Dynamic modelling and control of a rotating Euler–Bernoulli beam

2004 ◽  
Vol 274 (3-5) ◽  
pp. 863-875 ◽  
Author(s):  
J.B. Yang ◽  
L.J. Jiang ◽  
D.CH. Chen
Keyword(s):  
Dynamic Modelling ◽  
Bernoulli Beam ◽  
And Control ◽  
Euler Bernoulli Beam

Modeling and Control of a Nonlinear Beam

1993 ◽  
Author(s):  
H. T. Banks ◽  
Belinda B. King
Keyword(s):  
Linear Problem ◽  
Nonlinear Stiffness ◽  
Bernoulli Beam ◽  
Nonlinear Beam ◽  
Modeling And Control ◽  
Stiffness Properties ◽  
Linear Damping ◽  
And Control ◽  
Euler Bernoulli Beam ◽  
Nonlinear Analog

Abstract In this paper we develop a mathematical model for a nonlinear analog of the Euler-Bernoulli beam which possesses linear damping and nonlinear stiffness properties. This nonlinear model is used as a basis for approximation and linearization. Feedback design for the linear problem is applied to compute gains which are then used in the nonlinear system.

Vibration Analysis and Control of a Bridge Under Vehicular Random Excitation

2014 ◽  
Author(s):  
Firooz Bakhtiari-Nejad ◽  
Seyyed Mahdi Ostad Hosseyni ◽  
Mahnaz Shamshirsaz ◽  
Mahsan Bakhtiarinejad
Keyword(s):  
Control Algorithm ◽  
Coupled System ◽  
Random Excitation ◽  
System Response ◽  
Bernoulli Beam ◽  
Simply Supported ◽  
Moving Vehicles ◽  
Simple Support ◽  
And Control ◽  
Euler Bernoulli Beam

In this paper, vibration response of a bridge under vehicular loads has been analyzed and consequently been controlled by two actuators using active Neural Network (NN) control strategy. The bridge and the vehicles are modeled as a simply-supported Euler Bernoulli beam possessing a simple support precisely located at the middle and one-DOF vehicles respectively. With that goal, equations of the coupled system of the bridge and the vehicles are derived using Hamilton’s principle, and then randomness of vibrations transferred to the bridge due to the alternative velocities of the vehicles added, latterly controlled by the designed NN control algorithm. The randomness includes 10 percent of vehicle initial speed. Deflection of the first quarter-span is considered as the output of the system and tried to be controlled by two symmetric forces whose desirable positions are determined by recent studies. Furthermore the sensitivity of the system response has been investigated by applying the different conditions in which the number of the moving vehicles varies. It is shown that the increment in the number of moving vehicles has led to unsolicited deflection specifically when two or more cars moves concurrently, whereas the NN algorithm could either perfectly or effectively get over the issue.

Vibration Suppression of a Strain Gradient Microscale Beam Via an Adaptive Lyapunov Control Strategy

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Mohammad Ali Nojoumian ◽  
Ramin Vatankhah ◽  
Hassan Salarieh
Keyword(s):  
Strain Gradient ◽  
Vibration Suppression ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Bernoulli Beam ◽  
Control Effort ◽  
Lyapunov Control ◽  
Adaptation Law ◽  
And Control ◽  
Euler Bernoulli Beam

Vibration suppression of a strain gradient Euler–Bernoulli beam in presence of disturbance and uncertainties is considered in this investigation. Vibration of the system is suppressed by an adaptive boundary controller which has robustness to the environmental and control effort disturbances. The direct Lyapunov stability theorem is used to design the controller and adaptation law. The numerical results are presented to demonstrate the effectiveness of the proposed controller.

scholarly journals TMTDyn: A Matlab package for modeling and control of hybrid rigid–continuum robots based on discretized lumped systems and reduced-order models

2020 ◽  
pp. 027836491988168 ◽  
Author(s):  
S.M. Hadi Sadati ◽  
S. Elnaz Naghibi ◽  
Ali Shiva ◽  
Brendan Michael ◽  
Ludovic Renson ◽  
...  
Keyword(s):  
Software Package ◽  
Bernoulli Beam ◽  
Continuum Robots ◽  
Simulation Accuracy ◽  
Modeling And Control ◽  
Reduced Order ◽  
System Equation ◽  
And Control ◽  
Euler Bernoulli Beam ◽  
Discretized Model

A reliable, accurate, and yet simple dynamic model is important to analyzing, designing, and controlling hybrid rigid–continuum robots. Such models should be fast, as simple as possible, and user-friendly to be widely accepted by the ever-growing robotics research community. In this study, we introduce two new modeling methods for continuum manipulators: a general reduced-order model (ROM) and a discretized model with absolute states and Euler–Bernoulli beam segments (EBA). In addition, a new formulation is presented for a recently introduced discretized model based on Euler–Bernoulli beam segments and relative states (EBR). We implement these models in a Matlab software package, named TMTDyn, to develop a modeling tool for hybrid rigid–continuum systems. The package features a new high-level language (HLL) text-based interface, a CAD-file import module, automatic formation of the system equation of motion (EOM) for different modeling and control tasks, implementing Matlab C-mex functionality for improved performance, and modules for static and linear modal analysis of a hybrid system. The underlying theory and software package are validated for modeling experimental results for (i) dynamics of a continuum appendage, and (ii) general deformation of a fabric sleeve worn by a rigid link pendulum. A comparison shows higher simulation accuracy (8–14% normalized error) and numerical robustness of the ROM model for a system with a small number of states, and computational efficiency of the EBA model with near real-time performances that makes it suitable for large systems. The challenges and necessary modules to further automate the design and analysis of hybrid systems with a large number of states are briefly discussed.

scholarly journals Dynamic multi-patch isogeometric analysis of planar Euler-Bernoulli beams

2021 ◽  
Author(s):  
Duy Vo ◽  
Aleksandar Borković ◽  
Pruettha Nanakorna ◽  
Tinh Quoc Bui
Keyword(s):  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Simple Relation ◽  
Bernoulli Beam ◽  
Control Variables ◽  
Cross Sectional ◽  
Beam Structures ◽  
And Performance ◽  
And Control ◽  
Euler Bernoulli Beam

This study presents a novel isogeometric Euler-Bernoulli beam formulation for in-plane dynamic analysis of multi-patch beam structures. The kinematic descriptions involve only displacements of the beam axis, which are approximated by non-uniform rational B-spline (NURBS) curves. Translational displacements of the control points are here considered as control variables. The motivation of this work is to propose a penalty-free method to handle in-plane dynamic analysis of multi-patch beam structures. A simple relation between cross-sectional rotations at the ends of the beams and control variables is derived, allowing the incorporation of the end rotations as degrees of freedom. This improved setting can straightforwardly tackle beam structures with many rigid multi-patch connections, a major challenging issue when using existing isogeometric Euler-Bernoulli beam formulations. Additionally, rotational boundary conditions are conveniently prescribed. Numerical examples with complicated beam structures such as circular arches and frames with kinks are considered to show the accuracy and performance of the developed formulation. The computed results are verified with those derived from the conventional finite element method, and the superior convergence properties of the proposed formulation are illustrated. We additionally discuss about the possible extension of the present approach to spatial beam structures.

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