Ucunda ekleme bulunan elastik mesnetli konsol Timoshenko kirişin serbest titreşim analizi

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 EulerBernoulli kiriş yaklaşımlarının karşılaştırılması yapılmıştır. Sonuçlar göstermiştir ki doğal frekanslar uç kütlesinin artması ile düşmektedir. Burulma yayı sabitinin büyük değerleri, yüksek doğal frekansları ortaya çıkartmaktadır.

Anahtar Kelimeler:

Timoshenko kiriş, Titreşim, kütle-yay sistemi, Doğal frekanslar, Mod şekiller

Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments

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.

Keywords:

Timoshenko beam, Vibration, Spring-mass system, Natural frequencies, Mode shapes,

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