Question

Problem #1 A truck suspension system including tire model is shown in the figure. A load added to a truck results in a force F on the support spring, and the tire flexes. The truck vehicle mass is my and the tire mass is mt. Assume that the gravity is neglected. (a) Determine the two independent equations of motion. (b) Obtain the equations of motion in terms of Laplace transform, assuming that the initial conditions are zero. (c) Obtain the transfer function X (s)/F(s). Force of material placed in truck bed Truck vehicle mass k Shock absorber b = 3 k2 Tire

Answer 1

Ferial placed bod Truck vehicles TH my mu X-X) blix) Using D'Alembert's rule. myši, - b, 6x2 -,) – k, (x2-x,) - F= 0 mä + bx + kx, bir-Rix = F FBD of me bi (iz) kla2-x) - ① brik kak2 Using D'Alembert's rule: män + b₂ + kz X2 + b, (iz -x,) + R, (x2-x) = 0 mx + (b, + b₂) + (R₂ + R), b,a, -k, x = 0 - 2 6 and ③ are desired equations of motion Laplace transforms of derivatives with zero initial conditions are L%). = x(4) » La): x(1) Taking Laplace transform of ① and ② (my s +b, s tk, X, (s) - (b, s + k) X2 (s) = F(s) (m ² + (b, tbls + (k, tk.) ₂ (s) - (6, stk,) X, (s) = 0

Now, from 9 X2(6) = (b stk) [ Someopathys uk) - history altan 1 XG) - Fls) Stck+ me 3 + (6 +62)s +(kitka) - (m, ² tb, stk, [mp3 + lb, tb,)s + (k, kz] (bs the?