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By Vijay K. Garg

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5. Fig. 16. Wheel-axle set lateral displacement a n d yaw angle versus time as calculated by the R u n g e - K u t t a integration m e t h o d . 08 Time ( Seconds ) Fig. 17. Wheel-axle set lateral displacement a n d yaw angle versus time as calculated by the two-cycle iteration with trapezoidal rule m e t h o d . 001-Sec Time S t e p Integration scheme Stability C P U time (sec) Central difference predictor Newmark-/? 001 sec; wheel-axle set velocity = 60 miles/hr. remaining schemes were quite similar.

Oo Then, we obtain Fourier transforms of both sides of Eq. 128) as ΥΧω)[-ω 2 + αξ,ω + ω ] = ω ^ (ω), 2 r = 1, 2 , . . , η. 130) can be solved for Y (co) as r ΥΧω) = HAco)F (co) r r = 1, 2 , . . 131) where ΗΧω) = [1 - (ω/ω,) + Ω ^ ω / ω , ) ] , 2 - 1 r = 1, 2 , . . , η. 132) 77ze response correlation matrix [# (τ)] is given as χ 1 [Λ,(τ)] = lim Τ->οο f T/2 {x(0} {x(t + τ ) } dt. ]{y(0K we can write Eq. 135) J-T/2 1 is the response correlation matrix associated with generalized coordinates y (t) (r = 1, 2 , .

3a, b. *χ \ 2 F (t) 2 Fig. 1. Linear d y n a m i c system with two degrees of freedom. 9 ° 1 25 50 75 100 125 150 175 200 225 250 TIME ( Sec) Fig. 2. Response of linear d y n a m i c system using numerical integration m e t h o d s , (a) D y n a m i c response of Χ obtained by using numerical integration m e t h o d s , (b) d y n a m i c response of X obtained by using numerical integration m e t h o d s . ί 2 42 2 Numerical Integration Methods for Dynamic Response (a) (b) qI ° 25 50 75 100 125 150 175 200 TIME 225 250 (Sec) Fig.

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