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42891

VIBRATIONS CONTROL OF THE HARMONICALLY EXCITED NONLINEAR SYSTEM VIA POSITIVE POSITION FEEDBACK CONTROLLER

Article

Last updated: 03 Jan 2025

Subjects

-

Tags

Astronomy
Mathematics
Physics

Abstract

In this paper, the vibration reducing of the harmonically excited nonlinear system is presented via applying positive position feedback controller (PPF). The analytical results are obtained by applying the multiple-scale perturbation techniques (MSPT) up to second-order approximations. The frequency response equation (FRE) is studied to test the be havior of the steady state solutions near the simultaneous resonances. The effects of the several parameters and the behavior of the system at resonance case are investigated to illustrate the optimum working conditions for the PPF controller. The stabilit y analysis for the uncontrolled system is investigated by applying the phase portrait technique. Moreover, numerical simulation is used to compare between time-history and the analytical solution. The analytical and numerical solutions are compared to show the validity of the results. Finally, a comparison with the available results in the literature is presented  

DOI

10.21608/absb.2019.42891

Keywords

Nonlinear system, Multiple scales method, Resonance, PPF controller, Stability, phase plane

Authors

First Name

Y.

Last Name

Amer

MiddleName

A.

Affiliation

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

Email

-

City

-

Orcid

-

First Name

A.

Last Name

EL-Sayed

MiddleName

T.

Affiliation

Department of Basic Sciences, Modern Academy for Engineering and Technology, Maadi, Egypt

Email

-

City

-

Orcid

-

First Name

A.

Last Name

Saleh

MiddleName

A.

Affiliation

Department of Mathematics, Faculty of Science(Girls), Al-Azhar University, Nasr City, Egypt

Email

-

City

-

Orcid

-

First Name

A.

Last Name

Abdel-Wahab

MiddleName

M.

Affiliation

Department of Mathematics, Faculty of Science(Girls), Al-Azhar University, Nasr City, Egypt

Email

-

City

-

Orcid

-

First Name

Hala

Last Name

Salman

MiddleName

F.

Affiliation

Department of Basic Sciences, Faculty of Computers and Information, Cairo University, Giza, Egypt

Email

halasalman35@yahoo.com

City

-

Orcid

-

Volume

30

Article Issue

Issue 1-B

Related Issue

6736

Issue Date

2019-06-01

Receive Date

2019-02-18

Publish Date

2019-06-01

Page Start

9

Page End

26

Print ISSN

1110-2535

Online ISSN

2636-3305

Link

https://absb.journals.ekb.eg/article_42891.html

Detail API

https://absb.journals.ekb.eg/service?article_code=42891

Order

2

Type

Original Article

Type Code

520

Publication Type

Journal

Publication Title

Al-Azhar Bulletin of Science

Publication Link

https://absb.journals.ekb.eg/

MainTitle

VIBRATIONS CONTROL OF THE HARMONICALLY EXCITED NONLINEAR SYSTEM VIA POSITIVE POSITION FEEDBACK CONTROLLER

Details

Type

Article

Created At

22 Jan 2023