Free vibration analysis of elastically restrained cantilever Timoshenko beam with attachments

This paper investigates the vibration analysis 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 non-dimensional 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.

Ucunda ekleme bulunan elastik mesnetli konsol Timoshenko kiriþin serbest titreþim analizi

Bu çalýþmada ucunda eklemeler olan bir konsol Timoshenko kiriþin titreþim analizi yapýlmýþtýr. Kiriþin, serbest ucunda lineer yay ile baðlanmýþ kütle taþýdýðý ve sol ucunda dönme yayý bulunduðu varsayýlmýþtýr. Bu kabullere göre doðal frekanslar ve mod þekilleri, kütlenin, serbest uca baðlý lineer yayýn ve dönme yayýnýn etkilerini tanýmlayan boyutsuz parametreler cinsinden elde edilmiþtir. Sonuçlar tablolaþtýrýlmýþ ve bazý parametreler için Timoshenko ve Euler-Bernoulli kiriþ yaklaþýmlarýnýn karþýlaþtýrýlmasý yapýlmýþtýr. Sonuçlar göstermiþtir ki doðal frekanslar uç kütlesinin artmasý ile düþmektedir. Burulma yayý sabitinin büyük deðerleri, yüksek doðal frekanslarý ortaya çýkartmaktadýr.