scholarly journals Nonlinear model of a rotating hub-beams structure: Equations of motion

2018 ◽  
Author(s):  
Jerzy Warminski
Keyword(s):  
Nonlinear Model ◽  
Equations Of Motion ◽  
Structure Equations

Effects of Tip Mass and Interaction Force on Nonlinear Behavior of Force Modulation FM-AFM Cantilever

2016 ◽  
Vol 33 (2) ◽  
pp. 257-268 ◽  
Author(s):  
K. E. Torkanpouri ◽  
H. Zohoor ◽  
M. H. Korayem
Keyword(s):  
Frequency Shift ◽  
Nonlinear Model ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Interaction Force ◽  
Beam Model ◽  
Frequency Shifts ◽  
Excitation Mode ◽  
Force Modulation ◽  
Tip Mass

AbstractInfluences of the tip mass, excitation mode of Frequency Modulated Atomic Force Microscope (FM-AFM) on the resonance frequency shift in force modulation (FM) mode are studied. Governing equations of motion are determined based on Timoshenko beam model with concentrated end mass. Approach point and base amplitude are set such that the FM-AFM remains just in FM mode. Either the linearized and nonlinear Derjaguin-Muller-Toporov (DMT) model are investigated. Then frequency shifts are determined for various interaction force regimes. It is showed the effect of tip mass on frequency shift is significant even for small tips. Nonlinear model shows lower frequency shifts in comparison with linearized model. It is showed that the amplitude of response is increased by increasing the tip mass and order of base excitation. Deviation of frequency shift between linearized and nonlinear solution are studied. It is declared that the error between linearized and nonlinear model is complicated. A deviation index is used for explaining behavior of error while tip mass and excitation mode are changed. It is showed, this index predicts the trend of error in all excitation modes and force cases. Behavior of system is linearizing by increasing the order of excitation, generally.

Dynamic models for the contact analysis of a tensioned beam with a moving oscillator

2013 ◽  
Vol 228 (4) ◽  
pp. 676-689
Author(s):  
Kyuho Lee ◽  
Jintai Chung
Keyword(s):  
Natural Frequency ◽  
Nonlinear Model ◽  
Frequency Ratio ◽  
Dynamic Models ◽  
Equations Of Motion ◽  
Contact Analysis ◽  
Contact Forces ◽  
Accurate Analysis ◽  
Moving Oscillator ◽  
Velocity Decrease

Several dynamic models are proposed for the contact analysis of a tensioned beam with a moving oscillator. Depending on whether the strain and stress used to derive the equations of motion are nonlinear, four models are established to analyze the beam deflections and the contact force between the beam and moving oscillator. We find that the differences in the contact forces and deflections computed with the models become large as the beam tension and moving velocity decrease and the natural frequency ratio of the oscillator to the beam increases. The nonlinear model derived with nonlinear strain and stress is desirable for an accurate analysis.

scholarly journals Study on an Integral Algorithm of Load Identification Based on Displacement Response

Sensors ◽  
2021 ◽  
Vol 21 (19) ◽  
pp. 6403
Author(s):  
Xun Xu ◽  
Yashan Zhu ◽  
Kejing Tian ◽  
Tingcan Lin ◽  
Yunyu Li
Keyword(s):  
Basis Function ◽  
Equations Of Motion ◽  
Identification Accuracy ◽  
Problem Solution ◽  
Load Identification ◽  
Random Loads ◽  
Robustness To Noise ◽  
Structure Equations ◽  
Integral Structure ◽  
High Computational Efficiency

Load identification is a very important and challenging indirect load measurement method because load identification is an inverse problem solution with ill-conditioned characteristics. A new method of load identification is proposed here, in which a virtual function was introduced to establish integral structure equations of motion, and partial integration was applied to reduce the response types in the equations. The effects of loading duration, the type of basis function, and the number of basis function expansion items on the calculation efficiency and the accuracy of load identification were comprehensively taken into account. Numerical simulation and experimental results showed that our algorithm could not only effectively identify periodic and random loads, but there was also a trade-off between the calculation efficiency and identification accuracy. Additionally, our algorithm can improve the ill-conditionedness of the solution of load identification equations, has better robustness to noise, and has high computational efficiency.

