Inclusion of Static Indetermination in the Mathematical Model for Non-Linear Dynamic Analyses of Multi-Bearing Rotor System

1993 ◽  
Vol 164 (2) ◽  
pp. 267-280 ◽  
Author(s):  
J. Ding ◽  
J.M. Krodkiewski
Keyword(s):  
Mathematical Model ◽  
Rotor System ◽  
Linear Dynamic ◽  
Dynamic Analyses ◽  
Non Linear ◽  
The Mathematical Model

Design and Analysis of a Novel Locking Mechanism of MEMS Safety and Arming Device

2014 ◽  
Vol 609-610 ◽  
pp. 856-859 ◽  
Author(s):  
Fu Fu Wang ◽  
Wen Zhong Lou ◽  
Ying Wang ◽  
Fang Yi Liu ◽  
Jun Lu ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
The Other ◽  
Linear Dynamic ◽  
Locking Mechanism ◽  
Non Linear ◽  
The Mathematical Model

In this paper, a novel locking mechanism of MEMS S&A device has been proposed. Through establishing the mathematical model of the motion for the slider and simulating the physical model by the non-linear dynamic mechanics, appropriate novel locking mechanism is designed to meet two items, one item is the slider can slide to the bottom under the launch overload conditions; the other item is the slider cant be pulled back after the launch overload conditions. Through the experiment, the feasibility of the above research is confirmed.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

Non-linear dynamic behaviour of rotor—bearing system trained by bevel gears

2008 ◽  
Vol 222 (4) ◽  
pp. 617-627 ◽  
Author(s):  
M Li
Keyword(s):  
Equilibrium Points ◽  
Rotor System ◽  
Design Stage ◽  
Oil Film ◽  
Bevel Gears ◽  
Linear Dynamic ◽  
Non Linear ◽  
Rotor Bearing ◽  
Stability And Bifurcations ◽  
Bearing System

The vibrations of parallel geared rotor—bearing system have been intensively discussed; however, little attention has been paid to the dynamic analysis of angled bevel-geared system supported on journals. In the present work, the non-linear dynamics of a bevel-geared rotor system on oil film bearings is studied. First, the dynamic model is developed under some assumptions, such as rigid rotors, short-bearings, small teeth errors, and so forth. Then, the non-linear dynamic behaviours of both the balanced and unbalanced rotor system are analysed, respectively, in which the equilibrium points, limit cycles, their stability, and bifurcations are paid more attention. Numerical results show that in the bevel-geared rotor system under the action of non-linear oil film forces there exists a series of complex non-linear dynamic phenomena of rotor orbits, such as Hopf bifurcation, torus-doubling bifurcation, and jump phenomenon. All these features can help us to understand the dynamic characteristics of bevel-geared rotor—bearing system at design stage and during running period. Finally, some concerned problems during the investigation are also present.

scholarly journals Study of the non-linear dynamic response of a rotor system with faults and uncertainties

2012 ◽  
Vol 331 (3) ◽  
pp. 671-703 ◽  
Author(s):  
Jérôme Didier ◽  
Jean-Jacques Sinou ◽  
Béatrice Faverjon
Keyword(s):  
Dynamic Response ◽  
Rotor System ◽  
Linear Dynamic ◽  
Non Linear

Analysis of the Non-Linear Dynamic Responses of an Elastic Rotor With a Slant Crack

2012 ◽  
Author(s):  
Xiangmin Zhang ◽  
Changping Chen ◽  
Liming Dai
Keyword(s):  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Dynamic Responses ◽  
Cracked Rotor ◽  
Lagrange Equations ◽  
Linear Dynamic ◽  
Slant Crack ◽  
Non Linear ◽  
Line Spring Model

Considering a rotor system with a slant crack, and using an equivalent line-spring model to simulate the slant crack of the rotor, the flexibility model of the slant-cracked rotor is derived. Then considered the geometric non-linearity and based on the Lagrange equations, the non-linear dimensionless differential equations of motion for the slant-cracked rotor are obtained. Further the non-linear dynamic responses of the single rotor system with a slant crack are discussed by the Galerkin method and the harmonic balance method. It’s detailedly studied that the angle, the depth and the position of the slant crack on the rotor all affect on the non-linear dynamic responses of the rotor system, and the conclusion is very significant to the design of the rotor system in the practical reference aspect.

Seismic Assessment of Bell Towers of Mexican Colonial Churches

2010 ◽  
Vol 133-134 ◽  
pp. 585-590 ◽  
Author(s):  
Fernando Peña ◽  
Miguel Meza
Keyword(s):  
Seismic Assessment ◽  
Colonial Period ◽  
Linear Dynamic ◽  
Dynamic Analyses ◽  
Non Linear

The seismic assessment of bell towers of churches built during the colonial period in Mexico is studied. Two representative typologies of churches of the southwest of Mexico are considered. The results of non-linear static and the non-linear dynamic analyses are compared. The results show that it is not recommended the use of non-linear static analyses; being necessary the use of full non-linear dynamic analyses.

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