Rastgele Çatlak Esnekliğine Sahip Çatlaklı Mikro Kirişlerin Doğal Frekans Belirsizliği

Öz

Çatlak esnekliğindeki belirsizlik, özellikle mikro ölçekli yapılarda, titreşim karakteristiklerini önemli ölçüde etkileyen bir unsurdur. Bu çalışmada, rastgele çatlak esnekliğine sahip çatlaklı mikro kirişlerin stokastik serbest titreşim davranışı, değiştirilmiş çift gerilme teorisi çerçevesinde incelenmektedir. Çatlak, burulma yayı olarak modellenmiştir; yayın konumu çatlağın yerini tanımlarken, yay direngenliği, çatlak şiddetini karakterize etmektedir. Stokastik formülasyonda çatlak konumu sabit alınmış, çatlak esnekliği ise rastgele değişken olarak modellenmiştir. Basit mesnetli ve ankastre-ankastre mikro kirişler için doğal frekanslar, karakteristik denkleme dayalı sayısal bir yöntemle elde edilmiştir. Öncelikle, modal yanıtın çatlak konumu ve çatlak esnekliğine en duyarlı olduğu bölgeleri belirlemek amacıyla çatlak parametre düzleminde deterministik frekans haritaları oluşturulmuştur. Daha sonra, çatlak esnekliğindeki belirsizliği yaymak için Monte Carlo simülasyonu kullanılmış ve elde edilen birinci mod frekans örnekleri ortalama, standart sapma, değişim katsayısı ve yüzdelik aralıklar kullanılarak değerlendirilmiştir. Sonuçlar, değişim katsayısının, çatlak konumu kiriş ortasına yaklaştıkça arttığını ve basit mesnetli mikro kirişte, ankastre-ankastre mikro kirişe göre daha yüksek belirsizliğin ortaya çıktığını göstermektedir. Belirsizlik seviyesi duyarlılık analizi sonuçları ise, çatlak esnekliğindeki daha geniş dağılımın daha güçlü frekans belirsizliğine yol açtığını doğrulamaktadır.

Anahtar Kelimeler

• Çatlak esnekliği belirsizliği
• çatlaklı mikro kirişler
• doğal frekans
• modifiye çift gerilme teorisi
• stokastik serbest titreşim.

Natural-Frequency Uncertainty of Cracked Microbeams with Random Crack Flexibility

Öz

Uncertainty in crack flexibility can significantly affect the vibration characteristics of cracked microbeams, particularly in microscale structures. This study investigates the stochastic free vibration behavior of cracked microbeams with random crack flexibility within the framework of modified couple stress theory. The crack is modeled as a torsional spring; its position defines the crack location, while its rotational flexibility characterizes the crack severity. In the stochastic formulation, the crack location is kept deterministic, and the crack flexibility is modeled as a random variable. Natural frequencies are obtained for simply supported and clamped-clamped microbeams using a numerical procedure based on the characteristic equation. Deterministic frequency maps are first generated in the crack parameter plane to identify regions where the modal response is most sensitive to crack location and crack flexibility. Monte Carlo simulation is then used to propagate the uncertainty in crack flexibility, and the resulting samples of the first mode natural frequency are evaluated using the mean, standard deviation, coefficient of variation, and percentile intervals. The results show that the coefficient of variation increases as the crack location moves toward the midspan, and the simply supported microbeam exhibits larger uncertainty than the clamped-clamped microbeam. A sensitivity analysis of the uncertainty level further confirms that greater dispersion in crack flexibility leads to greater uncertainty in the natural frequency.

Anahtar Kelimeler

• Crack flexibility uncertainty
• cracked microbeams
• natural frequency
• modified couple stress theory
• stochastic free vibration

Kaynakça

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