scholarly journals Random Excitation of a System With Bilinear Hysteresis

1960 ◽  
Vol 27 (4) ◽  
pp. 649-652 ◽  
Author(s):  
T. K. Caughey
Keyword(s):  
Linear System ◽  
Random Excitation ◽  
Viscous Damping ◽  
Equivalent Linear ◽  
The Mean ◽  
Equivalent Linear System

An analysis is made of the response of a system with bilinear hysteresis to random excitation. It is shown that for moderately large inputs, the additional damping created by the bilinear hysteresis decreases the mean squared deflection compared with that for a linear system with the same viscous damping. However, for large inputs, the decrease in the stiffness of the system due to the bilinear hysteresis causes the mean squared deflection to increase over that for the equivalent linear system.

Formulation of Stochastic Linearization for Symmetric or Asymmetric M.D.O.F. Nonlinear Systems

1980 ◽  
Vol 47 (1) ◽  
pp. 209-211 ◽  
Author(s):  
P-T. D. Spanos
Keyword(s):  
Nonlinear Systems ◽  
Linear System ◽  
Solution Procedure ◽  
Stationary System ◽  
System Response ◽  
Equivalent Linear ◽  
Stochastic Linearization ◽  
Equivalent Linear System

A formulation of the method of stochastic linearization so that it is applicable for symmetric or asymmetric nonlinear systems is presented. Formulas for the generation of the equivalent linear system are given. The solution procedure for determining nonstationary or stationary system response statistics is outlined.

scholarly journals Observer-Based Controllers for Two-Wheeled Inverted Robots with Unknown Input Disturbance and Model Uncertainty

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Khanh G. Tran ◽  
Nam H. Nguyen ◽  
Phuoc D. Nguyen
Keyword(s):  
Linear System ◽  
Taylor Series ◽  
Model Uncertainty ◽  
Disturbance Observer ◽  
System Stability ◽  
Unknown Input ◽  
Input Disturbance ◽  
Equivalent Linear ◽  
Compound Disturbance ◽  
Equivalent Linear System

In this paper, two controllers with a compound disturbance observer are proposed for a two-wheeled inverted robot (TWIR) with model uncertainty and unknown input disturbance. First, an equivalent linear model of the TWIR with uncertainty and input disturbance is proposed using the Taylor series expansion for the nonlinear model of the TWIR at an equilibrium point, in which the nonlinear part of the Taylor series and the model uncertainty are combined with unknown input disturbance as compound input disturbance. Then, the compound input disturbance is estimated by using the Newton method and reference model. As the estimated compound disturbance is used to compensate for the compound disturbance, the equivalent linear system becomes closely definite without compound input disturbance. Finally, two controllers are proposed using the equivalent linear system. Stability analysis of the proposed control methods is also given. To illustrate the proposed methods, some simulations for the TWIR are performed and compared with the existing methods. The main contribution of this work includes the following: (i) simple controllers based on compound input disturbance observer for trajectory tracking and balancing of TWIRs with unknown input disturbance and model uncertainty are proposed; (ii) the stability of proposed closed-loop control systems is proved; (iii) our proposed methods are simulated and compared with the existing methods.

Random Vibration of Beams

1962 ◽  
Vol 29 (2) ◽  
pp. 267-275 ◽  
Author(s):  
S. H. Crandall ◽  
Asim Yildiz
Keyword(s):  
Timoshenko Beam ◽  
Dynamic Models ◽  
Random Excitation ◽  
Viscous Damping ◽  
Mean Square ◽  
Euler Beam ◽  
Rayleigh Beam ◽  
Mean Square Response ◽  
The Mean ◽  
Band Limited

The calculated response of a uniform beam to stationary random excitation depends greatly on the dynamical model postulated, on the damping mechanism assumed, and on the nature of the random excitation process. To illustrate this, the mean square deflections, slopes, bending moments, and shear forces have been compared for four different dynamical models, with three different damping mechanisms, subjected to a distributed transverse loading process which is uncorrelated spacewise and which is either ideally “white” timewise or band-limited with an upper cut-off frequency. The dynamic models are the Bernoulli-Euler beam, the Timoshenko beam, and two intermediate models, the Rayleigh beam, and a beam which has the shear flexibility of the Timoshenko beam but not the rotatory inertia. The damping mechanisms are transverse viscous damping, rotatory viscous damping, and Voigt viscoelasticity. It is found that many of the mean-square response quantities are finite when the excitation is ideally white (i.e., when the input has infinite mean square); however, some of the responses are unbounded. For these cases the rate of growth of the response as the cut-off frequency of the excitation is increased is obtained.

Balancing of Rotors Supported on Bearings Having Nonlinear Stiffness Characteristics

1994 ◽  
Vol 116 (3) ◽  
pp. 718-726 ◽  
Author(s):  
A. Turpin ◽  
A. M. Sharan
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Equations Of Motion ◽  
Real Life ◽  
Influence Coefficient ◽  
Rotor Systems ◽  
Equivalent Linear ◽  
Influence Coefficient Method ◽  
Stiffness Characteristics ◽  
Equivalent Linear System

In real-life applications, multi-disk-rotor systems are supported on bearings with nonlinear flexibility. The balancing of such systems at high speeds is a challenging task. This work presents a method of balancing such systems. The dynamic equations of motion for a nonlinear system are derived first using the influence coefficient method and then Lagrangian equations. An equivalent linear system is found using the optimization principles. Finally, the correct balance weights for the nonlinear system are obtained based on the equivalent linear system. The results thus obtained establish the utility of such a method of balancing nonlinear systems.

scholarly journals Response of a Nonlinear String to Random Loading

1959 ◽  
Vol 26 (3) ◽  
pp. 341-344
Author(s):  
T. K. Caughey
Keyword(s):  
Random Excitation ◽  
Additional Stress ◽  
Random Loading ◽  
Equivalent Linear ◽  
Linear String ◽  
The Mean ◽  
Nonlinear String

Abstract This paper considers the response of a nonlinear string to random excitation. It is shown that, owing to the additional stress induced by the stretching of the string, the mean squared deflection at every point is smaller than that for the equivalent linear string.

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