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| 1 | Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach显示文摘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. | C. W. Lim C. Li Ji-Lin Yu | 2010 | Acta Mechanica Sinica2010，26，5： | 7 |
| 2 | Invariant and energy analysis of an axially retracting beam显示文摘The mechanism of a retracting cantilevered beam has been investigated by the invariant and energy-based analysis. The time-varying parameter partial differential equation governing the transverse vibrations of a beam with retracting motion is derived based on the momentum theorem.The assumed-mode method is used to truncate the governing partial differential equation into a set of ordinary differential equations(ODEs) with time-dependent coefficients. It is found that if the order of truncation is not less than the order of the initial conditions, the assumed-mode method can yield accurate results. The energy transfers among assumed modes are discussed during retraction. The total energy varying with time has been investigated by numerical and analytical methods,and the results have good agreement with each other. For the transverse vibrations of the axially retracting beam, the adiabatic invariant is derived by both the averaging method and the Bessel function method. | Yang Xiaodong Liu Ming Zhang Wei Roderick V.N.Melnik | 2016 | Chinese Journal of Aeronautics2016，29，4： | 4 |
| 3 | 轴向运动结构的能量关系和守恒量研究进展显示文摘综述了轴向运动弦线和梁的能量关系和守恒量的研究进展。分别对于横向线性振动、横向非线性振动和耦合平面振动,确定能量变化的关键量以及轴向运动结构总机械能的时间导数,结果表明总机械能不是常数。对于上述振动,构造在振动过程中保持不变的守恒量,可以用来证明直线平衡位形的稳定性以及检验数值算法。最后提出若干有望取得进展的研究课题。 | 陈立群 | 2016 | 北京大学学报(自然科学版)2016，52，4： | 1 |
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