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Free Longitudinal Vibrations Analysis of Nanorods Based on Eringen’s Nonlocal Theory with Considering Surface Energy Using Wave Approach
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نویسندگان
1فارغ التحصیل از دانشگاه آزاد اسلامی واحد تهران شمال
2دپارتمان مهندسی مکانیک، دانشگاه علم و فرهنگ، تهران ، ایران
چکیده
In this paper, analysis of free longitudinal vibrations of continuous nanorod (nanotube) in cylindrical coordinate system, have been done by wave method. therefore, first the axial force equation of nanorod is derived from its motion equation. and then by using of Eringen's nonlocal elasticity theory, nanlocal axial force of nanorod is obtained. after deriving axial force equation which includes surface energy parameters, equations of motion and axial force of nanorod in terms of positive-going and negative-going waves are obtained. by placing the spring at the end of the boundaries of the nanorod, wave propagation matrix is obtained under boundary conditions of clamped-clamped and clamped-free. eventually by calculation the dimensionless frequency of nanorod for both of the mentioned boundary conditions, dimensionless frequency changes vs nonlocal parameter and also vs sureface energy parameters as diagram have been investigated. in each diagram, first three modes of dimensionless natural frequency under difference Poisson ratio are investigated.
کلیدواژه ها
موضوعات
 
Title
Free Longitudinal Vibrations Analysis of Nanorods Based on Eringen’s Nonlocal Theory with Considering Surface Energy Using Wave Approach
Authors
Mitra Siahnouri, Masih Loghmani
Abstract
In this paper, analysis of free longitudinal vibrations of continuous nanorod (nanotube) in cylindrical coordinate system, have been done by wave method. therefore, first the axial force equation of nanorod is derived from its motion equation. and then by using of Eringen's nonlocal elasticity theory, nanlocal axial force of nanorod is obtained. after deriving axial force equation which includes surface energy parameters, equations of motion and axial force of nanorod in terms of positive-going and negative-going waves are obtained. by placing the spring at the end of the boundaries of the nanorod, wave propagation matrix is obtained under boundary conditions of clamped-clamped and clamped-free. eventually by calculation the dimensionless frequency of nanorod for both of the mentioned boundary conditions, dimensionless frequency changes vs nonlocal parameter and also vs sureface energy parameters as diagram have been investigated. in each diagram, first three modes of dimensionless natural frequency under difference Poisson ratio are investigated.
Keywords
longitudinal vibration, nanorod, Eringens theory, surface energy