Uç Kütlesi Bulunan Mikrokirişlerin Manyetik Alan Altında Lineer Olmayan Titreşimlerinde Çatlakların Etkilerinin İncelenmesi

Öz

Mikroelektromekanik sistemler (MEMS), birçok endüstriyel alana uygulanabilmeleri sayesinde, modern teknolojik cihazların önemli elemanlarından biri haline gelmiştir. MEMS’ in fiziksel uygulamalarında sıklıkla ortaya çıkan çatlaklar, sistemin statik ve dinamik davranışlarını etkilemektedir. Bu makalede, manyetik alan etkisi altındaki, uç kütleye sahip mikrokirişler üzerindeki çatlakların etkileri incelenmiştir. Kirişin mikro boyut etkisi, değiştirilmiş çift gerilme teorisi kullanılarak modele dahil edilmiştir. Çatlak, bir burulma yayı kullanılarak modellenmiştir ve burulma yay katsayısı çatlak şiddetine karşılık gelmektedir. Böylece kiriş, burulma yayı aracılığı ile birbirine bağlı iki kısımdan oluşacak şekilde modellenmiştir. Hareket denklemleri Hamilton prensibi uygulanarak oluşturulmuştur. Elde edilen denklemler, bir perturbasyon yöntemi olan çok ölçekli metot kullanılarak çözülmüştür. Mikrokirişlerin hem lineer hem de nonlineer titreşimlerine ilişkin frekansları incelenmiştir. Bu çalışmada elde edilen sonuçlar, literatürde bulunan mevcut sayısal sonuçlar kullanılarak doğrulanmıştır. Çatlak şiddeti, çatlak konumu, uç kütle ve manyetik alan kuvveti gibi parametrelerin lineer ve nonlineer titreşimler üzerindeki etkileri sunulmuştur. Elde edilen sonuçlar, mikrokirişlerin doğal frekansları ve nonlineer frekanslarında, çatlak şiddetinin artmasıyla birlikte önemli ölçüde düşüş olduğunu göstermektedir.

Anahtar Kelimeler

• Nonlineer Titreşimler
• Çatlak İçeren Mikrokirişler
• Perturbasyon Teknikleri
• Değiştirilmiş Çift Gerilme Teorisi
• Çok Ölçekli Metot

Investigation of Crack Effects on the Nonlinear Vibrations of Microbeams with a Tip Mass in a Magnetic Field

Öz

Microelectromechanical systems (MEMS) are critical members of modern technological devices, due to their applications in various industrial fields. In the physical applications of MEMS, cracks are a common structural problem, affecting the static and dynamic behavior of the system. In this paper, the effects of cracks on microbeams with a tip mass under the influence of a magnetic field have been investigated. The micro-size effect of the beam has been involved into the model by using the modified couple stress theory. The crack has been modeled by using a torsional spring, with the spring coefficient corresponds to the severity of the crack. Thus, the beam has been modeled as consisting of two segments connected by a torsional spring. The equations of motion have been formulated using Hamilton’s principle. The obtained equations have been solved by using the method of multiple scales, a perturbation technique. Frequencies regarding both linear and nonlinear vibrations of the microbeams have been examined. The results obtained in this study have been validated by using available numerical results in the literature. The effects of parameters such as crack severity, crack location, tip mass and the magnetic field force on linear and nonlinear vibrations have been presented. The results indicate a significant decrease in the natural frequencies and nonlinear frequencies of microbeams with increasing crack severity.

Anahtar Kelimeler

• Nonlinear Vibrations
• Cracked Microbeams
• Perturbation Techniques
• Modified Couple Stress Theory
• Method of Multiple Scales

Kaynakça

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