Free tangential vibration of cracked nanotubes incorporating scale effects using doublet mechanics
محورهای موضوعی : Analytical and Numerical Methods in Mechanical Design
Alireza Fatahi-Vajari
1
,
Zahra Azimzadeh
2
1 - Department of Mechanical Engineering, Shahryar Branch, Islamic Azad University, Shahryar, Iran
2 - Department of Mathematics, College of Sciences, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran
کلید واژه: Tangential vibration, Cracked nanotube, Doublet mechanics, Natural frequency, Crack severity.,
چکیده مقاله :
This paper investigates the free tangential vibration of cracked nanotubes with considering scale parameter under various boundary conditions. The cracked nanotube is modeled by dividing it into two segments connected by a linear spring. The stiffness of the spring is dependent to the crack severity and obtained using fracture mechanics principles. Governing equations and corresponding boundary conditions are derived with the aid of doublet mechanics (DM). The natural frequencies are obtained analytically with solving characteristics equation and the influence of the crack severity, boundary conditions, tube chirality, and the dimensions of nanotube on the free tangential vibration of cracked nanotubes is studied in detail. It was shown that the frequency decreases with increase of the crack severity and scale parameter. This reduction is more apparent when the boundaries of the beam are changed from free end to clamped one. In addition, when the crack location is near the support, a larger decrease in the frequency can be observed. To validate accuracy and efficiency of the present method, the results obtained herein are compared with the available results in the literatures and good agreement is observed.
This paper investigates the free tangential vibration of cracked nanotubes with considering scale parameter under various boundary conditions. The cracked nanotube is modeled by dividing it into two segments connected by a linear spring. The stiffness of the spring is dependent to the crack severity and obtained using fracture mechanics principles. Governing equations and corresponding boundary conditions are derived with the aid of doublet mechanics (DM). The natural frequencies are obtained analytically with solving characteristics equation and the influence of the crack severity, boundary conditions, tube chirality, and the dimensions of nanotube on the free tangential vibration of cracked nanotubes is studied in detail. It was shown that the frequency decreases with increase of the crack severity and scale parameter. This reduction is more apparent when the boundaries of the beam are changed from free end to clamped one. In addition, when the crack location is near the support, a larger decrease in the frequency can be observed. To validate accuracy and efficiency of the present method, the results obtained herein are compared with the available results in the literatures and good agreement is observed.
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