Small-Amplitude Periodic Motions of Rapidly Forced Mechanical Systems

2005 ◽  
Author(s):  
S. Weibel ◽  
J. Baillieul ◽  
T.J. Kaper
Keyword(s):  
Small Amplitude ◽  
Mechanical Systems ◽  
Periodic Motions

scholarly journals A Modeling of Unsteady Aerodynamic Forces Based on the Aerodynamic Analyses around a Simplified Car Model in Periodic Motions(Mechanical Systems)

2010 ◽  
Vol 76 (768) ◽  
pp. 2006-2015 ◽  
Author(s):  
Mitsuyoshi KAWAKAMI ◽  
Norikazu SATO ◽  
Peter ASCHWANDEN ◽  
Yoshihiro KATO ◽  
Masaki NAKAGAWA ◽  
...  
Keyword(s):  
Mechanical Systems ◽  
Periodic Motions ◽  
Aerodynamic Forces ◽  
Car Model ◽  
Unsteady Aerodynamic

Vibration Suppression of Rotating Machinery Utilizing an Automatic Ball Balancer and Discontinuous Spring Characteristics

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Jun Liu ◽  
Yukio Ishida
Keyword(s):  
Rotational Speed ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Critical Speed ◽  
Vibration Suppression ◽  
Rotating Machinery ◽  
Almost Periodic ◽  
Periodic Motions ◽  
Speed Range ◽  
Suppression Method

Automatic ball balancer is a balancing device where two balls inside a hollow rotor move to optimal rest positions automatically to eliminate unbalance. As a result, vibrations are suppressed to the zero amplitude in the rotational speed range higher than the major critical speed. However, it has the following defects. The amplitude of vibration increases in the rotational speed range lower than the major critical speed. In addition, almost periodic motions with large amplitude occur in the vicinity of the major critical speed due to the rolling of balls inside the rotor. Because of these defects, an automatic ball balancer has not been used widely. This paper proposes the vibration suppression method utilizing the discontinuous spring characteristics together with an automatic ball balancer to overcome these defects and to suppress vibration. The validity of the proposed method is confirmed theoretically, numerically, and experimentally. The results show that amplitude of vibration can be suppressed to a small amplitude in the vicinity of the major critical speed and the zero amplitude in the range higher than the major critical speed.

On generating pre-defined periodic motions in underactuated mechanical systems: the cart-pendulum example*

2011 ◽  
Vol 44 (1) ◽  
pp. 4588-4593 ◽  
Author(s):  
Leonid Freidovich ◽  
Francisco Gordillo ◽  
Anton Shiriaev ◽  
Fabio Gómez-Estern
Keyword(s):  
Mechanical Systems ◽  
Periodic Motions ◽  
Underactuated Mechanical Systems

Rain-Wind Induced Vibrations of a Simple Oscillator

2001 ◽  
Author(s):  
A. H. P. van der Burgh
Keyword(s):  
Linear Approximation ◽  
Cross Section ◽  
Wind Field ◽  
Small Amplitude ◽  
Aerodynamic Force ◽  
Circular Cross Section ◽  
Horizontal Cylinder ◽  
Periodic Motions ◽  
Stay Cables ◽  
Rain Drops

Abstract In this paper a relatively simple mechanical oscillator is considered which may be used to study rain-wind induced vibrations of stay cables of cable-stayed bridges. In recent publications mention is made of vibrations of (inclined) stay cables which are excited by a wind-field containing rain drops. The rain drops that hit the cables generate a rivulet on the surface of the cable. The presence of flowing water on the cable changes the cross section of the cable experienced by the wind-field. A symmetric flow pattern around the cable with circular cross section may became asymmetric due to the presence of the rivulet and may consequently induce a lift-force as a mechanism for vibration. During the motion of the cable the position of rivulet (s) may vary as the motion of the cable induces an additional varying aerodynamic force perpendicular to the direction of the wind-field. It seems not to easy to model this phenomenon: several author state that there is no model available y ct. The idea to model this problem is to consider a horizontal cylinder supported by springs in such a way that only one degree of freedom i.e. vertical vibrations are possible. We consider a ridge on the surface of the cylinder parallel to the axis of the cylinder. Let additionally the cylinder with ridge be able to oscillate, with small amplitude, around the axis such that the oscillationare excited by an external force. It may be clear that the small amplitude oscillations of the cylinder and hence of the ridge induce a varying lift and drag force. In this approach it is assumed that the motion of the ridge models the dynamics of the rivulet(s) on the cable. By using a quasi-steady approach to model the aerodynamic forces one arrives at a nonlinear second order equation displaying three different kinds of excitation mechanisms: self-excitation, parametric excitation and ordinary forcing. The firstresults of the analysis of the equation of motion show that even in a linear approximation for certain values of the parameters involved stable periodic motions are possible. In the relevant cases where in linear approximation unstable periodic motions are found, results of an analysis of the nonlinear equation are presented.

