Active Damping of Vibrations of a Cantilever Beam by Axial Force Control

2007 ◽  
Author(s):  
Thomas Pumho¨ssel ◽  
Horst Ecker
Keyword(s):  
Cantilever Beam ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Open Loop ◽  
Active Damping ◽  
Nonlinear Feedback ◽  
Euler Beam ◽  
Bending Vibrations ◽  
Loop Control ◽  
Damping Of Vibrations

In several fields, e.g. aerospace applications, robotics or the bladings of turbomachinery, the active damping of vibrations of slender beams which are subject to free bending vibrations becomes more and more important. In this contribution a slender cantilever beam loaded with a controlled force at its tip, which always points to the clamping point of the beam, is treated. The equations of motion are obtained using the Bernoulli-Euler beam theory and d’Alemberts principle. To introduce artificial damping to the lateral vibrations of the beam, the force at the tip of the beam has to be controlled in a proper way. Two different methods are compared. One concept is the closed-loop control of the force. In this case a nonlinear feedback control law is used, based on axial velocity feedback of the tip of the beam and a state-dependent amplification. By contrast, the concept of open-loop parametric control works without any feedback of the actual vibrations of the mechanical structure. This approach applies the force as harmonic function of time with constant amplitude and frequency. Numerical results are carried out to compare and to demonstrate the effectiveness of both methods.

Vibration Analysis of a Partially Covered Double Sandwich Cantilever Beam With Concentrated Mass at the Free End

1993 ◽  
Author(s):  
C. Levy ◽  
Q. Chen
Keyword(s):  
Loss Factor ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Physical Parameters ◽  
Mass Ratio ◽  
Euler Beam ◽  
Concentrated Mass ◽  
Sandwich Type ◽  
Euler Beam Theory ◽  
Two Parameters

Abstract The partially covered, sandwich-type cantilever with concentrated mass at the free end is studied. The equations of motion for the system modeled via Euler beam theory are derived and the resonant frequency and loss factor of the system are analyzed. The variations of resonance frequency and system loss factor for different geometrical and physical parameters are also discussed. Variation of these two parameters are found to strongly depend on the geometrical and physical properties of the constraining layers and the mass ratio.

Nonlinear Dynamic Modeling of Elastic Beam Fixed on a Moving Cart and Carrying Lumped Tip Mass Subjected to External Periodic Force

2009 ◽  
Author(s):  
Fadi A. Ghaith
Keyword(s):  
Linear Model ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Open Loop ◽  
Beam Deflection ◽  
Mode Shapes ◽  
Euler Beam ◽  
Periodic Force ◽  
Assumed Mode Method ◽  
Tip Mass

In the present work, a Bernoulli – Euler beam fixed on a moving cart and carrying lumped tip mass subjected to external periodic force is considered. Such a model could describe the motion of structures like forklift vehicles or ladder cars that carry heavy loads and military airplane wings with storage loads on their span. The nonlinear equations of motion which describe the global motion as well as the vibration motion were derived using Lagrangian approach under the inextensibility condition. In order to investigate the influence of the axial movement of the cart on the response of the system, unconstrained modal analysis has been carried out, and accurate mode shapes of the beam deflection were obtained. The assumed mode method was utilized for approximating the beam elastic deformation based on the single unconstrained mode shapes. Numerical simulation has been carried out to estimate the open-loop response of the nonlinear beam-mass-cart model as well as for the simplified linear model under the influence of the periodic excitation force. Also a comparison study between the responses of the linear and nonlinear models was established. It was shown that the maximum values of the beam tip deflection estimated from the nonlinear model are lower than the corresponding values obtained via the linear model, which reveals the importance of considering nonlinear hardening term in formulating the equations of motion for such system in order to come with more accurate and reliable model.

