Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method

Gökhan Güçlü; Uğur Kafkas

doi:10.31466/kfbd.1706419

TR EN

Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method

Öz

This study used analytical and numerical methods to investigate Euler-Bernoulli beams’ free axial vibration behavior with homogeneous and linearly elastic properties. The equations derived within the framework of Hamilton’s principle were simplified through a non-dimensionalization approach and the system parameters were consolidated into a single dimensionless stiffness ratio. The analytical solution enabled the computation of natural frequencies by determining the roots of a transcendental equation. The approximate solutions obtained via the Ritz method were compared with the analytical results to assess the method’s convergence properties. The results indicate that increasing the number of parameters significantly enhances the agreement of the approximate solutions derived from the Ritz method with the analytical results, thereby validating the method’s applicability and effectiveness in structural dynamics analyses.

Anahtar Kelimeler

Euler-Bernoulli beam, Axial free vibration, Hamilton’s principle, Ritz method

Kaynakça

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Ayrıntılar

Birincil Dil

İngilizce

Konular

Katı Mekanik, Sürekli Ortam Mekaniği

Bölüm

Araştırma Makalesi

Yazarlar

Gökhan Güçlü ^*
0000-0003-2931-9501
Türkiye

Uğur Kafkas
0000-0003-1730-7810
Türkiye

Yayımlanma Tarihi

6 Mart 2026

Gönderilme Tarihi

26 Mayıs 2025

Kabul Tarihi

28 Eylül 2025

Yayımlandığı Sayı

Yıl 2026 Cilt: 16 Sayı: 1

DOI

https://doi.org/10.31466/kfbd.1706419

IZ

https://izlik.org/JA88TZ89ZK

APA

Güçlü, G., & Kafkas, U. (2026). Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method. Karadeniz Fen Bilimleri Dergisi, 16(1), 366-382. https://doi.org/10.31466/kfbd.1706419

AMA

1.Güçlü G, Kafkas U. Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method. KFBD. 2026;16(1):366-382. doi:10.31466/kfbd.1706419

Chicago

Güçlü, Gökhan, ve Uğur Kafkas. 2026. “Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method”. Karadeniz Fen Bilimleri Dergisi 16 (1): 366-82. https://doi.org/10.31466/kfbd.1706419.

EndNote

Güçlü G, Kafkas U (01 Mart 2026) Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method. Karadeniz Fen Bilimleri Dergisi 16 1 366–382.

IEEE

[1]G. Güçlü ve U. Kafkas, “Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method”, KFBD, c. 16, sy 1, ss. 366–382, Mar. 2026, doi: 10.31466/kfbd.1706419.

ISNAD

Güçlü, Gökhan - Kafkas, Uğur. “Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method”. Karadeniz Fen Bilimleri Dergisi 16/1 (01 Mart 2026): 366-382. https://doi.org/10.31466/kfbd.1706419.

JAMA

1.Güçlü G, Kafkas U. Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method. KFBD. 2026;16:366–382.

MLA

Güçlü, Gökhan, ve Uğur Kafkas. “Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method”. Karadeniz Fen Bilimleri Dergisi, c. 16, sy 1, Mart 2026, ss. 366-82, doi:10.31466/kfbd.1706419.

Vancouver

1.Gökhan Güçlü, Uğur Kafkas. Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method. KFBD. 01 Mart 2026;16(1):366-82. doi:10.31466/kfbd.1706419

Karadeniz Fen Bilimleri Dergisinde yayınlanan makaleler Creative Commons Attribution-NonCommercial 4.0 International kapsamında lisanslanmıştır.

Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method

Ritz Yöntemi ile Euler-Bernoulli Kirişlerinin Eksenel Serbest Titreşimi

Öz

Anahtar Kelimeler

Axial Free Vibration of Euler-Bernoulli Beams via Ritz Method

Öz

Anahtar Kelimeler

Kaynakça

Ayrıntılar

Birincil Dil

Konular

Bölüm

Yazarlar

Yayımlanma Tarihi

Gönderilme Tarihi

Kabul Tarihi

Yayımlandığı Sayı

DOI

IZ

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