Vibration Suppression of Rotating Machinery Utilizing an Automatic Ball Balancer and Discontinuous Spring Characteristics

2007 ◽  
Author(s):  
Jun Liu ◽  
Yukio Ishida
Keyword(s):  
Rotational Speed ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Critical Speed ◽  
Vibration Suppression ◽  
Rotating Machinery ◽  
Almost Periodic ◽  
Periodic Motions ◽  
Speed Range ◽  
Suppression Method

Automatic ball balancer is a balancing device where two balls inside a hollow rotor move to optimal rest positions automatically to eliminate unbalance. As the result, vibrations are suppressed to a small amplitude or a zero amplitude in the rotational speed range higher than the major critical speed. However, it has the following defects. The amplitude of vibration increases in the rotational speed range lower than the major critical speed. In addition, almost periodic motions with large amplitude occur due to the rolling of balls inside the rotor in the vicinity of the major critical speed. Due to those defects, the automatic ball balancer has not been used widely. This paper proposes the vibration suppression method utilizing the discontinuous spring characteristics together with an automatic ball balancer to suppress vibration and to overcome these defects of the automatic ball balancer. The validity of proposed method is confirmed theoretically, numerically and experimentally. The results show that amplitude of vibration can be suppressed to a small amplitude in the vicinity of the major critical speed and the zero amplitude in the range higher than the major critical speed.

Nonlinear Phase-Based Oscillator to Generate and Assist Periodic Motions

2016 ◽  
Author(s):  
Juan De la Fuente ◽  
Thomas G. Sugar ◽  
Sangram Redkar ◽  
Andrew R. Bates
Keyword(s):  
Phase Angle ◽  
Nonlinear Oscillator ◽  
Mechanical Systems ◽  
Oscillatory Behavior ◽  
Periodic Motions ◽  
Nonlinear Phase ◽  
Forcing Function ◽  
Hip Motion ◽  
The Stability ◽  
Bendixson Criterion

Oscillatory behavior is important for tasks such as walking and running. We are developing methods to add energy to enhance or vary the oscillatory behavior based on the system’s phase angle. We define a nonlinear oscillator using a forcing function based on the sine and cosine of the system’s phase angle that can modulate the amplitude and frequency of oscillation. The stability of the system is proved using the Poincaré-Bendixson criterion. Linear and rotational mechanical systems are simulated using our phase controller. The method is implemented and tested to control a pendulum. Lastly, we propose how to assist hip motion during walking using the phase-based forcing function.

scholarly journals On subharmonic motions of a pendulum in a movable platform

2019 ◽  
Vol 486 (5) ◽  
pp. 547-553
Author(s):  
A. P. Markeev
Keyword(s):  
Small Amplitude ◽  
Linear Problem ◽  
Relative Equilibria ◽  
Unperturbed System ◽  
Periodic Motions ◽  
Rotating Platform ◽  
Stability Change ◽  
Existence And Stability ◽  
Movable Platform ◽  
Splitting Of Separatrices

The motion of a pendulum on a rotating platform is investigated in the presence of disturbances caused by its vertical harmonic oscillations of small amplitude. The parameters of the unperturbed system are considered close to the values, upon passing through which the number of relative equilibria of the pendulum and the nature of their stability change. The non-linear problem of the existence and stability of periodic motions of the pendulum relative to the platform with a period multiple to the period of its vertical oscillations is solved. The question of the splitting of separatrices of the unperturbed system is also considered.

scholarly journals A harmonic balance approach for designing compliant mechanical systems with nonlinear periodic motions

2020 ◽  
Vol 39 (6) ◽  
pp. 1-14
Author(s):  
Pengbin Tang ◽  
Jonas Zehnder ◽  
Stelian Coros ◽  
Bernhard Thomaszewski
Keyword(s):  
Harmonic Balance ◽  
Mechanical Systems ◽  
Periodic Motions ◽  
Balance Approach
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