Non-Linear Modal Interactions in a Suspension Rope System with Time-Varying Length

2006 ◽  
Vol 5-6 ◽  
pp. 217-224 ◽  
Author(s):  
Rodanthi Salamaliki-Simpson ◽  
Stefan Kaczmarczyk ◽  
Phil Picton ◽  
Scott Turner
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Time Varying ◽  
Modal Interaction ◽  
Modal Interactions ◽  
Autoparametric Resonance ◽  
Non Linear ◽  
Varying Length ◽  
Host Structure ◽  
Rope System

This paper focuses on the investigation of the autoparametric coupling effects and modal interactions in a suspension rope system with a time varying length. Equations of motion of a multi-degree-of-freedom discrete, non-stationary and non-linear model are presented and are used to analyze the dynamic response of an elevator suspension rope system under resonance conditions. The equations of motion involve quadratic and cubic non-linear terms which are responsible for the modal interaction between the lateral and longitudinal oscillations of the rope and the car motions. The model takes into account the periodic excitations caused by motion of the host structure. The results confirm that adverse responses may arise and internal autoparametric resonance phenomena may occur.

Non-linear dynamic analysis of time varying length flexible body

2020 ◽  
Vol 2020 (0) ◽  
pp. 513
Author(s):  
Masato TAKEUCHI ◽  
Kensuke HARA ◽  
Hiroshi YAMAURA
Keyword(s):  
Dynamic Analysis ◽  
Flexible Body ◽  
Time Varying ◽  
Linear Dynamic ◽  
Non Linear ◽  
Varying Length

scholarly journals Dynamic Response of Parallel Hoisting System under Drive Deviation between Ropes with Time-Varying Length

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Guohua Cao ◽  
Xiang Cai ◽  
Naige Wang ◽  
Weihong Peng ◽  
Jishun Li
Keyword(s):  
Differential Equations ◽  
Dynamic Response ◽  
Differential Algebraic Equations ◽  
Dynamic Responses ◽  
Dynamic Equations ◽  
Time Varying ◽  
Algebraic Equations ◽  
Varying Length ◽  
Hoisting System ◽  
Design And Manufacture

The dynamic responses of parallel hoisting system with time-varying length and rigid guidance under drive deviation are investigated considering tension and torsion characteristics of the ropes. The variable-domain three-node elements of rope are employed and the corresponding differential algebraic equations (DAEs) are derived using Lagrange’s equations of the first kind. The slack situation of the rope is considered, and the dynamic equations which are systems of DAEs are transformed to ordinary differential equations (ODEs). The dynamic responses of tension, torsion, and acceleration are analyzed considering radius’ error of the drums, which indicates that the drive deviation between ropes can cause large influence on the tension difference and even cause one of the ropes to slack. However, the torsion of the corresponding rope is active. And unreasonable discordance between ropes should be controlled for the design and manufacture of drum on super deep parallel hoisting system.

A NOVEL DRIVING STRATEGY FOR DYNAMIC SIMULATION OF HOISTING ROPE WITH TIME-VARYING LENGTH

2013 ◽  
Vol 04 (03) ◽  
pp. 1350009 ◽  
Author(s):  
JINJIE WANG ◽  
GUOHUA CAO ◽  
YANDONG WANG ◽  
RONGHUA WU
Keyword(s):  
Equations Of Motion ◽  
Simulation Method ◽  
Time Varying ◽  
Concentrated Mass ◽  
Lagrange’S Equation ◽  
Simulation Efficiency ◽  
Runge Kutta Method ◽  
Adams Simulation ◽  
Varying Length ◽  
Hoisting System

A simulation method for investigating the vibration behavior of hoisting rope with time-varying length is improved. By previously creating markers in the MSC.ADAMS software package, the parametric model of the rope wound along helix is established based on the concentrated-mass theory with multi-degree of freedom (multi-DOF). A novel driving strategy, cooperating fixed joints with angle sensors under the control of driving script, is proposed to substitute conventional contact force. Researching on the hoisting rope in the sinking winch mechanism, an equivalent discretization model is obtained with complicated boundary conditions considered. The differential equations of motion of the hoisting system are formulated employing Lagrange's equation and numerically solved using Runge–Kutta method. The simulation indicates that the horizontal swing is decreased in principle and the simulation with 800 discrete ropes is not performed more than 61 min. Therefore, this feasible strategy could not only guarantee the accuracy but also promote simulation efficiency and stability. The motion curves exported from ADAMS simulation coincide with one in numerical simulation, which validates both the numerical model and the driving strategy.

Effect of Intermediate Location and Time-Varying End Mass on the Dynamic Response of a Flexible Robot Manipulator in Tracing Multi-Straight-Line Path

2012 ◽  
Vol 463-464 ◽  
pp. 1246-1251 ◽  
Author(s):  
Mojtaba Kazemi ◽  
Mostafa Ghayour
Keyword(s):  
Dynamic Response ◽  
Robot Manipulator ◽  
Equations Of Motion ◽  
Numerical Results ◽  
Graphical Form ◽  
Time Varying ◽  
Flexible Robot ◽  
Prismatic Joint ◽  
Straight Line ◽  
Line Path

This paper presents the effects of intermediate location and time-varying end mass on the dynamic response of flexible robot manipulator with rotating-prismatic joint in tracing multi-straight-line path. The tip end of the flexible robot manipulator traces a multi-straight-line path under the action of external driving torque and axial force. Flexible arm which consist of a rotating-prismatic joint, is assumed to be an Euler-Bernoulli beam carrying an end mass. The Lagrangian dynamics in conjunction with the assumed modes method is utilized in deriving the equations of motion. Effect of rotary inertia, axial shortening and gravitation has been considered in developing the dynamic model. Equations of motion are numerically solved by using the Runge-Kutta method. Numerical results of computer simulations for tip deflection are presented in graphical form. Physical trends of the obtained numerical results are discussed.

Adaptive control of time-varying non-linear plants by speed-gradient algorithms

2019 ◽  
pp. 37-44 ◽  
Author(s):  
O. P. Tomchina ◽  
D. N. Polyakhov ◽  
O. I. Tokareva ◽  
A. L. Fradkov
Keyword(s):  
Adaptive Control ◽  
Adaptive Systems ◽  
Reference Model ◽  
Maximum Deviation ◽  
Model Parameters ◽  
Time Varying ◽  
System Solution ◽  
Non Linear ◽  
Initial Uncertainty ◽  
Speed Gradient

Introduction: The motion of many real world systems is described by essentially non-linear and non-stationary models. A number of approaches to the control of such plants are based on constructing an internal model of non-stationarity. However, the non-stationarity model parameters can vary widely, leading to more errors. It is only assumed in this paper that the change rate of the object parameters is limited, while the initial uncertainty can be quite large.Purpose: Analysis of adaptive control algorithms for non-linear and time-varying systems with an explicit reference model, synthesized by the speed gradient method.Results: An estimate was obtained for the maximum deviation of a closed-loop system solution from the reference model solution. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limit error in the system can be made arbitrarily small. Systems designed by the direct approach and systems based on the identification approach are both considered. The procedures for the synthesis of an adaptive regulator and analysis of the synthesized system are illustrated by an example.Practical relevance: The obtained results allow us to build and analyze a broad class of adaptive systems with reference models under non-stationary conditions.

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