• 대한수학회지
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• 제32권4호
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• pp.725-737
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• 1995

Let $X_t = (X_t^(1), X_t^(2))', t \geqslant 0$, be a real stationary 2-dimensional Gaussian process with $EX_t^(1) = EX_t^(2) = 0$ and $$ EX_0 X'_t = (_{\rho(t) r(t)}^{r(t) \rho(t)}), $$ where $r(t) \sim $\mid$t$\mid$^-\alpha, 0 < \alpha < 1/2, \rho(t) = o(r(t)) as t \to \infty, r(0) = 1, and \rho(0) = \rho (0 \leqslant \rho < 1)$. For $t > 0, u > 0, and \upsilon > 0, let L_t (u, \upsilon)$ be the time spent by $X_s, 0 \leqslant s \leqslant t$, above the level $(u, \upsilon)$.

• 소음진동
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• 제10권3호
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• pp.465-473
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• 2000

In this crankshaft of marine diesel engines the exciting torques are produced by gas pressure and reciprocating masses. These torques are periodically changing and are extremely out of balance. To calculate the torsional vibrations of propulsion shafting caused by unbalanced torque the torque harmonics are utilized. Until now to calculate the torsional vibrations of propulsion shafting. the torque harmonics have been supplied by the engine maker. When the torque harmonics of an engine are not available the torque harmonics of a similar engine type had to be used. However such data is not suitable for the reliable calculations of torsional vibrations. In this paper the combustion characteristics of marine diesel engines including $\rho{-}\upsilon$ diagram are investigated and the torque harmonics based on these are theoretically calculated. reliability of the calculations is confirmed by comparing them with those of an engine maker. This study should prove useful for the calculations of torsional vibrations for diesel engine propulsion shafting. particularly for 4-stroke engines whose torque harmonics are difficult to obtain directly from the engine and not ordinarily supplied by the engine maker.