DYNAMIC RESPONSE ANALYSIS OF A 3-STORY SHEAR FRAME SUBJECTED TO HARMONIC LOADING: AN ANALYTICAL APPROACH

Yıl 2019, Cilt: 24 Sayı: 2, 725 - 734, 30.08.2019

Ahmet Tüken

https://doi.org/10.17482/uumfd.449686

Öz

The multi-story
buildings are likely to be subjected to various types of dynamic loadings. In
the present study, a three-story shear frame subjected to a harmonic force at
the top floor is studied and the equations for the floor displacements as
functions of time have been obtained. Then normalized response amplitudes under
the applied harmonic loading is plotted against the frequency ratio w/w₁. These
frequency-response curves show three resonance conditions at w=w₁, w=w₂ and w=w₃; at these exciting frequencies the steady-state
response is unbounded. At other exciting frequencies, the vibration is finite
and could be calculated from the derived equations. The structure experiences
resonance at some frequency if the structure is excited with harmonic loading
over a range of frequencies. When the frequency of the excitation is equal to
the natural frequency of the structure, resonance occurs. The structure
experiences its largest response at the resonant frequency as compared to any
other frequency of loading. 

Anahtar Kelimeler

Harmonic loading, Shear frame, Frequency-response curves, Normalized response, MDOF system

Harmonik Yüklemeye Maruz Kalan 3-Katlı Kayma Çerçevesinin Dinamik Tepki Analizi: Analitik Bir Yaklaşım

Öz

Çok katlı binaların çeşitli tiplerde dinamik yüklemelere maruz
kalması muhtemeldir. Bu çalışmada, en üst katta harmonik bir kuvvete maruz
kalan üç katlı bir kayma çerçevesi çalışılmış ve zamanın fonksiyonu olarak kat yer
değiştirmeleri için denklemler elde edilmiştir. Daha sonra uygulanan harmonik
yükleme altındaki normalleştirilmiş tepki büyüklükleri, frekans oranı ω/ω₁'e
karşı çizilmiştir. Bu frekans-tepki eğrileri, ω=ω₁, ω=ω₂
ve ω=ω₃ değerlerinde üç rezonans durumu gösterir; bu uyarıcı
frekanslarda durağan-durum tepkisi sınırsızdır. Diğer uyarıcı frekanslarda,
titreşim sonludur ve türetilmiş denklemlerden hesaplanabilir. Yapı bir dizi
frekans üzerinden harmonik yükleme ile uyarıldığında, bazı frekanslarda rezonans yaşar.
Rezonans frekansı yapının doğal frekansına eşit olduğunda rezonans oluşur.
Rezonans frekansında, yapı diğer herhangi bir yükleme frekansına kıyasla en
büyük tepkisini tecrübe eder.

Anahtar Kelimeler

Harmonik yükleme, Kayma çerçevesi, Frekans-tepki eğrisi, Normalleştirilmiş tepki, Çok serbestlik dereceli sistem (ÇSDS)

Kaynakça

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• Chopra A.K. (2014) Dynamics of Structures, 4th Global Edition, Pearson, Prentice Hall.
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