Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach

• Published in: Acta mechanica Sinica 2010-10, Vol.26 (5), p.755-765
• Main Authors: Lim, C. W., Li, C., Yu, Ji-Lin
• Format: Article
• Language: English
• Subjects: Axial stress; Classical and Continuum Physics; Computational Intelligence; Critical velocity; Engineering; Engineering Fluid Dynamics; Mathematical analysis; Mathematical models; Nanocomposites; Nanomaterials; Nanostructure; Research Paper; Theoretical and Applied Mechanics; Vibration; 动力学行为; 弹性分析法; 横向自由振动; 自然频率; 轴向拉力; 轴向运动; 运动微分方程; 非局部
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-010-0374-z

In this article, transverse free vibrations of axially moving nanobeams subjected to axial tension are studied based on nonlocal stress elasticity theory. A new higher-order differential equation of motion is derived from the variational principle with corresponding higher-order, non-classical boundary conditions. Two supporting conditions are investigated, i.e. simple supports and clamped supports. Effects of nonlocal nanoscale, dimensionless axial velocity, density and axial tension on natural frequencies are presented and discussed through numerical examples. It is found that these factors have great influence on the dynamic behaviour of an axially moving nanobeam. In particular, the nonlocal effect tends to induce higher vibration frequencies as compared to the results obtained from classical vibration theory. Analytical solutions for critical velocity of these nanobeams when the frequency vanishes are also derived and the influences of nonlocal nanoscale and axial tension on the critical velocity are discussed.