The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s ...The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.展开更多
Characteristics of cross flow around three rectangular cylinders with two aspect ratios of breadth to width arranged in connected and separated Y-shape at various angles of incident flow were studied by means of force...Characteristics of cross flow around three rectangular cylinders with two aspect ratios of breadth to width arranged in connected and separated Y-shape at various angles of incident flow were studied by means of force measurement in a wind tunnel. Flow visualizations with smoke-wire technique for typical cases were also given. Different types of flow patterns were formed for individual models at different angles of incident flow. From the results of fluctuating velocity measurement in the wake, features of vibration were determined. It shows that as the wind blows along the lines of one limb or rectangular cylinder of the model, oscillation is weak, whereas when the wind blows along the bisector lines of two limbs or cylinders, strong vibration is observed. It is associated with the regular vortex shedding.展开更多
The nonlinear hydrodynamic interaction between a floating elliptic cylinder and a vibrating circular cylinder immersed in an infinite fluid was investigated. By taking the added masses of the two-cylinder system into ...The nonlinear hydrodynamic interaction between a floating elliptic cylinder and a vibrating circular cylinder immersed in an infinite fluid was investigated. By taking the added masses of the two-cylinder system into account, the dynamical equations of motion were formulated from the Lagrange equations of motion. The dynamical behaviors of these two cylinders were analyzed numerically for some typical situations, and the results show that the presence of a vibrating circular cylinder has a significant influence on the planar motion of a floating elliptic cylinder. The hydrodynamic interaction between them results in complicated nonlinear behaviors of the floating cylinder. It is found that oscillatory motion of the elliptic cylinder takes place in response to the vibrating mode of the circular one.展开更多
The wave propagation in an infinite, homogeneous, transversely isotropic solid cylin- der of arbitrary cross-section is studied using Fourier expansion collocation method, within the frame work of linearized, three-di...The wave propagation in an infinite, homogeneous, transversely isotropic solid cylin- der of arbitrary cross-section is studied using Fourier expansion collocation method, within the frame work of linearized, three-dimensional theory of thermoelasticity. Three displacement po- tential functions are introduced, to uncouple the equations of motion and the heat conduction. The frequency equations are obtained for longitudinal and flexural （symmetric and antisymmet- ric） modes of vibration and are studied numerically for elliptic and parabolic cross-sectional zinc cylinders. The computed non-dimensional wave numbers are presented in the form of dispersion curves.展开更多
基金the National Natural Science Foundation of China (10472067)
文摘The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.
基金The project supported by the National Natural Science Foundation of China(10172008)
文摘Characteristics of cross flow around three rectangular cylinders with two aspect ratios of breadth to width arranged in connected and separated Y-shape at various angles of incident flow were studied by means of force measurement in a wind tunnel. Flow visualizations with smoke-wire technique for typical cases were also given. Different types of flow patterns were formed for individual models at different angles of incident flow. From the results of fluctuating velocity measurement in the wake, features of vibration were determined. It shows that as the wind blows along the lines of one limb or rectangular cylinder of the model, oscillation is weak, whereas when the wind blows along the bisector lines of two limbs or cylinders, strong vibration is observed. It is associated with the regular vortex shedding.
基金Project supported by the the Hong Kong Research Grants Council (Grant Nos: HKU 7066/97E and HKU 7068/00E).
文摘The nonlinear hydrodynamic interaction between a floating elliptic cylinder and a vibrating circular cylinder immersed in an infinite fluid was investigated. By taking the added masses of the two-cylinder system into account, the dynamical equations of motion were formulated from the Lagrange equations of motion. The dynamical behaviors of these two cylinders were analyzed numerically for some typical situations, and the results show that the presence of a vibrating circular cylinder has a significant influence on the planar motion of a floating elliptic cylinder. The hydrodynamic interaction between them results in complicated nonlinear behaviors of the floating cylinder. It is found that oscillatory motion of the elliptic cylinder takes place in response to the vibrating mode of the circular one.
文摘The wave propagation in an infinite, homogeneous, transversely isotropic solid cylin- der of arbitrary cross-section is studied using Fourier expansion collocation method, within the frame work of linearized, three-dimensional theory of thermoelasticity. Three displacement po- tential functions are introduced, to uncouple the equations of motion and the heat conduction. The frequency equations are obtained for longitudinal and flexural （symmetric and antisymmet- ric） modes of vibration and are studied numerically for elliptic and parabolic cross-sectional zinc cylinders. The computed non-dimensional wave numbers are presented in the form of dispersion curves.
