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.

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.

A Parameter Optimization Method to Determine Ski Stiffness Properties From Ski Deformation Data

2011 ◽  
Vol 27 (1) ◽  
pp. 81-86 ◽  
Author(s):  
Dieter Heinrich ◽  
Martin Mössner ◽  
Peter Kaps ◽  
Werner Nachbauer
Keyword(s):  
Parameter Optimization ◽  
Beam Theory ◽  
Optimization Method ◽  
Computational Method ◽  
Torsional Stiffness ◽  
Multiple Shooting ◽  
Bernoulli Beam ◽  
Linear Combinations ◽  
Stiffness Properties ◽  
Euler Bernoulli Beam

The deformation of skis and the contact pressure between skis and snow are crucial factors for carved turns in alpine skiing. The purpose of the current study was to develop and to evaluate an optimization method to determine the bending and torsional stiffness that lead to a given bending and torsional deflection of the ski. Euler-Bernoulli beam theory and classical torsion theory were applied to model the deformation of the ski. Bending and torsional stiffness were approximated as linear combinations of B-splines. To compute the unknown coefficients, a parameter optimization problem was formulated and successfully solved by multiple shooting and least squares data fitting. The proposed optimization method was evaluated based on ski stiffness data and ski deformation data taken from a recently published simulation study. The ski deformation data were used as input data to the optimization method. The optimization method was capable of successfully reproducing the shape of the original bending and torsional stiffness data of the ski with a root mean square error below 1 N m2. In conclusion, the proposed computational method offers the possibility to calculate ski stiffness properties with respect to a given ski deformation.

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.

Nonlinear Beam-Column Element Under Consistent Deformation

2015 ◽  
Vol 15 (05) ◽  
pp. 1450068 ◽  
Author(s):  
Yi Qun Tang ◽  
Zhi Hua Zhou ◽  
Siu Lai Chan
Keyword(s):  
Shear Deformation ◽  
Beam Theory ◽  
Displacement Function ◽  
Shear Locking ◽  
Bernoulli Beam ◽  
Equilibrium Equations ◽  
Nonlinear Beam ◽  
Euler Bernoulli Beam ◽  
Column Element ◽  
Force Equilibrium

A new nonlinear beam-column element capable of considering the shear deformation is proposed under the concept of consistent deformation. For the traditional displacement interpolation function, the beam-column element produces membrane locking under large deformation and shear locking when the element becomes slender. To eliminate the membrane and shear locking, force equilibrium equations are employed to derive the displacement function. Numerical examples herein show that membrane locking in the traditional nonlinear beam-column element could cause a considerable error. Comparison of the present improved formulae based on the Timoshenko beam theory with that based on the Euler–Bernoulli beam theory indicates that the present approach requires several additional parameters to consider shear deformation and it is suitable for computer analysis readily for incorporation into the frames analysis software using the co-rotational approach for large translations and rotations. The examples confirm that the proposed element has higher accuracy and numerical efficiency.

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.

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
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