On the Stability of the Impact Damper

1966 ◽  
Vol 33 (3) ◽  
pp. 586-592 ◽  
Author(s):  
S. F. Masri ◽  
T. K. Caughey
Keyword(s):  
Exact Solution ◽  
Stability Analysis ◽  
Asymptotically Stable ◽  
Impact Damper ◽  
The Stability ◽  
The Impact

The exact solution for the symmetric two-impacts-per-cycle motion of the impact damper is derived analytically, and its asymptotically stable regions are determined. The stability analysis defines the zones where the modulus of all the eigenvalues of a certain matrix relating conditions after each of two consecutive impacts is less than unity.

scholarly journals Impedance Aggregation Method of Multiple Wind Turbines and Accuracy Analysis

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2035 ◽  
Author(s):  
Liang Chen ◽  
Heng Nian ◽  
Yunyang Xu
Keyword(s):  
Stability Analysis ◽  
Reference Frame ◽  
Wind Turbines ◽  
Power Distribution ◽  
Wind Farm ◽  
System Level ◽  
Small Signal ◽  
Impedance Model ◽  
The Stability ◽  
The Impact

The sequence domain impedance modeling of wind turbines (WTs) has been widely used in the stability analysis between WTs and weak grids with high line impedance. An aggregated impedance model of the wind farm is required in the system-level analysis. However, directly aggregating WT small-signal impedance models will lead to an inaccurate aggregated impedance model due to the mismatch of reference frame definitions among different WT subsystems, which may lead to inaccuracy in the stability analysis. In this paper, we analyze the impacts of the reference frame mismatch between a local small-signal impedance model and a global one on the accuracy of aggregated impedance and the accuracy of impedance-based stability analysis. The results revealed that the impact is related to the power distribution of the studied network. It was found that that the influence of mismatch on stability analysis became subtle when subsystems were balanced loaded. Considering that balanced loading is a common configuration of the practical application, direct impedance aggregation by local small-signal models can be applied due to its acceptable accuracy.

scholarly journals Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
V. Nosov ◽  
J. A. Meda-Campaña ◽  
J. C. Gomez-Mancilla ◽  
J. O. Escobedo-Alva ◽  
R. G. Hernández-García
Keyword(s):  
Stability Analysis ◽  
Finite Number ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Switched System ◽  
Linear Functions ◽  
Asymptotically Stable ◽  
Multiple Lyapunov Functions ◽  
Stability Theorems ◽  
The Stability

The stability of autonomous dynamical switched systems is analyzed by means of multiple Lyapunov functions. The stability theorems given in this paper have finite number of conditions to check. It is shown that linear functions can be used as Lyapunov functions. An example of an exponentially asymptotically stable switched system formed by four unstable systems is also given.

Stability analysis and optimal control of an epidemic model with vaccination

2015 ◽  
Vol 08 (03) ◽  
pp. 1550030 ◽  
Author(s):  
Swarnali Sharma ◽  
G. P. Samanta
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Epidemic Model ◽  
Asymptotically Stable ◽  
Control Pair ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
The Cost ◽  
Objective Functional ◽  
Disease Free

In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number (R0) of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0when R0< 1. When R0> 1 endemic equilibrium E1exists and the system becomes locally asymptotically stable at E1under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB. Epidemiological implications of our analytical findings are addressed critically.

Uncertainty Model of Concrete Elastic Modulus Effect to Critical Reinforced Concrete Buckling Load

2014 ◽  
Vol 931-932 ◽  
pp. 525-528
Author(s):  
Sanguan Vongchavalitkul
Keyword(s):  
Elastic Modulus ◽  
Stability Analysis ◽  
Statistical Data ◽  
Stability Index ◽  
Buckling Load ◽  
Design Code ◽  
Critical Buckling Load ◽  
Uncertainty Model ◽  
The Stability ◽  
The Impact

There are differences in each countrys design code for concrete elastic modulus that cause uncertainty in stability analysis of critical buckling load column. This paper investigates the impact of uncertainty on concrete elastic modulus for designing of critical buckling load of building column. The statistical data on materials and applied load being collected in Thailand are used together with an investigation on the uncertainty of the concrete elastic modulus in the design code from 8 countries. Finally the Monte Carlo simulation is used to find out the stability index in term of reliability index. The results show that the uncertainty of the concrete elastic modulus plays an important role in stability analysis and should be considered in the design.

Stability Analysis about the Impact of Soft Rock to the Underground Cavern Group

2013 ◽  
Vol 706-708 ◽  
pp. 560-564
Author(s):  
Yi Huan Zhu ◽  
Guo Jian Shao ◽  
Zhi Gao Dong
Keyword(s):  
Finite Element ◽  
Rock Mass ◽  
Stability Analysis ◽  
Soft Rock ◽  
Element Model ◽  
Underground Excavation ◽  
Power Station ◽  
Excavation Process ◽  
The Stability ◽  
The Impact

Soft rock is frequently encountered in underground excavation process. It is difficult to excavate and support in soft rock mass which has low strength, large deformation and needs much time to be out of shape but little time to be self-stabilized. Based on a large underground power station, finite element model analysis was carried out to simulate the excavation process and the results of displacement, stress and plasticity area were compared between supported and unsupported conditions to evaluate the stability of the rock mass.

Effect of Gravity on the Performance of an Impact Damper: Part 2. Stability of Vibrational Modes

1970 ◽  
Vol 12 (4) ◽  
pp. 278-287 ◽  
Author(s):  
M. M. Sadek ◽  
C. J. H. Williams
Keyword(s):  
Vibrational Modes ◽  
Impact Damper ◽  
Main Mass ◽  
Modes Of Vibration ◽  
The Stability ◽  
The Impact

This paper is c oncerned with the stability of the various modes of vibration of the impact damper system described in Part 1†. Charts are presented showing the ranges of dynamically stable and kinematically viable periodic two-impact-per-cycle motion. The condition of kinematic viability ensures that the trajectory of the free mass remains within the container throughout the motion. It is shown that in general stable, viable, two-impact-per-cycle motion of the system exists under resonant conditions of the main mass and that away from resonance, where any damper is ineffective, this type of motion is generally unstable.

scholarly journals Mathematical analysis of an age structured epidemic model with a quarantine class

2021 ◽  
Author(s):  
Bedreddine AINSEBA ◽  
Tarik Touaoula ◽  
Zakia Sari
Keyword(s):  
Reproduction Number ◽  
Asymptotic Behavior Of Solutions ◽  
Model Parameters ◽  
Qualitative Behavior ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
The Stability ◽  
The Impact

In this paper, an age structured epidemic Susceptible-Infected-Quarantined-Recovered-Infected (SIQRI) model is proposed, where we will focus on the role of individuals that leave their class of quarantine before being completely recovered and thus will participate again to the transmission of the disease. We investigate the asymptotic behavior of solutions by studying the stability of both trivial and positive equilibria. In order to see the impact of the different model parameters like the relapse rate on the qualitative behavior of our system, we firstly, give the explicit expression of the epidemic reproduction number $R_{0}.$ This number is a combination of the classical epidemic reproduction number for the SIQR model and a new epidemic reproduction number corresponding to the individuals infected by a relapsed person from the R-class. It is shown that, if $R_{0}\leq 1$, the disease free equilibrium is globally asymptotically stable and becomes unstable for $R_{0}>1$. Secondly, while $R_{0}>1$, a suitable Lyapunov functional is constructed to prove that the unique endemic equilibrium is globally asymptotically stable on some subset $\Omega_{0}.$

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.

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