therefore unaffected by the structure flexibility. In this paper, a concept of nominal motion is defined, and a methodology is proposed in which the above restriction is removed, allowing the vehicle nominal motion to become unknown, and encompassing the traditional approach as a particular case. General nonlinear equations of motion of a building block model, applicable to both wheel-on-rail and magnetically levitated vehicles, are derived. These equations are simplified to a set of mildly nonlinear equations upon introducing additional assumptions — essentially on small structural deformation. An example is given to illustrate the present formulation.

Dynamic Behavior of Unbalanced Rigid Shaft Supported on Turbulent Journal Bearings—Theory and Experiment

1990 ◽  
Vol 112 (2) ◽  
pp. 404-408 ◽  
Author(s):  
H. Hashimoto ◽  
S. Wada
Keyword(s):  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Experimental Results ◽  
Fluid Film ◽  
Force Components ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Analytical Expressions

In this paper, the combined effects of turbulence and fluid film inertia on the dynamic behavior of an unbalanced rigid shaft supported horizontally on two identical aligned short journal bearings are investigated theoretically and experimentally. Utilizing analytical expressions for the dynamic fluid film force components considering the effects of turbulence and fluid film inertia, the nonlinear equations of motion for the rotor-bearing systems are solved by the improved Euler’s forward integration method. The journal center trajectories with unbalance eccentricity ratio of εμ = 0, 0.1 and 0.2 are examined theoretically for Reynolds number of Re = 2750, 4580, and 5500, and the theoretical results are compared with experimental results. From the theoretical and experimental results, it was found that the fluid film inertia improves the stability of unbalanced rigid shaft under certain operating conditions.

Experimental Synchronization Study of the Gyroscopic Vibration Absorber

1974 ◽  
Vol 96 (3) ◽  
pp. 983-987
Author(s):  
J. E. Sneckenberger ◽  
H. W. Butler ◽  
In-Meei Neou
Keyword(s):  
Theoretical Consideration ◽  
Laboratory Tests ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Vibration Absorber ◽  
Governing Equations ◽  
Experimental Development ◽  
Moments Of Inertia ◽  
Excitation Frequencies

Analysis of the Gyroscopic Vibration Absorber (GVA) is made with a view to improve its effectiveness as a linear synchronous absorber. Theoretical consideration reveals that much of the nonlinearity of the governing equations of motion of the structure-absorber system involves terms containing an absorber parameter IE. The experimental development of a GVA for which this parameter is made to vanish by appropriate proportionment of certain absorber moments of inertia is shown to be feasible. Laboratory tests examining the nulling potential of this experimental GVA show that linear synchronization of the antiresonant frequency to the speed of the GVA rotor can be obtained for a wider range of excitation frequencies than when the absorber parameter is not equal to zero. Comparison of the experimental results with analytical predictions is also favorable.

Vibration Control of the Flexible Robotic Arm through Modal Interaction

2014 ◽  
Vol 490-491 ◽  
pp. 1142-1145
Author(s):  
Zhi Hui Gao ◽  
Bing Dong Liu ◽  
Bo Shan
Keyword(s):  
Vibration Control ◽  
Control Method ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Rigid Motion ◽  
Robotic Arm ◽  
Vibration Absorber ◽  
Modal Interaction ◽  
Flexible Arm ◽  
Nonlinear Equations Of Motion

A vibration control method is proposed to suppress nonlinear large vibration of the flexible robotic arm undergoing rigid motion. The method takes advantage of modal interaction and is implemented based on internal resonance. To attenuate vibration of the flexible arm, another vibrating system, consisting of a rigid link, a flexible joint and a damper, is introduced as a vibration absorber. Perturbation technique is used to study the transient response of the nonlinear equations of motion. Numerical simulation results preliminarily verify that the proposed control strategy is able to effectively reduce vibration of the flexible robotic arm.

Design of a slender turning cutting tool via a vibration absorber equipped with piezoelectric ceramic

2021 ◽  
pp. 107754632110144
Author(s):  
Yiqing Yang ◽  
Haoyang Gao ◽  
Qiang Liu
Keyword(s):  
Piezoelectric Ceramic ◽  
Cutting Tool ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Electrical Energy ◽  
Diameter Ratio ◽  
Vibration Absorber ◽  
Machined Surface ◽  
Structural Part ◽  
Machined Surface Roughness

Turning cutting tool with large length–diameter ratio has been essential when machining structural part with deep cavity and in-depth hole features. However, chatter vibration is apt to occur with the increase of tool overhang. A slender turning cutting tool with a length–diameter ratio of 7 is developed by using a vibration absorber equipped with piezoelectric ceramic. The vibration absorber has dual functions of vibration transfer to the absorber mass and vibration conversion to the electrical energy via the piezoelectric effect. Equations of motion are established considering the dual damping from the piezoelectric ceramic and rubber gasket. The equivalent damping of piezoelectric ceramic is derived, and the geometries are optimized to achieve optimal vibration suppression. The modal analysis demonstrates that the cutting tool with the vibration absorber can reach 80.1% magnitude reduction. Machining tests are carried out in the end. The machining acceleration and machined surface roughness validate the vibration suppression of the VA, and the output voltage by the piezoelectric ceramic demonstrates the ability of vibration sensing.

Less=Moor: A Time-Efficient Computational Tool to Assess the Behavior of Moored Ships in Waves

2017 ◽  
Author(s):  
Yijun Wang ◽  
Alex van Deyzen ◽  
Benno Beimers
Keyword(s):  
Dynamic Response ◽  
Research Effort ◽  
Equations Of Motion ◽  
Line Tension ◽  
Mooring Line ◽  
Induced Response ◽  
Wave Forces ◽  
Computational Tool ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion

In the field of port design there is a need for a reliable but time-efficient method to assess the behavior of moored ships in order to determine if further detailed analysis of the behavior is required. The response of moored ships induced by gusting wind and/or waves is dynamic. Excessive motion response may cause interruption of the (un)loading operation. High line tension may cause lines to snap, introducing dangerous situations. A (detailed) Dynamic Mooring Analysis (DMA), however, is often a time-consuming and expensive exercise, especially when responses in many different environmental conditions need to be assessed. Royal HaskoningDHV has developed a time-efficient computational tool in-house to assess the wave (sea or swell) induced dynamic response of ships moored to exposed berths. The mooring line characteristics are linearized and the equations of motion are solved in the frequency domain with both the 1st and 2nd wave forces taken into account. This tool has been termed Less=Moor. The accuracy and reliability of the computational tool has been illustrated by comparing motions and mooring line forces to results obtained with software that solves the nonlinear equations of motion in the time domain (aNySIM). The calculated response of a Floating Storage and Regasification Unit (FSRU) moored to dolphins located offshore has been presented. The results show a good comparison. The computational tool can therefore be used to indicate whether the wave induced response of ships moored at exposed berths proves to be critical. The next step is to make this tool suitable to assess the dynamic response of moored ships with large wind areas, e.g. container ships, cruise vessels, RoRo or car carriers, to gusting wind. In addition, assessment of ship responses in a complicated wave field (e.g. with reflected infra-gravity waves) also requires more research effort.

Sign in / Sign up

Export Citation Format

Share Document