Green's Function and Periodic Solutions of a Spring-Mass System in which the Forces are Functionally Dependent on Piecewise Constant Argument

Duygu Aruğaslan; Nur Cengiz

doi:10.19113/sdufbed.67047

Green's Function and Periodic Solutions of a Spring-Mass System in which the Forces are Functionally Dependent on Piecewise Constant Argument

Abstract

In this paper, damped spring-mass systems with generalized piecewise constant argument and with functional dependence on generalized piecewise constant argument are considered. These spring-mass systems have piecewise constant forces of the forms $Ax(\gamma(t))$ and $Ax(\gamma(t))+h(t,x_{t},x_{\gamma(t)})$, respectively. These spring-mass systems are examined without reducing them into discrete equations. While doing this examination, we make use of the results which have been obtained for differential equations with functional dependence on generalized piecewise constant argument in \cite{2}. Sufficient conditions for the existence and uniqueness of solutions of the spring-mass system with functional dependence on generalized piecewise constant argument are given. The periodic solution of the spring-mass system which has functional force is created with the help of the Green's function, and its uniqueness is proved. The obtained theoretical results are illustrated by an example. This illustration shows that the damped spring-mass systems with functional dependence on generalized piecewise constant argument with proper parameters has a unique periodic solution which can be expressed by Green's function.

Keywords

Differential equations with functional dependence on piecewise constant argument of generalized type,Periodic solutions; Green's function; Spring-Mass system

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Details

Primary Language

Turkish

Subjects

-

Journal Section

-

Authors

Duygu Aruğaslan

Nur Cengiz

Publication Date

March 29, 2017

Submission Date

September 9, 2016

Acceptance Date

-

Published in Issue

Year 2017 Volume: 21 Number: 1

DOI

https://doi.org/10.19113/sdufbed.67047

IZ

https://izlik.org/JA99CN77ZR

Cite

RIS / Bibtex

APA

Aruğaslan, D., & Cengiz, N. (2017). Green’s Function and Periodic Solutions of a Spring-Mass System in which the Forces are Functionally Dependent on Piecewise Constant Argument. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21(1), 266-278. https://doi.org/10.19113/sdufbed.67047

AMA

1.Aruğaslan D, Cengiz N. Green’s Function and Periodic Solutions of a Spring-Mass System in which the Forces are Functionally Dependent on Piecewise Constant Argument. J. Nat. Appl. Sci. 2017;21(1):266-278. doi:10.19113/sdufbed.67047

Chicago

Aruğaslan, Duygu, and Nur Cengiz. 2017. “Green’s Function and Periodic Solutions of a Spring-Mass System in Which the Forces Are Functionally Dependent on Piecewise Constant Argument”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 (1): 266-78. https://doi.org/10.19113/sdufbed.67047.

EndNote

Aruğaslan D, Cengiz N (April 1, 2017) Green’s Function and Periodic Solutions of a Spring-Mass System in which the Forces are Functionally Dependent on Piecewise Constant Argument. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 1 266–278.

IEEE

[1]D. Aruğaslan and N. Cengiz, “Green’s Function and Periodic Solutions of a Spring-Mass System in which the Forces are Functionally Dependent on Piecewise Constant Argument”, J. Nat. Appl. Sci., vol. 21, no. 1, pp. 266–278, Apr. 2017, doi: 10.19113/sdufbed.67047.

ISNAD

Aruğaslan, Duygu - Cengiz, Nur. “Green’s Function and Periodic Solutions of a Spring-Mass System in Which the Forces Are Functionally Dependent on Piecewise Constant Argument”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21/1 (April 1, 2017): 266-278. https://doi.org/10.19113/sdufbed.67047.

JAMA

1.Aruğaslan D, Cengiz N. Green’s Function and Periodic Solutions of a Spring-Mass System in which the Forces are Functionally Dependent on Piecewise Constant Argument. J. Nat. Appl. Sci. 2017;21:266–278.

MLA

Aruğaslan, Duygu, and Nur Cengiz. “Green’s Function and Periodic Solutions of a Spring-Mass System in Which the Forces Are Functionally Dependent on Piecewise Constant Argument”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 21, no. 1, Apr. 2017, pp. 266-78, doi:10.19113/sdufbed.67047.

Vancouver

1.Duygu Aruğaslan, Nur Cengiz. Green’s Function and Periodic Solutions of a Spring-Mass System in which the Forces are Functionally Dependent on Piecewise Constant Argument. J. Nat. Appl. Sci. 2017 Apr. 1;21(1):266-78. doi:10.19113/sdufbed.67047

Cited By

New Results on a Partial Differential Equation with General Piecewise Constant Argument

Turkish Journal of Mathematics and Computer Science

https://doi.org/10.47000/tjmcs.1166651