scholarly journals Dynamics of a rigid rotor in the elastic bearings

2004 ◽  
Vol 31 (1) ◽  
pp. 73-83 ◽  
Author(s):  
Inga Arkhipova
Keyword(s):  
Linear System ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Rotation Frequency ◽  
Rigid Rotor ◽  
Plane Parallel ◽  
Vertical Rotor ◽  
Parallel Motion ◽  
Non Linear ◽  
Unlimited Growth

As a rule in the studies of a rigid rotor in the elastic bearings the authors consider the linear system corresponding to the plane-parallel motion and the effect of self-centring under unlimited growth of the rotation frequency. In the present paper rotor is considered as a mechanical system with four degrees of freedom. Different motions of a statically and dynamically unbalanced vertical rotor supported in the non-linear bearings are studied.

Asymptotic trends in time-varying oscillatory period for a dual-staged torsional system

2016 ◽  
Vol 231 (22) ◽  
pp. 4126-4138
Author(s):  
Michael D Krak ◽  
Rajendra Singh
Keyword(s):  
Linear System ◽  
Mechanical System ◽  
Time Domain ◽  
Effective Stiffness ◽  
Step Response ◽  
Analysis Tool ◽  
Time Varying ◽  
Non Linear ◽  
Non Linear System ◽  
Oscillatory Period

The primary goal of this article is to propose a new analysis tool that estimates the asymptotic trends in the time-varying oscillatory period of a non-linear mechanical system. The scope is limited to the step-response of a torsional oscillator containing a dry friction element and dual-staged spring. Prior work on the stochastic linearization techniques is extended and modified for application in time domain. Subsequently, an instantaneous expected value operator and the concept of instantaneous effective stiffness are proposed. The non-linear system is approximated at some instant during the step-response by a linear time-invariant mechanical system that utilizes the instantaneous effective stiffness concept. The oscillatory period of the non-linear step-response at that instant is then approximated by the natural period of the corresponding linear system. The proposed method is rigorously illustrated via two computational example cases (a near backlash and near pre-load non-linearities), and the necessary digital signal processing parameters for time domain analysis are investigated. Finally, the feasibility and applicability of the proposed method is demonstrated by estimating the softening and hardening trends in the time-varying oscillatory period of the measured response for two laboratory experiments that contain clearance elements and multi-staged torsional springs.

Targeted energy transfer in a 2-DOF mechanical system coupled to a non-linear energy sink with varying stiffness

2015 ◽  
Vol 23 (16) ◽  
pp. 2567-2577 ◽  
Author(s):  
Claude-Henri Lamarque ◽  
F Thouverez ◽  
B Rozier ◽  
Z Dimitrijevic
Keyword(s):  
Energy Transfer ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Dynamical Behavior ◽  
Practical Investigations ◽  
Targeted Energy Transfer ◽  
Constant Stiffness ◽  
Non Linear ◽  
Energy Sink ◽  
Linear Mechanical System

The dynamical behavior of a non-linear mechanical system with two degrees of freedom (DOFs) during free and forced excitations is studied analytically and numerically. The non-linearity of the system is represented intentionally by a smooth non-linear simple function with periodically varying stiffness around a constant value for the sake of practical investigations. Analysis of the system leads to a method that could be used to design the non-linear energy sink (NES) so that the behavior of the system during relaxation and its strongly modulated response (SMR) could be improved versus the constant stiffness configuration.

A novel LSSVM-L Hammerstein model structure for system identification and nonlinear model predictive control of CSTR servo and regulatory control

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Akshaykumar Naregalkar ◽  
Subbulekshmi Durairaj
Keyword(s):  
Linear System ◽  
Regulatory Control ◽  
Hammerstein Model ◽  
Support Vector ◽  
Model Structure ◽  
Linear Dynamics ◽  
Vector Machines ◽  
Non Linear ◽  
Laguerre Filters ◽  
Non Linear System

Abstract A continuous stirred tank reactor (CSTR) servo and the regulatory control problem are challenging because of their highly non-linear nature, frequent changes in operating points, and frequent disturbances. System identification is one of the important steps in the CSTR model-based control design. In earlier work, a non-linear system model comprises a linear subsystem followed by static nonlinearities and represented with Laguerre filters followed by the LSSVM (least squares support vector machines). This model structure solves linear dynamics first and then associated nonlinearities. Unlike earlier works, the proposed LSSVM-L (least squares support vector machines and Laguerre filters) Hammerstein model structure solves the nonlinearities associated with the non-linear system first and then linear dynamics. Thus, the proposed Hammerstein’s model structure deals with the nonlinearities before affecting the entire system, decreasing the model complexity and providing a simple model structure. This new Hammerstein model is stable, precise, and simple to implement and provides the CSTR model with a good model fit%. Simulation studies illustrate the benefit and effectiveness of the proposed LSSVM-L Hammerstein model and its efficacy as a non-linear model predictive controller for the servo and regulatory control problem.

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