Free vibration of a cantilever tapered Timoshenko beam

Cekus, Dawid

doi:10.17512/jamcm.2012.4.02

Cited by 8 publications

(2 citation statements)

References 12 publications

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“…In that study, differential quadrature element method (DQEM) is used and the changing of the frequencies of the beam is studied in terms of parameters of the mass. Cekus [17] studied the free vibration of a cantilever tapered Timoshenko beam by using Lagrange multiplier formalism. The governing equations for the Timoshenko beams with geometrical non-uniformity and material inhomogeneity along the beam axis have been simplified by a new method [18].…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments

Pala,

Kahya

2023

Pamukkale J Eng Sci

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This paper investigates the lateral vibration of a cantilever Timoshenko beam with attachments. It is assumed that the beam carries a mass attached to the free end with a linear spring and there exists a rotational spring at the left end. Depending upon these assumptions, mode shapes and natural frequencies are obtained in terms of nondimensional parameters which describe the effects of additional mass, linear spring and rotational spring. The results are tabulated, and the comparison of Timoshenko and Euler-Bernoulli beam approaches are carried out for some parameters. Results reveal that natural frequencies decrease while the values of end mass increase. Large values of the rotational spring constant cause high natural frequencies. Bu çalışmada ucunda eklemeler olan bir konsol Timoshenko kirişin titreşim analizi yapılmıştır. Kirişin, serbest ucunda lineer yay ile bağlanmış kütle taşıdığı ve sol ucunda dönme yayı bulunduğu varsayılmıştır. Bu kabullere göre doğal frekanslar ve mod şekilleri, kütlenin, serbest uca bağlı lineer yayın ve dönme yayının etkilerini tanımlayan boyutsuz parametreler cinsinden elde edilmiştir. Sonuçlar tablolaştırılmış ve bazı parametreler için Timoshenko ve Euler-Bernoulli kiriş yaklaşımlarının karşılaştırılması yapılmıştır. Sonuçlar göstermiştir ki doğal frekanslar uç kütlesinin artması ile düşmektedir. Burulma yayı sabitinin büyük değerleri, yüksek doğal frekansları ortaya çıkartmaktadır.

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Section: Introductionmentioning

confidence: 99%

Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments

Pala,

Kahya

2023

Pamukkale J Eng Sci

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show abstract

“…homotopy analysis [3] or the Green's functions method [4]. However, in most cases, in order to obtain a solution it is necessary to apply approximate methods, such as finite difference method [5], the power series method [6], differential transformation method (DTM) -"improved" Taylor method [5,7,8] or by the use of the Lagrange multiplier formalism [9]. This paper is a continuation of consideration, shown at [10], relating to the use of a matrix and power series methods for solving ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%