Stability Analysis and Bidirectional Vibration Control of Structure

2020 ◽  
pp. 275-287 ◽  
Author(s):  
Satyam Paul ◽  
Wen Yu ◽  
Raheleh Jafari
Keyword(s):  
Stability Analysis ◽  
Vibration Control

Stability analysis of linear systems with switchable stiffness using the Floquet theory

2018 ◽  
Vol 25 (5) ◽  
pp. 963-976
Author(s):  
L. Moreno-Ahedo ◽  
S. Diarte-Acosta
Keyword(s):  
Stability Analysis ◽  
Vibration Control ◽  
Linear Systems ◽  
System Parameter ◽  
Floquet Theory ◽  
Extreme Values ◽  
Active Vibration Control ◽  
State Dependent ◽  
Novel Approach ◽  
Control Of Linear Systems

In this paper, a novel approach based on the Floquet theory is applied for the stability analysis of a mass–spring system with switchable stiffness. The Reid model is used to describe the dynamics of this semi-active vibration control problem. The semi-active control is achieved by a spring which commutes between a maximum and minimum stiffness according to a prescribed state-dependent rule and its performance is characterized by a system parameter, which relates to the extreme values of the stiffness. In order to apply the Floquet theorem, the Reid model is written as a linear periodic differential equation by converting the state-dependent rule into a time-periodic control law. The application of the theory allows us to obtain the Floquet multipliers and exponents in terms of the system parameter. The multipliers lie inside the unitary circle showing asymptotic stability, while the exponents are used to solve an optimization problem by applying a sensitivity analysis. Our results are validated by analyzing the Reid model using nonlinear analysis techniques. According to our findings, the present approach provides a useful tool to analyze the vibration control of linear systems with switchable stiffness in a natural and straightforward way, which also gives mathematical tractability for optimization purposes. In addition, this approach can be extended to study the cases of multi-degree-of-freedom systems and forced systems.

Research on Periodic Motion Stability of Multi-DOF Rotor-Bearing System with Crack Fault

2011 ◽  
Vol 148-149 ◽  
pp. 3-6 ◽  
Author(s):  
Chao Feng Li ◽  
Qin Liang Li ◽  
Jie Liu ◽  
Bang Chun Wen
Keyword(s):  
Stability Analysis ◽  
Vibration Control ◽  
Shooting Method ◽  
Crack Depth ◽  
Continuous System ◽  
Oil Film ◽  
Rotor Bearing ◽  
The Stability ◽  
The Impact ◽  
Bearing System

Multi-DOF model of double-disc rotor-bearing system taking crack and oil film support into account is established, and the continuation shooting method combined with Newmark is also applied to stability analysis of continuous system. This paper mainly studied the variation law of five parameters domain in crack depth and location, then a number of conclusions are found: first, it’s feasible to study the stability of nonlinear rotor-bearing system with crack faults using FEM; secondly, the crack depth and location has a certain impact on instability speed, but the impact is not great and owns its certain law. As the crack depth and location is getting close to the middle position of rotor, due to its impact on the oil film support, the instability speed of system increases. This method and results in this paper provides a theoretical reference for stability analysis and vibration control in more complex relevant rotor-bearing system with crack fault.

STABILITY ANALYSIS AND VIBRATION CONTROL OF A CLASS OF NEGATIVE IMAGINARY SYSTEMS

2015 ◽  
Vol 77 (17) ◽  
Author(s):  
Auwalu M. Abdullahi ◽  
Z. Mohamed ◽  
M. S. Zainal Abidin ◽  
R. Akmeliawati ◽  
Amiru A. Bature
Keyword(s):  
Finite Element Method ◽  
Stability Analysis ◽  
Vibration Control ◽  
Horizontal Plane ◽  
Closed Loop ◽  
Flexible Manipulator ◽  
The Finite Element Method ◽  
Closed Loop System ◽  
Resonance Modes ◽  
Resonant Controller

This paper presents stability analysis and vibration control of a class of negative imaginary systems. A flexible manipulator that moves in a horizontal plane is considered and is modelled using the finite element method. The system with two poles at the origin is shown to possess negative imaginary properties. Subsequently, an integral resonant controller (IRC) which is a strictly negative imaginary controller is designed for the position and vibration control of the system. Using the IRC, the closed-loop system is observed to be internally stable and simuation results show that satisfactory hub angle response is achieved. Furthermore, vibration magnitudes at the resonance modes are suppressed by 48 dB.

DYNAMIC STABILITY ANALYSIS AND VIBRATION CONTROL OF A ROTATING ELASTIC BEAM CONNECTED WITH AN END MASS

2013 ◽  
Vol 13 (03) ◽  
pp. 1250066 ◽  
Author(s):  
CHUNG-FENG JEFFREY KUO ◽  
HUNG MIN TU ◽  
VU QUANG HUY ◽  
CHIEN-HUI LIU
Keyword(s):  
Stability Analysis ◽  
Vibration Control ◽  
Dynamic Stability ◽  
Controller Design ◽  
System Modeling ◽  
Elastic Beam ◽  
Vibration Modes ◽  
Lagrange’S Equation ◽  
Control Scheme ◽  
Linear And Nonlinear Systems

In this paper, dynamic stability analysis and vibration control for a rotating elastic beam connected with an end mass driven by a direct current (DC) motor is considered. A complete strategy including mathematical modeling, dynamic analysis, vibration controller design and simulation for linear and nonlinear systems are presented. Once the rotating flexible physical system has been described by a set of governing partial differential equations, they are manipulated to achieve an appropriate mathematical format for vibration control system design and computer simulation, respectively. Hamilton principle, Lagrange's equation, assumed-modes and the fourth-order Runge–Kutta methods are applied in the system modeling derivation, descretization, and numerical analysis. The correctness of the numerical results and the characteristic property between mathematics and dynamics are demonstrated as well. Also, a realizable vibration control scheme is developed which not only can stabilize all the vibration modes but also make this rotating elastic beam system efficient for good transient response.

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