Free axial vibration of cracked nanotubes incorporating scale effects using doublet mechanics

Normal 0 false false false EN-US X-NONE AR-SA /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0mm 5.4pt 0mm 5.4pt; mso-para-margin-top:0mm; mso-para-margin-right:0mm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0mm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:Arial; mso-bidi-theme-font:minor-bidi;} This paper investigates the free axial 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, the boundary conditions, the tube chirality, and the dimensions of nanotube on the free axial 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.