Free vibration calculations of an euler-bernoulli beam on an elastic foundation using he’s variational iteration method

Alima Tazabekova; Desmond Adair; Askar Ibrayev; Jong Kim

doi:10.1007/978-3-319-97115-5_30

Free vibration calculations of an euler-bernoulli beam on an elastic foundation using he’s variational iteration method

Alima Tazabekova, Desmond Adair, Askar Ibrayev, Jong Kim

Research output: Contribution to journal › Conference article › peer-review

Abstract

Free vibration characteristics for an Euler-Bernoulli beam supported using a simple Winkler linear elastic foundation are calculated. The method of solution is by He’s variational iteration method developed for various boundary (end) conditions. The beam’s natural frequencies and mode shapes are obtained, with rapid convergence noted during the calculations. The calculation method is tested using a clamped-clamped beam. In this paper a robust and efficient algorithm is also given, based on He’s method, which can be easily modified for more complicated elastic foundations.

Original language	English
Pages (from-to)	1022-1026
Number of pages	5
Journal	Springer Series in Geomechanics and Geoengineering
Issue number	216849
DOIs	https://doi.org/10.1007/978-3-319-97115-5_30
Publication status	Published - Jan 1 2018
Event	China-Europe Conference on Geotechnical Engineering, 2016 - Vienna, Austria Duration: Aug 13 2016 → Aug 16 2016

Keywords

Free vibrations
He’s variational method
Winkler foundation

ASJC Scopus subject areas

Geotechnical Engineering and Engineering Geology
Mechanics of Materials

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title = "Free vibration calculations of an euler-bernoulli beam on an elastic foundation using he{\textquoteright}s variational iteration method",

abstract = "Free vibration characteristics for an Euler-Bernoulli beam supported using a simple Winkler linear elastic foundation are calculated. The method of solution is by He{\textquoteright}s variational iteration method developed for various boundary (end) conditions. The beam{\textquoteright}s natural frequencies and mode shapes are obtained, with rapid convergence noted during the calculations. The calculation method is tested using a clamped-clamped beam. In this paper a robust and efficient algorithm is also given, based on He{\textquoteright}s method, which can be easily modified for more complicated elastic foundations.",

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author = "Alima Tazabekova and Desmond Adair and Askar Ibrayev and Jong Kim",

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doi = "10.1007/978-3-319-97115-5_30",

language = "English",

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journal = "Springer Series in Geomechanics and Geoengineering",

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T1 - Free vibration calculations of an euler-bernoulli beam on an elastic foundation using he’s variational iteration method

AU - Tazabekova, Alima

AU - Adair, Desmond

AU - Ibrayev, Askar

AU - Kim, Jong

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Free vibration characteristics for an Euler-Bernoulli beam supported using a simple Winkler linear elastic foundation are calculated. The method of solution is by He’s variational iteration method developed for various boundary (end) conditions. The beam’s natural frequencies and mode shapes are obtained, with rapid convergence noted during the calculations. The calculation method is tested using a clamped-clamped beam. In this paper a robust and efficient algorithm is also given, based on He’s method, which can be easily modified for more complicated elastic foundations.

AB - Free vibration characteristics for an Euler-Bernoulli beam supported using a simple Winkler linear elastic foundation are calculated. The method of solution is by He’s variational iteration method developed for various boundary (end) conditions. The beam’s natural frequencies and mode shapes are obtained, with rapid convergence noted during the calculations. The calculation method is tested using a clamped-clamped beam. In this paper a robust and efficient algorithm is also given, based on He’s method, which can be easily modified for more complicated elastic foundations.

KW - Free vibrations

KW - He’s variational method

KW - Winkler foundation

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SP - 1022

EP - 1026

JO - Springer Series in Geomechanics and Geoengineering

JF - Springer Series in Geomechanics and Geoengineering

SN - 1866-8755

IS - 216849

T2 - China-Europe Conference on Geotechnical Engineering, 2016

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