Controllable Truss-Frame Nodes in Semi-Active Damping of Vibrations

2016 ◽  
Vol 101 ◽  
pp. 89-94 ◽  
Author(s):  
Blazej Poplawski ◽  
Cezary Graczykowski ◽  
Łukasz Jankowski
Keyword(s):  
Cantilever Beam ◽  
Control Strategy ◽  
Strain Energy ◽  
Vibration Mode ◽  
Vibration Damping ◽  
Active Damping ◽  
Active Management ◽  
Complex Structures ◽  
Published Research ◽  
Damping Of Vibrations

In recent years, vibration damping strategies based on semi-active management of strain energy have attracted a large interest and were proven highly effective. However, most of published research considers simple one degree of freedom systems or study the same basic example (the first vibration mode of a cantilever beam) with the same control strategy. This contribution focuses on truss-frame nodes with controllable moment-bearing ability. It proposes and tests an approach that allows the control strategy to be extended to more complex structures and vibration patterns.

scholarly journals Vibrations of a Beam Moving Over Supports with Clearance

1994 ◽  
Vol 1 (6) ◽  
pp. 549-557
Author(s):  
H.P. Lee
Keyword(s):  
Piecewise Linear ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Euler Beam ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Euler Beam Theory ◽  
The Stability ◽  
Effect Of Support ◽  
Piecewise Linear Stiffness

The transverse vibration of a beam moving over two supports with clearance is analyzed using Euler beam theory. The equations of motion are formulated based on a Lagrangian approach and the assumed mode method. The supports with clearance are modeled as frictionless supports with piecewise-linear stiffness. A feature of the present formulation is that its complexity does not increase with increased number of supports. Results of numerical simulations are presented for various prescribed motions of the beam. The effect of support clearance on the stability of the beam is investigated.

scholarly journals High performance open loop control of scanning with a small cylindrical cantilever beam

2011 ◽  
Vol 330 (8) ◽  
pp. 1762-1771 ◽  
Author(s):  
Matthew J. Kundrat ◽  
Per G. Reinhall ◽  
Cameron M. Lee ◽  
Eric J. Seibel
Keyword(s):  
Cantilever Beam ◽  
High Performance ◽  
Open Loop ◽  
Open Loop Control ◽  
Loop Control

Frictional Impact-Contacts in Multiple Flexible Links

2021 ◽  
pp. 2150075
Author(s):  
M. Ahmadizadeh ◽  
A. M. Shafei ◽  
R. Jafari
Keyword(s):  
Differential Equations ◽  
Recursive Algorithm ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Open Loop ◽  
Mode Shapes ◽  
Special Treatment ◽  
Exact Moment ◽  
Impact Phase ◽  
The Impact

Multiple impacts of 2D (planar) open-loop robotic systems composed of [Formula: see text] elastic links and revolute joints are studied in this paper. The dynamic equations of motion for such systems are derived by the Gibbs-Appell recursive algorithm, while the regularized method is employed to model the impact-contact mechanism. The Timoshenko beam theory is used to model the transverse vibrations of the links. Also, both the structural damping and air damping are considered to enhance the modeling accuracy. The system joints are assumed to be frictionless and slack-free, but friction force is included for the links colliding with the ground. The [Formula: see text]-flexible-link system considered goes through a flight phase and an impact phase during its motion. In the impact phase, new equations of motion are derived by including the terms caused by the viscoelastic forces in the system’s differential equations. Owing to the extremely short acting time of the impact force, the related differential equations can be solved only via special treatment, i.e. by detecting the exact moment of impact. To this end, entering or leaving the impact phase is analyzed and controlled with high precision by a special computational algorithm presented in this work. To demonstrate the efficacy and precision of the algorithm developed, computer simulations are conducted to study the dynamic behavior of a 3-link robotic mechanism. To investigate the effect of mode shape on the elastic deformation of links, four different mode shapes are used in the simulations and their results are compared.

Experimental Results on Parametric Excitation Damping of an Axially Loaded Cantilever Beam

2009 ◽  
Author(s):  
Horst Ecker ◽  
Thomas Pumho¨ssel
Keyword(s):  
Cantilever Beam ◽  
Parametric Excitation ◽  
Vibration Suppression ◽  
Excitation Frequency ◽  
Open Loop ◽  
Piezo Actuator ◽  
Combination Frequency ◽  
Bending Vibrations ◽  
Periodic Force ◽  
Parametrically Excited

