Nonlinear Vibration Caused by Beam of Cable Structures
The nonlinear vibrations of cables excited by thevibration of beam were investigated. At first, a simpleconnection condition and boundary condition of thecable-stayed beam structure were applied. Thenonlinear equations of motion of the cable-stayedbeam structure were derived, and the static sag of thecable as well as the geometric nonlinearity wasconsidered, moreover, Appling the multi-scaleperturbation method, the nonlinear vibrations ofcables were studied, the nonlinear vibration responseof cables was analyzed by the Runge-Kutta numericalmethod to obtain the frequency-response curves. Theresults indicate that the beam small scale vibration canstimulate the cable the large scale movement whenlocal oscillation frequency of beams is in the certainregion, it affects the cable-stayed beam structure thestability and the security in the Engineering. For thesystem in which the damping and the frequency ratiowas given, the enough low excitation amplitudes canavoid the system resonances.
Non-linear planar dynamics of suspended cables investigated by the continuation technique
In this paper, the continuation technique is used to investigate the non-linear response of a suspended cable under harmonic excitation. Taking into account the geometric non-linearity of the suspended cable as well as the assumption of quasi-static stretching, a mathematical model of the suspended cable is formulated. The periodic solution for the suspended cable is obtained by means of the shooting method, and the continuation technique is used to trace the frequency-response curves of the suspended cable, while the non-periodic motions are studied through direct simulations. Moreover, the results obtained by this method and the numerical integration are compared in detail. Finally, the effects of the amplitude of the harmonic excitation on the periodic motion of the suspended cable are investigated.
Laminar heat or mass transfer in rectangular channels and in cylindrical tubes for fully developed flow: comparison of solutions obtained for various boundary conditions
Abstract A comparison is made of results obtained with various boundary conditions at the wall of the channels. By comparing blood Sherwood numbers for finite wall resistance with those for constant concentration boundary condition only a small variation is found for various points along the blood channel.