A modified torsion pendulum apparatus is developed for measuring the shear modu- lus of single filaments with uniform micro-sized diameter. A single filament fixed at both ends and with a ring-shaped mass attached at ...A modified torsion pendulum apparatus is developed for measuring the shear modu- lus of single filaments with uniform micro-sized diameter. A single filament fixed at both ends and with a ring-shaped mass attached at the middle is used as a clamped-clamped torsion pendulum. The shear modulus of single filaments can be expressed as a function of the oscillation frequency of the torsion pendulum. The oscillation motion is measured with a CCD laser displacement sensor, and its frequency is determined by the Fast Fourier Transform （FFT） method. The shear moduli of three types of filaments： copper wires, tungsten wires and carbon fibers are accurately measured with this technique. It is found that the size effect in shear moduli of both copper wires and tungsten wires is minor. Finally, the error analysis of our measurement technique is presented in detail.展开更多
A derivation of an analytical expression for the inviscid velocity fieldinduced by a single right-handed helical vortex filament is presented. The vortex filament movesuniformly and rigidly without change of form in a...A derivation of an analytical expression for the inviscid velocity fieldinduced by a single right-handed helical vortex filament is presented. The vortex filament movesuniformly and rigidly without change of form in a cylindrical tube, where the vortex filamentrotates around its axis with a constant angular velocity and translates along its axis with aconstant translational velocity. The key to solve the problem is to set up a moving cylindricalcoordinate system fixed on the vortex filament. The result shows that the velocity field is atime-periodic function, and may degenerate into Okulovs' s formula when the helical vortex filamentslips along the filament itself or stays immobile.展开更多
基金supported by the National Natural Science Foundation of China(No.11072084 and 11272131)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20110142110039)
文摘A modified torsion pendulum apparatus is developed for measuring the shear modu- lus of single filaments with uniform micro-sized diameter. A single filament fixed at both ends and with a ring-shaped mass attached at the middle is used as a clamped-clamped torsion pendulum. The shear modulus of single filaments can be expressed as a function of the oscillation frequency of the torsion pendulum. The oscillation motion is measured with a CCD laser displacement sensor, and its frequency is determined by the Fast Fourier Transform （FFT） method. The shear moduli of three types of filaments： copper wires, tungsten wires and carbon fibers are accurately measured with this technique. It is found that the size effect in shear moduli of both copper wires and tungsten wires is minor. Finally, the error analysis of our measurement technique is presented in detail.
文摘A derivation of an analytical expression for the inviscid velocity fieldinduced by a single right-handed helical vortex filament is presented. The vortex filament movesuniformly and rigidly without change of form in a cylindrical tube, where the vortex filamentrotates around its axis with a constant angular velocity and translates along its axis with aconstant translational velocity. The key to solve the problem is to set up a moving cylindricalcoordinate system fixed on the vortex filament. The result shows that the velocity field is atime-periodic function, and may degenerate into Okulovs' s formula when the helical vortex filamentslips along the filament itself or stays immobile.