In various fields of engineering, e.g. aerospace applications, robotics or the bladings of turbomachinery, slender beam-like structures are in use and subject to free bending vibrations. Since such vibrations often are not wanted because they may degrade the performance or function of the structure, it is important to have a suitable means of vibration suppression available. In this experimental study we investigate a slender cantilever beam loaded with a controlled force at its tip. The force is always oriented towards the clamping point of the beam and generated by a piezo-actuator. Force control is based on an open-loop control without feedback from the structure. To enhance vibration suppression we take advantage of the additional damping observed when a periodic force modulation at a certain frequency is applied. From several theoretical studies it is known that parametrically excited systems show increased stability, and therefore enhanced damping properties, when the parametric excitation frequency is chosen near a certain combination frequency. Due to the almost axially applied force the cantilever beam system becomes a parametrically excited system and the effect mentioned can be observed. Numerous measurement runs have been carried out and vibration suppression as a function of the excitation frequency, the excitation amplitude and the beam initial deflection has been investigated. The results are in very good agreement with theoretical predictions and for the first time the numerical and analytical results obtained earlier are confirmed by experimental work.

Transverse Vibrations of a Rotating Twisted Timoshenko Beam Under Axial Loading

1993 ◽  
Vol 115 (3) ◽  
pp. 285-294 ◽  
Author(s):  
W.-R. Chen ◽  
L. M. Keer
Keyword(s):  
Timoshenko Beam ◽  
Twist Angle ◽  
Equations Of Motion ◽  
Axial Loading ◽  
Beam Theory ◽  
The Finite Element Method ◽  
Bending Vibrations ◽  
Parametric Studies ◽  
General Eigenvalue Problem ◽  
Twisted Beam

Transverse bending vibrations of a rotating twisted beam subjected to an axial load and spinning about its axial axis are established by using the Timoshenko beam theory and applying Hamilton’s Principle. The equations of motion of the twisted beam are derived in the twist nonorthogonal coordinate system. The finite element method is employed to discretize the equations of motion into time-dependent ordinary differential equations that have gyroscopic terms. A symmetric general eigenvalue problem is formulated and used to study the influence of the twist angle, rotational speed, and axial force on the natural frequencies of Timoshenko beams. The present model is useful for the parametric studies to understand better the various dynamic aspects of the beam structure affecting its vibration behavior.

Nonlinear Vibration Analysis of Elastic Four-Bar Linkages

1974 ◽  
Vol 96 (2) ◽  
pp. 411-419 ◽  
Author(s):  
J. P. Sadler ◽  
G. N. Sandor
Keyword(s):  
Equations Of Motion ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Bending Vibrations ◽  
Elastic Bending ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Nonlinear Equations Of Motion ◽  
Four Bar Linkage ◽  
Euler Bernoulli Beam

A method of kineto-elastodynamic analysis is developed employing lumped parameter models for simulating moving mechanism components subject to elastic bending vibrations. The mechanism analyzed is the general planar four-bar linkage and the analytical model includes the response coupling associated with both the transmission of forces at the pin joints and the dependence of the undeformed motion of a link on the elastic motion of other links. Nonlinear equations of motion are derived by way of Euler-Bernoulli beam theory, and numerical solution of these equations is illustrated for specific examples. The model is suitable for the analysis of mechanisms with non-periodic motion and with nonuniform cross-section members.

Dynamics and Control of Single-Line Kites

2006 ◽  
Vol 110 (1111) ◽  
pp. 615-621 ◽  
Author(s):  
G. Sánchez
Keyword(s):  
Wind Velocity ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Open Loop ◽  
Single Line ◽  
Atmospheric Conditions ◽  
Loop Control ◽  
Loop Control System ◽  
Dynamics And Control ◽  
The Stability

Abstract This paper presents a dynamic analysis of a single-line kite with two degrees of freedom. A Lagrangian formulation is used to write convenient equations of motion. The equilibrium states of the system and their stability are studied; Eigenvalues and eigenmodes are calculated by using linear theory. The stability in the parametric plane δ – W0 is discussed, where δ defines the bridle geometry and W0 is wind velocity. The system goes through a Hopf bifurcation and periodic branches of solutions appear. The orbits and their stability have been calculated numerically using Floquet theory and wind velocity seems to play an important role in their existence. Finally the kite response against gusts is considered and an open loop control system developed to keep the flight altitude invariant under changing atmospheric conditions. Modifying the bridle’s geometry seems to be a convenient way to control a kite’s performance.

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