425054

Vibration control of nonlinear dynamical system via negative cubic velocity feedback

Article

Last updated: 04 May 2025

Subjects

-

Tags

Section C: Mathematics

Abstract

    The aim of this study is to highlight how specific parameters, especially nonlinear feedback control, can enhance system stability and optimize vibration control. Our findings contribute to the ongoing development of advanced strategies for managing vibrations in nonlinear dynamic systems. In this research paper, we investigate the reduction of vibrations in a hybrid Rayleigh-van der Pol-Duffing oscillator using negative cubic velocity feedback control. This system is modeled as a single-degree-of-freedom oscillator that incorporates both cubic and fifth-order nonlinear terms, along with an externally applied force. To derive a solution from the initial approximation, the multiple scales method was utilized, providing an effective analytical approach for examining the nonlinear behavior of the system. We conducted a comprehensive analysis both graphically and numerically, examining the system's behavior before and after implementing negative cubic velocity feedback, with a particular focus on the primary resonance condition. MATLAB was used as the main computational tool to explore the effects of different parameters, including the impact of negative cubic velocity feedback on the primary system's response.

DOI

10.21608/erurj.2025.331356.1197

Keywords

Negative Cubic velocity feedback, Multiple scales method, Primary resonance, stability, fixed point

Authors

First Name

Abdullah

Last Name

Shref

MiddleName

Reda

Affiliation

Faculty of Artificial Intelligence, Egyptian Russian University, Badr City, 11829, Cairo, Egypt

Email

redaabdallah316@gmail.com

City

-

Orcid

-

First Name

Y.A.

Last Name

Amer

MiddleName

-

Affiliation

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

Email

yaser31270@yahoo.com

City

-

Orcid

-

First Name

M. N.

Last Name

Abd El-Salam

MiddleName

-

Affiliation

Basic Sciences Department, Higher Technological Institute, 10th of Ramadan City, Egypt

Email

mansour.naserallah@yahoo.com

City

-

Orcid

-

First Name

O. M.

Last Name

khaled

MiddleName

-

Affiliation

Department of Mathematical and Computer Science, Faculty of Sci. Port said University, Port Said, Egypt

Email

osama_mohareb@sci.psu.edu.eg

City

-

Orcid

-

First Name

E.S.M.

Last Name

Youssef

MiddleName

-

Affiliation

Faculty of Artificial Intelligence, Egyptian Russian University, Cairo 11829, Egypt

Email

eslamsobhy144@gmail.com

City

-

Orcid

-

Volume

4

Article Issue

2

Related Issue

55428

Issue Date

2025-04-01

Receive Date

2024-12-28

Publish Date

2025-04-01

Page Start

2,630

Page End

2,643

Print ISSN

2812-6211

Online ISSN

2812-622X

Link

https://erurj.journals.ekb.eg/article_425054.html

Detail API

http://journals.ekb.eg?_action=service&article_code=425054

Order

425,054

Type

Original Article

Type Code

2,445

Publication Type

Journal

Publication Title

ERU Research Journal

Publication Link

https://erurj.journals.ekb.eg/

MainTitle

Vibration control of nonlinear dynamical system via negative cubic velocity feedback

Details

Type

Article

Created At

04 May 2025