Answer Happy

6.115 A heavy machine tool mounted on the first floor of a building, Fig. 6.43(a), has been modeled as a three-degree-of-freedom system as indicated in Fig. 6.43(b). (a) For k, = 875 kN/m, k2 = 87 kN/m, kz = 350 kN/m, 6 = 62 = cz = 2000 N-s/m, my = 8700 kg, my = 1800 kg, mg = 350 kg, and F(t) = 4000 cos 60 N, find the steady-state vibration of the system using the mechanical impedance method described in Section 5.6. (b) If the maximum response of the machine tool head (x3) has to be reduced by 25%, how should the stiffness of the mounting (K2) be changed? (c) Is there any better way of achieving the goal stated in (b)? Provide details. Machine tool head (equivalent mass, mh) Wall F(t), cutting force Machine tool base (equivalent mass, mo) Mounting Floor (equivalent mass, m) (a) FO x3(0) 소 ma Machine tool head C3 x2(1) I ть Base and mounting k 2 I m; Floor ki 中。 (b) FIGURE 6.43 Machine tool mounted on first floor of building.