scholarly journals Vibration control of a linear flexible beam structure excited by multiple harmonics

2021 ◽  
Vol 9 (4B) ◽  
Author(s):  
Bassam A. Albassam ◽  
Keyword(s):  
Equations Of Motion ◽  
Superposition Principle ◽  
Nodal Point ◽  
Excitation Frequency ◽  
Stationary Points ◽  
Flexible Beam ◽  
Control Force ◽  
Algebraic Equations ◽  
Beam Structure ◽  
Control Forces

This paper deals with designing a control force to create nodal point(s) having zero displacement and/or zero slope at selected locations in a vibrating beam structure excited by multiple harmonic forces. It is shown that the steady state vibrations at desired points can be eliminated using applied control forces. The control forces design method is implemented using dynamic Green’s functions that transform the equations of motion from differential to algebraic equations, in which the resulting solution is analytic and exact. The control problem is greatly simplified by utilizing the superposition principle that leads to calculating the control forces to create node(s) for each excitation frequency independently. The calculated control forces can be realized using passive elements such as masses and springs connected to the beam having reaction forces equal to the calculated control forces. The effectiveness of the proposed method is demonstrated on various cases using numerical examples. Through examples, it was shown that creating node(s) with zero deflection, as well as zero slope, not only results in isolated stationary points, but also suppresses the vibrations along a wide region of the beam.

scholarly journals Creating Nodes at Selected Locations in a Harmonically Excited Structure Using Feedback Control and Green’s Function

2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Bassam A. Albassam
Keyword(s):  
Steady State ◽  
Feedback Control ◽  
Green’S Function ◽  
Green's Function ◽  
Nodal Point ◽  
Control Force ◽  
Velocity Measurements ◽  
Numerical Examples ◽  
Control Forces

The paper deals with designing a control force to create nodal point(s) having zero displacements and/or zero slopes at selected locations in a harmonically excited vibrating structure. It is shown that the steady-state vibrations at desired points can be eliminated using feedback control forces. These control forces are constructed from displacement and/or velocity measurements using sensors located either at the control force position or at some other locations. Dynamic Green’s function is exploited to derive a simple and exact closed from expression for the control force. Under a certain condition, this control force can be generated using passive elements such as springs and dampers. Numerical examples demonstrate the applicability of the method in various cases.

Theoretical and Experimental Investigation of an L-Shape Beam Structure

2008 ◽  
Author(s):  
Dong-Xing Cao ◽  
Wei Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Space Station ◽  
Dynamic Responses ◽  
Flexible Beam ◽  
Beam Structure ◽  
Large Space ◽  
Chaotic Motions ◽  
Experimental Apparatus

Flexible multi-beam structures are significant components of large space station, architecture engineering and other structural systems. The understanding of the dynamic characteristics of these structures is essential for their design and control of vibrations. In this paper, the planar nonlinear vibrations and chaotic dynamics of an L-shape flexible beam structure will be investigated using theoretical and experimental methods. The L-shape beam structure considered here is composed of two flexible beams with right-angle. The governing equations of motion for the L-shape beam structure are established firstly. Then, the method of multiple scales is utilized to obtain a four-dimensional averaged equation. Numerical method is used to analyze the nonlinear dynamic responses and chaotic motions. Finally, The experimental apparatus and schemes for measuring the amplitude of nonlinear vibrations for the L-shape beam structure are introduced briefly. Then, the detailed analysis for experimental data and signals which represent the nonlinear responses of the beam structure are given.

A Lyapunov-Based Piezoelectric Controller for Flexible Cartesian Robot Manipulators

2004 ◽  
Vol 126 (2) ◽  
pp. 347-358 ◽  
Author(s):  
Mohsen Dadfarnia ◽  
Nader Jalili ◽  
Bin Xian ◽  
Darren M. Dawson
Keyword(s):  
Robot Manipulator ◽  
Experimental Testing ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Control Voltage ◽  
Linear Actuator ◽  
Flexible Beam ◽  
Control Force ◽  
Cross Sectional ◽  
Infinite Dimensional

A Lyapunov-based control strategy is proposed for the regulation of a Cartesian robot manipulator, which is modeled as a flexible cantilever beam with a translational base support. The beam (arm) cross-sectional area is assumed to be uniform and Euler-Bernoulli beam theory assumptions are considered. Moreover, two types of damping mechanisms; namely viscous and structural dampings, are considered for the arm material properties. The arm base motion is controlled utilizing a linear actuator, while a piezoelectric (PZT) patch actuator is bonded on the surface of the flexible beam for suppressing residual beam vibrations. The equations of motion for the system are obtained using Hamilton’s principle, which are based on the original infinite dimensional distributed system. Utilizing the Lyapunov method, the control force acting on the linear actuator and control voltage for the PZT actuator are designed such that the base is regulated to a desired set-point and the exponential stability of the system is attained. Depending on the composition of the controller, some favorable features appear such as elimination of control spillovers, controller convergence at finite time, suppression of residual oscillations and simplicity of the control implementation. The feasibility of the controller is validated through both numerical simulations and experimental testing.

scholarly journals Thermally induced vibration suppression in a thermoelastic beam structure

2021 ◽  
pp. 82-82
Author(s):  
Kenan Yildirim
Keyword(s):  
Vibration Suppression ◽  
Initial Boundary ◽  
Control Force ◽  
Beam Structure ◽  
Thermally Induced ◽  
Distributed Parameters ◽  
Thermoelastic Beam ◽  
Thermally Induced Vibrations ◽  
Control Forces ◽  
Objective Functional

In this paper, the problem of thermally induced vibration suppression in a thermoelastic beam is studied. Physical equivalent of the present problem is that a thermoelastic beam is suddenly entering into daylight zone and vibrations are induced due to heating on the upper surface of the beam or thermoelastic beam in a spacecraft enters to intensive sunlight area just after leaving a shadow of a planet. Thermally induced vibrations are suppressed by means of minimum using of control forces to be applied to dynamic space actuators. Objective functional of the problem is chosen as a modified quadratical functional of the kinetic energy of the thermoelastic beam. Necessary optimality condition to be satisfied by an optimal control force is derived in the form of maximum principle, which converts the optimal vibration suppression problem to solving a system of distributed parameters system linked by initial-boundary-terminal conditions. Solution of the system is achieved via MATLAB? and simulated results reveal that thermally induced vibration suppression by means of dynamic space actuators are very effective and robust.

Optimized Modeling of Flexible Beam Structure with Pole-Zero Estimation

2019 ◽  
Vol 13 (3) ◽  
pp. 148
Author(s):  
Rickey Pek Eek Ting ◽  
Intan Zaurah Mat Darus ◽  
Shafishuhaza Sahlan ◽  
Mat Hussin Ab Talib
Keyword(s):  
Flexible Beam ◽  
Beam Structure

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

Vibration control of a flexible beam structure using squeeze-mode ER mount

2004 ◽  
Vol 273 (1-2) ◽  
pp. 185-199 ◽  
Author(s):  
W.J. Jung ◽  
W.B. Jeong ◽  
S.R. Hong ◽  
S.-B. Choi
Keyword(s):  
Vibration Control ◽  
Flexible Beam ◽  
Beam Structure

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Sign in / Sign up

Export Citation Format

Share Document