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

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)

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

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.

Keywords:

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

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