Nonlinear Polarisationoscillations in a Biophysical Model-System I: Internal Dynamics

1981 ◽  
Vol 36 (9-10) ◽  
pp. 888-892 ◽  
Author(s):  
F. Kaiser ◽  
Z. Szabo
Keyword(s):  
Nonlinear Model ◽  
Biological System ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Dipole Interaction ◽  
Model Potential ◽  
Model System ◽  
Biophysical Model ◽  
Internal Dynamics ◽  
Dipole State

Abstract To describe a metastable electrical dipole state in a biological system. Fröhlich suggested a nonlinear model potential. In this paper we investigate a system of two such dipoles coupled by a dipole-dipole interaction. M athem atically this model is described by two coupled nonlinear differential equations. In the investigation of the dynamics of the system we distinguish three solution types of the equations of motion.

Dynamic Modeling and Control of an Electromechanical Control Actuation System

2017 ◽  
Author(s):  
Ümit Yerlikaya ◽  
R. Tuna Balkan
Keyword(s):  
Nonlinear Model ◽  
Equations Of Motion ◽  
Ball Screw ◽  
Loop Control ◽  
Modeling And Control ◽  
Performance Requirements ◽  
Actuation System ◽  
Lever Mechanism ◽  
Actuation Systems ◽  
And Control

Electromechanical actuators are widely used in miscellaneous applications in engineering such as aircrafts, missiles, etc. due to their momentary overdrive capability, long-term storability, and low quiescent power/low maintenance characteristics. This work focuses on electromechanical control actuation systems (CAS) that are composed of a brushless direct current motor, ball screw, and lever mechanism. In this type of CAS, nonlinearity and asymmetry occur due to the lever mechanism itself, saturation limits, Coulomb friction, backlash, and initial mounting position of lever mechanism. In this study, both nonlinear and linear mathematical models are obtained using governing equations of motion. By using the linear model, it is shown that employing a PI-controller for position and a P-controller for velocity will be sufficient to satisfy performance requirements in the inner-loop control of an electromechanical CAS. The unknown controller parameters and anti-windup coefficient are obtained by the Optimization Tools of MATLAB using nonlinear model. Results obtained from the nonlinear model and real-time unloaded and loaded tests on a prototype developed are compared to verify the nonlinear model.

Nonlinear Model Predictive Control of a Stewart Platform Motion Stabilizer

2020 ◽  
Author(s):  
Takeyuki Ono ◽  
Ryosuke Eto ◽  
Junya Yamakawa ◽  
Hidenori Murakami
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Nonlinear Model ◽  
Equations Of Motion ◽  
Stewart Platform ◽  
Nonlinear Model Predictive Control ◽  
Operating Table ◽  
Prediction Errors ◽  
Time Step ◽  
Moving Vehicle

Abstract In an operating room of a hospital ship, to remotely perform surgery on a patient laid on an operating table utilizing the surgical manipulators attached to the table, the rotation and translation of the operating table must be properly isolated from the wave-induced motion of the floor. Similarly, on a moving vehicle, when a sensitive equipment is transported or a manipulator is utilized to perform precise positioning tasks, it becomes necessary to isolate them from undesirable motion of the vehicle. In response to the need for a motion stabilizer, which isolates a manipulator from undesirable ship or vehicle motion, we present a nonlinear model predictive control (NMPC) of a six degrees-of-freedom, base-moving Stewart platform. Analytical nonlinear equations of motion are utilized for nonlinear model predictive control, wherein an optimization problem in a finite time horizon at each time step is solved adopting C/GMRES algorithm. To predict the future motion caused by a ship or a moving vehicle, we employ an auto regressive moving average model which forecasts future behavior based on past behavior. Furthermore, to incorporate prediction errors as disturbance at each time step, we endow NMPC with the robustness. As a result, even if prediction errors exist, the set of all possible output states are predicted using the equations of motion in a finite time, while the system kinematic constraints are precisely satisfied. In order to assess the performance of the proposed controller, numerical simulations are presented for a base-moving Stewart platform.

scholarly journals Quadcopter Aggressive Maneuvers along Singular Configurations: An Energy-Quaternion Based Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Ayman A. El-Badawy ◽  
Mohamed A. Bakr
Keyword(s):  
Control Problem ◽  
Nonlinear Model ◽  
Equations Of Motion ◽  
Singular Configurations

