ÇOK SAYIDA TOPAKLANMIŞ KÜTLE TAŞIYAN ÇOK AÇIKLIKLI TIMOSHENKO KİRİŞİNİN SERBEST TİTREŞİM ANALİZİ

Abstract

In this paper, the natural frequencies and mode shapes of Timoshenko multi-span beam carrying multiple point masses are calculated by using Numerical Assembly Technique (NAT) and Differential Transform Method (DTM). At first, the coefficient matrices for leftend support, an intermediate point mass, an intermediate pinned support and right-end support of Timoshenko beam are derived. Equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multi-span beam carrying multiple point masses for the different values of axial force are given in tables

Keywords

• Differential Transform Method, free vibration, intermediate point mass, natural frequency, Numerical Assembly Technique, Timoshenko multi-span beam

FREE VIBRATION ANALYSIS OF TIMOSHENKO MULTI-SPAN BEAM CARRYING MULTIPLE POINT MASSES

Abstract

Bu çalışmada, çok sayıda topaklanmış kütle taşıyan Timoshenko kirişinin doğal frekansları ve mod şekilleri Nümerik Toplama Tekniği (NTT) ve Diferansiyel Transformasyon Metodu (DTM) kullanılarak hesaplanmıştır. İlk olarak, Timoshenko kirişinin sol uç mesnetinin, ara noktada topaklanmış kütlenin, ara mesnetin ve sağ uç mesnetin katsayılar matrisleri elde edilmiştir. Genel katsayılar matrisinin determinantı sıfıra eşitlenerek titreşen sistemin doğal frekansları hesaplanmış ve integrasyon sabitlerinin ilgili özdeğer fonksiyonlarında yerine yazılmasıyla aranan mod şekilleri elde edilmiştir. Analitik çözümden sonra, DTM kullanılarak diferansiyel hareket denklemleri çözülmüştür. Farklı eksenel kuvvet değerleri için çok sayıda topaklanmış kütle taşıyan Timoshenko kirişinin doğal frekans değerleri tablolar halinde sunulmuştur

Keywords

• Diferansiyel Transformasyon Metodu, serbest titreşim, ara noktalarda topaklanmış kütle, doğal frekans, Nümerik Toplama Tekniği, çok açıklıklı Timoshenko kirişi

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