• Journal of Advanced Marine Engineering and Technology
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• v.23 no.6
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• pp.794-805
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• 1999

Pneumatic cushioning cylinders are commonly employed for vibration and shock control. A mathematical simulation model of a double acting pneumatic cushioning cylinder designed to absorb shock loads is presented which is based on the following assumptions; ideal equation of state isentropic flow through a port conservation of mass polytropic thermodynamics single degree of freedom piston dynamics and energy equivalent linear damping. These differential equation can be solved through numerical integration using the fourth order Runge-Kutta method. An experimental study was conducted to validate the results obtained by the numerical integra-tion technique. Simulated results show good agreement with experimental data. The computer simulation model presented here has been extremely useful not only in understanding the has been extremely useful not only in understanding the basic cushioning but also in evaluating different designs.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.3
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• pp.329-337
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• 2001

In this study a compound planetary gear combined with three planet gears, which is used for continuously variable transmission, is modeled that consider variable nonlinear gear mesh stiffness and damping when gear rotates, and thus equation of motion of compound planetary gear is derived. Locus of sun gear center causing noise and vibration is being determined from performing derived state equation with numerical analysis in fourth order Runge-Kutta method.

• Journal of Korean Society of Steel Construction
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• v.24 no.3
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• pp.289-299
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• 2012

The goal of this paper is to apply the multi-step Taylor method to a space truss, a non-linear discrete dynamic system, and analyze the non-linear dynamic response and unstable behavior of the structures. The accurate solution based on an analytical approach is needed to deal with the inverse problem, or the dynamic instability of a space truss, because the governing equation has geometrical non-linearity. Therefore, the governing motion equations of the space truss were formulated by considering non-linearity, where an accurate analytical solution could be obtained using the Taylor method. To verify the accuracy of the applied method, an SDOF model was adopted, and the analysis using the Taylor method was compared with the result of the 4th order Runge-Kutta method. Moreover, the dynamic instability and buckling characteristics of the adopted model under step excitation was investigated. The result of the comparison between the two methods of analysis was well matched, and the investigation shows that the dynamic response and the attractors in the phase space can also delineate dynamic snapping under step excitation, and damping affects the displacement of the truss. The analysis shows that dynamic buckling occurs at approximately 77% and 83% of the static buckling in the undamped and damped systems, respectively.