scholarly journals On the Existence of Time Delay for Rotating Beam with Proportional–Derivative Controller

2021 ◽  
pp. 98-122
Author(s):  
Y. A. Amer ◽  
Taher A. Bahnasy ◽  
Ashraf M. Elmhlawy
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
State Solution ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Resonance Case ◽  
Rotating Beam ◽  
Response Curves ◽  
Near Resonance ◽  
Different Response

A rotating beam at varying speed mathematical model is studied. Multiple time scales method is applied to the nonlinear system of differential equations and investigated the system behavior approximate solution in the instance of resonance case. We studied the system in case of applying the delayed control on the displacement and the velocity with Proportional–derivative (PD) controller. The consistency of the steady state solution in the near-resonance case is reviewed and analyzed using the Routh-Huriwitz approach. The factors on the steady state solution of the various parameters are recognized and discussed. Simulation effects are obtained using MATLAB software package. Different response curves are involved to show and compare controller effects at various system parameters.

An Alternative Perturbation Procedure of Multiple Scales for Nonlinear Dynamics Systems

1989 ◽  
Vol 56 (3) ◽  
pp. 667-675 ◽  
Author(s):  
S. L. Lau ◽  
Y. K. Cheung ◽  
Shuhui Chen
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Degrees Of Freedom ◽  
Multiple Scales ◽  
Steady State Solution ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Almost Periodic ◽  
Perturbation Procedure ◽  
Incremental Harmonic Balance

An alternative perturbation procedure of multiple scales is presented in this paper which is capable of treating various periodic and almost periodic steady-state vibrations including combination resonance of nonlinear systems with multiple degrees-of-freedom. This procedure is a generalization of the Lindstedt-Poincare´ method. To show its essential features a typical example of cubic nonlinear systems, the clamped-hinged beam, is analyzed. The numerical results for the almost periodic-free vibration are surprisingly close to that obtained by the incremental harmonic balance (IHB) method, and the analytical formulae for steady-state solution are, in fact, identical with that of conventional method of multiple time scales. Moreover, detail calculations of this example revealed some interesting behavior of nonlinear responses, which is of significance for general cubic systems.

Torsional Response of Systems

1967 ◽  
Vol 89 (3) ◽  
pp. 316-324 ◽  
Author(s):  
E. I. Pollard
Keyword(s):  
Steady State ◽  
Test Data ◽  
Digital Computer ◽  
Steady State Solution ◽  
State Solution ◽  
Computer Solution ◽  
Torsional Response ◽  
Rotating Systems ◽  
Near Resonance ◽  
Acceleration Test

Torsional resonance in coupled rotating systems such as multiunit turbine-gear-compressor trains is sometimes a serious problem and several shaft failures have been reported. Often it is desirable to know the magnitude of vibration in or near resonance. A procedure is developed whereby an alternating exciting torque of known magnitude and frequency is applied at any required point in the system and a digital computer solution is obtained for the resulting steady-state, torque in each shaft and deflection of each inertia. Use of this in the analysis of test data is illustrated. Methods are also developed whereby the foregoing steady-state solution is used to obtain approximate transient torques appearing in shafts when an a-c machine is short-circuited, and during acceleration through resonance. Correlation of computations with acceleration test data is shown.

scholarly journals Vibration Control of a Compressor Blade Using Position and Velocity Feedback

2019 ◽  
Vol 24 (No 1) ◽  
Author(s):  
Ali Kandil ◽  
Magdy Kamel
Keyword(s):  
Primary Resonance ◽  
Time History ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Nonlinear Behaviour ◽  
Response Curves ◽  
Velocity Feedback ◽  
Rotating Speed ◽  
Coupled Mode ◽  
Different Response

Position and velocity feedback controllers are applied in this work to reduce the oscillations of a rotating blade dynamical system running at an unsteady rotating speed. Both the primary resonance and the principal parametric resonance are controlled as they are the worst cases that were verified numerically. The two modes of vibrations are found to be powerfully linearly coupled, so we have applied the controller to only one mode and the other, coupled mode follows it. The overall nonlinear behaviour of the system with and without control is investigated through the multiple time scales method. Time history and different response curves of the controlled system are included to show the controller effect.

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

scholarly journals Comparison of Solvers Performance for Load Flow Analysis

2019 ◽  
Vol 3 (1) ◽  
pp. 26 ◽  
Author(s):  
Vishnu Sidaarth Suresh
Keyword(s):  
Steady State ◽  
Power System ◽  
Reactive Power ◽  
Flow Analysis ◽  
Steady State Solution ◽  
Load Flow ◽  
State Solution ◽  
Computational Time ◽  
Load Flow Analysis ◽  
Active And Reactive Power

Load flow studies are carried out in order to find a steady state solution of a power system network. It is done to continuously monitor the system and decide upon future expansion of the system. The parameters of the system monitored are voltage magnitude, voltage angle, active and reactive power. This paper presents techniques used in order to obtain such parameters for a standard IEEE – 30 bus and IEEE-57 bus network and makes a comparison into the differences with regard to computational time and effectiveness of each solver

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