• Journal of Advanced Marine Engineering and Technology
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• v.24 no.6
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• pp.7-14
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• 2000

Nowadays, the viscous damper using high viscosity oil was much to be used for engine shafting system to reduce the excessive additional stress by torsional vibration. In general, it was assumed that the viscous damper could be modelled having only damping coefficient, that is to say, whose stiffness be ignored. But it is found that there exists a jump phenomenon, as a kind of non-linear vibration, in the actual engine shafting system with a damper of high viscosity. Therefore the damper ring and the casing are modelled as two mass elastic system with a complex viscosity. Also, to analyze a non-linear phenomenon, it is assumed that the viscous damper has a linear stiffness coefficient in proportion to the angular amplitude and a non-linear stiffness coefficient in proportion to cube of the angular amplitude. For the analysis, Quasi-Newton method with BFGS(Broyden-Fletcher-Goldfarb-Shanno) formula is used. Both calculated and measured values are provided in this paper which confirm the possibility of applying non-linear theory to engine shafting system with viscous damper.

• Journal of Korean Association for Spatial Structures
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• v.20 no.4
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• pp.149-158
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• 2020

The governing equation for a dome-type shallow spatial truss subjected to a transverse load is expressed in the form of the Duffing equation, and it can be derived by considering geometrical non-linearity. When this model under constant load exceeds the critical level, unstable behavior is appeared. This phenomenon changes sensitively as the number of free-nodes increases or depends on the imperfection of the system. When the load is a periodic function, more complex behavior and low critical levels can be expected. Thus, the dynamic unstable behavior and the change in the critical point of the 3-free-nodes space truss system were analyzed in this work. The 4-th order Runge-Kutta method was used in the system analysis, while the change in the frequency domain was analyzed through FFT. The sinusoidal wave and the beating wave were utilized as the periodic load function. This unstable situation was observed by the case when all nodes had same load vector as well as by the case that the load vector had slight difference. The results showed the critical buckling level of the periodic load was lower than that of the constant load. The value is greatly influenced by the period of the load, while a lower critical point was observed when it was closer to the natural frequency in the case of a linear system. The beating wave, which is attributed to the interference of the two frequencies, exhibits slightly more behavior than the sinusoidal wave. And the changing of critical level could be observed even with slight changes in the load vector.