... to the second order approximation. All possible resonance cases are deduced at this approximation and some of them are confirmed by applying the Rung–Kutta method. The main attention is focused on the stability of the steady-state solution near the simultaneous principal resonance and the effects of different...

... by the axial force component has a significant influence on the dynamic response of the shaft, even when the axial force and speed are low and, hence, must be considered in such problems as turning operations. shafts beams (structures) rotation vibrations Runge-Kutta methods Turning is a very...

... equations are solved using the Runge-Kutta algorithm. 26 04 2005 28 11 2005 vibrations structural acoustics transient response Runge-Kutta methods differential equations Rayleigh-Ritz methods damping state-space methods vibration open cylindrical shell cylindrical panel...

... is assumed which has the linear thermal expansion and resistivity. Using the Runge–Kutta method, the amplitude versus time and velocity versus amplitude for the first mode and the first two modes are dertermined. The results show that the transient vibratory behaviors of the beam are influenced...