Farklı Uç Koşullarına sahip Uç Kütleli bir Ankastre Kirişin Eğilme Titreşimleri için Geliştirilmiş Yeni Bir Yöntem

Year 2025, EARLY VIEW, 1 - 1

Orçun Biçer , Mustafa Yıldız , Sadettin Orhan

https://doi.org/10.2339/politeknik.1726887

Abstract

Tek serbestlik dereceli toplu model, uç kütlesi olan konsol kirişin eğilme titreşimini incelerken basitliği nedeniyle sıklıkla kullanılır. Bu amaçla, bazı varsayımlarla eşdeğer tek serbestlik dereceli bir model elde edilir. Bu varsayımlar sonucun doğruluğunu etkiler. Bu çalışma, uç kütlesinin kiriş kütlesine oranının bir fonksiyonu olarak tanımlanan ve ilk doğal frekans değerini elde etmek için kullanılan orantı parametresi η için yeni bir formülasyon önermektedir. Önerilen formüle bağlı olarak, ilk doğal frekansın kütle oranına göre hesaplanması basitleştirilmiş ve sonuçlar iyileştirilmiştir. Orantı parametresinin yeni formülasyonu, etkinliğini doğrulamak için literatürde incelenen referans modele uygulanmıştır. Doğrulandıktan sonra, üç yeni karmaşık durum ele alınmış ve karşılık gelen eşdeğer yay sabiti ve doğal frekans parametresi elde edilmiştir. Son olarak, yalnızca yükseklik konikliği, yalnızca genişlik konikliği ve çift koniklikten oluşan uç kütlesi olan ve olmayan üç farklı konik durum için ilk boyutsuz doğal frekanslar elde edilmiştir. Sonuçların literatürde sunulan teorik frekanslara yakın olduğu görülebilir.

Keywords

Uç Kütleli Ankastre Kiriş , Doğal Frekans , Kütle-Yay Sistemi , Eğilme Titreşimleri , Ayrık Titreşim Modeli

An Improved Approach for Bending Vibrations of Cantilever Beam with Tip Mass at Different End Conditions

Abstract

Single dof lumped model is frequently utilized due to its simlicity, when studying bending vibration of cantilever beam with a tip mass. For this purpose, an equivalent single dof model is obtained with some assumptions. These assumptions effect the accuracy of the result. This study proposes a new formulation of proportion parameter η which is defined as a function of ratio of the tip mass to the beam mass and used to obtain the value of the first natural frequency. Depending on proposed formula, calculation of the first natural frequency with respect to the mass ratio was simplified and the results were improved. The new formulation of the proportion parameter was applied to the reference model studied in literature to verify its effectiveness. After it is verified, three complex new cases were considered and the corresponding equivalent spring constant and natural frequency parameter were obtained. Lastly, the first non-dimensional natural frequencies were obtained for three different tapered cases with and without tip mass consisting of only height taper, only width taper and double taper. One can see that the results are close to theoretical frequencies presented in the literature.

Keywords

Cantilever beam with tip mass , Natural frequency , Mass-spring system , Lateral Vibrations , Discrete vibration model

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