Question

Q5: Fig. Q5 is a simplified model of car (Quarter car model). It is assumed that (1) the vehicle is constrained to one degree of freedom in the vertical direction, (2) the spring constant of the tires is infinite, that is, the road roughness is transmitted directly to the suspension system of the vehicle, and (3) the tires do not leave the road surface. Assume a trailer has 1,o00 kg mass fully loaded and 250 kg empty. The spring of the suspension is of 350kN/m. The damping factor is o.50 when the trailer is fully loaded. The speed is 100 km/hr. The road varies sinusoidally with 5m/cycle. Determine the amplitude ratio of the trailer when fully loaded and empty l cycle- Fig. Q5

Answer 1

Solution 202 2_ kļ2 C. 2. 25Q m 18 9 oacǐn Vemi. Now, the natusal frequsrcǐ of th vehicle, vpivalent stifness of ile vekicke is geven by OW Malu AstRe s Spsins are in porolel conmections stittne3s O

. Nafaha e ub glvelM ve- 1000 26, 46 and/s chen th vehicle loaded, (condition· 25O 52.915 had/s Whenthe vehicle went C condition. fonmula f0% tte amplitude of 8foodt state vibratone Vibnclow case of forced vibaatows isðvem , → Amplitude of foxced Vibha tions : When vehicle is full Looded, 34-9 222 264+2x0.5 4972 264- 1-5122 n vekicle s empty

cJ 72 34.9 .יר +2x0-5x 34-9_71 52.9 2.91 otlK 0.86846 21 1-5122 Amplitude fullyloaded Amplitude wheet 0-86846 X1 0-574-3 2 Note: When th vehicle is enfty amplitude of foaced vibrations dus to hood ill be wonl loaded ond it ui quite obvious mohe than han the vehicle s fullt