It has been a known fact in classical mechanics of materials that Young’s modulus is an indicator of material stiffness and materials with a higher Young’s modulus are stiffer. At the nanoscale, within the scope and...It has been a known fact in classical mechanics of materials that Young’s modulus is an indicator of material stiffness and materials with a higher Young’s modulus are stiffer. At the nanoscale, within the scope and under specific circumstances described in this paper, however, a nanorod (or a nanotube) with a smaller Young’s modulus (smaller stress-strain rate) is stiffer. In such a scenario, Young’s modulus is not a stiffness indicator for nanostructures. Furthermore, the nonlocal stress-strain rate is dependent on types of load, boundary conditions and location. This is likely to be one of the many possible reasons why numerous experiments in the past obtained significantly varying values of Young’s modulus for a seemingly identical nanotube, i.e. because the types of loading and/or boundary conditions in the experiments were different, as well as at which point the property was measured. Based on the nonlocal elasticity theory and within the scope of material and geometric linearity, this paper reports the strange and hitherto unrealized effect that a nanorod (or a nanotube) with a lower Young’s modulus (smaller stress-strain rate) indicates smaller extension in tensile analysis. Similarly, it is also predicted that a nanorod (or a nanotube) with a lower Young’s modulus results in smaller bending deflection, higher critical buckling load, higher free vibration frequency and higher wave propagation velocity, which are at all consequences of a stiffer nanostructure.展开更多
This paper investigates the transverse vibration of a simply supported nanobeam with an initial axial tension based on the nonlocal stress field theory with a nonlocal size parameter. Considering an axial elongation d...This paper investigates the transverse vibration of a simply supported nanobeam with an initial axial tension based on the nonlocal stress field theory with a nonlocal size parameter. Considering an axial elongation due to transverse vibration, the internal axial tension is not precisely equal to the external initial tension. A sixth-order nonlinear partial differential equation that governs the transverse vibration for such nonlocal nanobeam is derived. Using a perturbation method, the relation between natural frequency and nonlocal nanoscale parameter is derived and the transverse vibration mode is solved. The external axial tension and nonlocal nanoscale parameter are proven to play significant roles in the nonlinear vibration behavior of nonlocal nanobeams. Such effects enhance the natural frequency and stiffness as compared to the predictions of the classical continuum mechanics models. Additionally, the frequency is higher if the precise internal axial load is considered with respect to that when only the approximate internal axial tension is assumed.展开更多
基金supported by the Research Grants Council of the HongKong Special Administrative Region (Grant No. CityU 117406)
文摘It has been a known fact in classical mechanics of materials that Young’s modulus is an indicator of material stiffness and materials with a higher Young’s modulus are stiffer. At the nanoscale, within the scope and under specific circumstances described in this paper, however, a nanorod (or a nanotube) with a smaller Young’s modulus (smaller stress-strain rate) is stiffer. In such a scenario, Young’s modulus is not a stiffness indicator for nanostructures. Furthermore, the nonlocal stress-strain rate is dependent on types of load, boundary conditions and location. This is likely to be one of the many possible reasons why numerous experiments in the past obtained significantly varying values of Young’s modulus for a seemingly identical nanotube, i.e. because the types of loading and/or boundary conditions in the experiments were different, as well as at which point the property was measured. Based on the nonlocal elasticity theory and within the scope of material and geometric linearity, this paper reports the strange and hitherto unrealized effect that a nanorod (or a nanotube) with a lower Young’s modulus (smaller stress-strain rate) indicates smaller extension in tensile analysis. Similarly, it is also predicted that a nanorod (or a nanotube) with a lower Young’s modulus results in smaller bending deflection, higher critical buckling load, higher free vibration frequency and higher wave propagation velocity, which are at all consequences of a stiffer nanostructure.
基金supported by a collaboration scheme from University of Science and Technology of China-City University of Hong Kong Joint Advanced Research Institute and by City University of Hong Kong of China (Grant No. 7002699 (BC))
文摘This paper investigates the transverse vibration of a simply supported nanobeam with an initial axial tension based on the nonlocal stress field theory with a nonlocal size parameter. Considering an axial elongation due to transverse vibration, the internal axial tension is not precisely equal to the external initial tension. A sixth-order nonlinear partial differential equation that governs the transverse vibration for such nonlocal nanobeam is derived. Using a perturbation method, the relation between natural frequency and nonlocal nanoscale parameter is derived and the transverse vibration mode is solved. The external axial tension and nonlocal nanoscale parameter are proven to play significant roles in the nonlinear vibration behavior of nonlocal nanobeams. Such effects enhance the natural frequency and stiffness as compared to the predictions of the classical continuum mechanics models. Additionally, the frequency is higher if the precise internal axial load is considered with respect to that when only the approximate internal axial tension is assumed.
