THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION

Duygu Dönmez Demir; B. Gültekin Sınır; Emine Kahraman

THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION

Abstract

The structural engineering researches have attracted considerable attention by many scientist for several decades. Determining the dynamical behaviors of structural elements with some discontinuous is of great importance in many engineering applications. The mentioned structures can be modelled two different ways. In the first approximation so-called the classical approach, a fourth order differential equation are written for each part of beam separated in the distinct discontinuity locations. Therefore, we obtain a system of equation containing number of the differential equation with boundary and transient conditions. Secondly, the real problem can be reformulated by only one differential equation having discontinuity function. In this study, we introduce the method of multiple scales as the solution technique. Since we encountered by the differential equation with discontinuity function in the part of order discretization during the perturbative solution, we have used a numerical technique for the solution. The mentioned technique is applied on the beam model lying on lineer spring foundation called as Winkler type foundation.

Keywords

References

[1] Dutta, SC, Roy, R: A critical review on idealization and modeling for interaction among soil-foundation-structure system. Computers & Structures, 80(20-21), 1579-1594 (2002).
[2] Wang, CM, Reddy, JN, Lee, KH: Shear deformable beams and plates, relationships with classical solutions. Elsevier (2000).
[3] Hayir, A: Dynamic behavior of an elastic beam on a Winkler foundation under a moving load. International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, 4, 1-4 (2010).
[4] Friswell, MI, Penny, JET: A simple nonlinear model of a cracked beam. Proc. 10th Int. Modal Analysis Conf., San Diego, U.S.A., 1, 516-521 (1992).
[5] Failla, G: On the dynamics of viscoelastic discontinuous beams. Mechanics Research Communications, 60, 52-63 (2014).
[6] Failla, G, Santini, A: A solution method for Euler–Bernoulli vibrating discontinuous beams. Mechanics Research Communications, 35, 517-529 (2008).
[7] Failla, G, Santini, A: On Euler–Bernoulli discontinuous beam solutions via uniform-beam Green’s functions. International Journal of Solids and Structures, 44, 7666–7687 (2007).
[8] Li, QS: Free vibration analysis of non-uniform beams with an arbitrary number of cracks and concentrated masses. Journal of Sound and Vibration, 252(3), 509-525 (2002).

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Duygu Dönmez Demir This is me
0000-0003-0886-624X
Türkiye

B. Gültekin Sınır This is me
0000-0002-9478-1666
Türkiye

Emine Kahraman This is me
0000-0002-6876-6817
Türkiye

Publication Date

June 1, 2019

Submission Date

August 8, 2018

Acceptance Date

May 3, 2019

Published in Issue

Year 2019 Volume: 37 Number: 2

IZ

https://izlik.org/JA48XR47CY

Cite

RIS / Bibtex

APA

Dönmez Demir, D., Sınır, B. G., & Kahraman, E. (2019). THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION. Sigma Journal of Engineering and Natural Sciences, 37(2), 495-506. https://izlik.org/JA48XR47CY

AMA

1.Dönmez Demir D, Sınır BG, Kahraman E. THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION. SIGMA. 2019;37(2):495-506. https://izlik.org/JA48XR47CY

Chicago

Dönmez Demir, Duygu, B. Gültekin Sınır, and Emine Kahraman. 2019. “THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION”. Sigma Journal of Engineering and Natural Sciences 37 (2): 495-506. https://izlik.org/JA48XR47CY.

EndNote

Dönmez Demir D, Sınır BG, Kahraman E (June 1, 2019) THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION. Sigma Journal of Engineering and Natural Sciences 37 2 495–506.

IEEE

[1]D. Dönmez Demir, B. G. Sınır, and E. Kahraman, “THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION”, SIGMA, vol. 37, no. 2, pp. 495–506, June 2019, [Online]. Available: https://izlik.org/JA48XR47CY

ISNAD

Dönmez Demir, Duygu - Sınır, B. Gültekin - Kahraman, Emine. “THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION”. Sigma Journal of Engineering and Natural Sciences 37/2 (June 1, 2019): 495-506. https://izlik.org/JA48XR47CY.

JAMA

1.Dönmez Demir D, Sınır BG, Kahraman E. THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION. SIGMA. 2019;37:495–506.

MLA

Dönmez Demir, Duygu, et al. “THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION”. Sigma Journal of Engineering and Natural Sciences, vol. 37, no. 2, June 2019, pp. 495-06, https://izlik.org/JA48XR47CY.

Vancouver

1.Duygu Dönmez Demir, B. Gültekin Sınır, Emine Kahraman. THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION. SIGMA [Internet]. 2019 Jun. 1;37(2):495-506. Available from: https://izlik.org/JA48XR47CY