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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with Association for Scientific Research (ASR).
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Article

Free Vibration Analysis of Beams on Variable Winkler Elastic Foundation by Using the Differential Transform Method

by
Alev Kacar
,
H. Tugba Tan
and
Metin O. Kaya
*
Faculty of Aeronautics and Astronautics Istanbul Technical University, 34469, Maslak Istanbul, Turkey
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2011, 16(3), 773-783; https://doi.org/10.3390/mca16030773
Published: 1 December 2011
Versions Notes

Abstract

In this study, free vibration of an Euler-Bernoulli beam resting on a variable Winkler foundation is considered. Structures which are supported along their length such as beams or pipelines resting on elastic soil are very commonly modeled with a Winkler foundation. In this problem, the elastic coefficient of the foundation is variable along the beam major axis. Constant, linear and parabolic variations are considered. The problem is handled for three different boundary conditions: simply supported-simply supported, clamped-clamped and cantilever (clamped-free) beams. The governing differential equations of the beam are solved by using Differential Transform Method (DTM). DTM is an easy transformation technique based on Taylor expansion series, providing high accuracy.
Keywords: Differential Transform Method; DTM, Elastic soil; Vibration; Beam; Pipeline Differential Transform Method; DTM, Elastic soil; Vibration; Beam; Pipeline

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MDPI and ACS Style

Kacar, A.; Tan, H.T.; Kaya, M.O. Free Vibration Analysis of Beams on Variable Winkler Elastic Foundation by Using the Differential Transform Method. Math. Comput. Appl. 2011, 16, 773-783. https://doi.org/10.3390/mca16030773

AMA Style

Kacar A, Tan HT, Kaya MO. Free Vibration Analysis of Beams on Variable Winkler Elastic Foundation by Using the Differential Transform Method. Mathematical and Computational Applications. 2011; 16(3):773-783. https://doi.org/10.3390/mca16030773

Chicago/Turabian Style

Kacar, Alev, H. Tugba Tan, and Metin O. Kaya. 2011. "Free Vibration Analysis of Beams on Variable Winkler Elastic Foundation by Using the Differential Transform Method" Mathematical and Computational Applications 16, no. 3: 773-783. https://doi.org/10.3390/mca16030773

APA Style

Kacar, A., Tan, H. T., & Kaya, M. O. (2011). Free Vibration Analysis of Beams on Variable Winkler Elastic Foundation by Using the Differential Transform Method. Mathematical and Computational Applications, 16(3), 773-783. https://doi.org/10.3390/mca16030773

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