Automatic aggressive maneuvers with quadcopters are regarded as a highly challenging control problem. The aim is to tackle the singularities that exist in a vertical looping maneuver. Modeling singularities are resolved by writing the equations-of-motion of the quadcopter in quaternion form. Physical singularities due to underactuation are resolved by using an energy-based control. Energy-based control is utilized to overcome the uncontrollability of the quadcopter at physical singular configurations, for instance, when commanding the quadcopter to gain altitude while pitched at90∘. Three looping strategies (circular, clothoidal, and newly developed constant thrust) are implemented on a nonlinear model of the quadcopter. The three looping strategies are discussed along with their advantages and limitations.

THE PAPAPETROU EQUATIONS AND MOTION OF A TEST BODY IN GRAVITATIONAL FIELD

1995 ◽  
Vol 04 (01) ◽  
pp. 69-78
Author(s):  
R.I. KHRAPKO
Keyword(s):  
Gravitational Field ◽  
Additional Condition ◽  
Evolution Equations ◽  
World Line ◽  
Equations Of Motion ◽  
Test Body ◽  
Particle Structure ◽  
Structure Equations

The Papapetrou equations for a dipole particle are criticized in favor of the evolution equations obtained by Dixon and Madore. It is concluded that an additional condition (Pirani, Dixon, Corinaldesi, etc.) which permits the calculation of a unique world line of a particle is a substitute for data of a particle structure. Equations of motion of an extended test body in terms of multipoles are presented.

Test Response of a Turbocharger Supported on Floating Ring Bearings: Part II — Comparisons to Nonlinear Rotordynamic Predictions

2003 ◽  
Author(s):  
Chris Holt ◽  
Luis San Andre´s ◽  
Sunil Sahay ◽  
Peter Tang ◽  
Gerry La Rue ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Nonlinear Model ◽  
Equations Of Motion ◽  
Forced Response ◽  
Rotor Imbalance ◽  
Nonlinear Responses ◽  
Reaction Forces ◽  
Bearing Force ◽  
Linear And Nonlinear ◽  
Large Rotor

Linear and nonlinear analysis results for the operation of a small automotive turbocharger supported on floating ring bearings are presented. A comprehensive fluid film bearing model predicting the forced response of floating ring bearings is also described. The linear rotordynamic model predicts well the rotor free-free modes and onset speed of instability using linearized bearing force coefficients. The nonlinear model incorporating instantaneous bearing reaction forces in the numerical integration of the rotor equations of motion predicts the limit cycle amplitudes with two fundamental sub synchronous whirl frequencies. Comparisons of both models to experimental results follow. The predictions evidence two unstable whirl ratios at approximately 1/2 ring speed and 1/2 ring speed plus 1/2 journal speed. The transient nonlinear responses reveal the importance of rotor imbalance in suppressing the subsynchronous instabilities at large rotor speeds as also observed in the experiments.

A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part I—Derivation of Governing Equations

1997 ◽  
Vol 119 (1) ◽  
pp. 126-131 ◽  
Author(s):  
J. Datta ◽  
K. Farhang
Keyword(s):  
Nonlinear Model ◽  
Contact Region ◽  
Equations Of Motion ◽  
Rolling Contact ◽  
Rolling Element Bearings ◽  
Structural Vibrations ◽  
Nonlinear Springs ◽  
Rolling Element ◽  
Rolling Elements ◽  
Constituent Elements

This paper, the first of two companion papers, presents a model for investigating structural vibrations in rolling element bearings. The analytical formulation accounts for tangential and radial motions of the rolling elements, as well as the cage, the inner and the outer races. The contacts between the rolling elements and races are treated as nonlinear springs whose stiffnesses are obtained by application of the equation for Hertzian elastic contact deformation. The derivation of the equations of motion is facilitated by assuming that only rolling contact exists between the races and rolling elements. Application of Lagrange’s equations leads to a system of nonlinear ordinary differential equations governing the motion of the bearing system. These equations are then solved using the Runge-Kutta integration technique. Using the formulation in the second part—“A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part II—Simulation and Results,” a number of effects on bearing structural vibrations are studied. This work is unique from previous studies in that the model simulates vibration from intrinsic properties and constituent elements of the bearing, and takes into account every contact region within the bearing, representing it by a nonlinear spring.

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