Question

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An automobile simulation rig is assumed to be an undamped two-degree-of-freedom system as shown in Figure 3 where the motion is only in the plane of the paper, and, Spring stiffnesses, k,=400 N/m ; kz= 500 N/m Automobile mass, m = 27kg IF 10m and 1=8m Moment of inertia about G, Jo = 708 kgm? a) Analyze the natural frequencies and mode shapes of the system. b) Evaluate the performance of the system based on ISO 2631-1, human sensitivity to vibration dependent on frequency G lg ky к, х Figure 3 Vibration frequency sensitivity of different human body part based on ISO 2631. Part Body Head Eyeballs Chest Wall Spine Arm Hand Pelvic Mass Buttocks Legs Frequency (Hz) 25 30-60 60 10-12 16-30 50-150 4-8 2-20

Answer 1

SURYA Gold Pas А 2 1 Trio T СК, xa og Testing moment about Applying f'Atemberautos prapople Directions te masoni W. Kot M=Fxd. CM), JO a Fs, - Spring force in ko Isa spring force in ka. & Mext - FS, (l) -Fs, (la) =-k, x, l. - kazala, Assume o small LO x= lo , = haige sul in Ego - , e - K4°s, . Jo = -K, 2, 20, - Ka la 02. =) Jotk, 2, 20, tkz ²0 20 Considering translation of the body. Jo + k, l, 20 tka l20 tmo=o. a o më tcx + Kx=0 Wn m.

SURYA Gold -Page Wn b) substituting k, e, ² r s la Jtm the values sec W. 400x105008² 9,897 the sady 708 +27. W=anf f = 20 9.897 As all the vibration fequencies are above natural frequencies, sesonance does not occus. añ 0 6348 Hz