Answer Happy

(a) What Degrees of Freedom are necessary to model this system, for the purposes of analysing loads on the cargo (akin to passenger comfort in a passenger vehicle). Draw a neat, labelled diagram that explicitly shows the DOF and what their positive direction is. Be clear about which degrees of freedom you are NOT including and WHY! (b) It is NOT sufficient to re-state the assumptions above verbatim. You MUST explain how these impact your decisions about the model, and clearly explain any additional assumptions your make. (c) Pay particular attention to the flexibility of the trailing arm and connecting rod, and what must be included vs what may be neglected (d) Derive the matrix-vector Equation of Motion for the N DOF system. You may apply either Newtonian or Energy Methods. (e) Find the modal frequencies and mode shapes (Eigenvalues and Eigenvectors) for your model, based on the input values in Table 1. (f) Describe the mode shapes, in terms of what displacements you would see observing from a stationery view point. You are advised to use diagrams to assist with this.
Back View Shock absorber Ms Wheel Mw Bottom View Trailing Arm Vehicle Body MB Arm Hinge YA Z X S b A- A lw
do. DETAIL J SCALE 1:2 OD SECTION E-E SCALE 1: 10 a DETAIL G SCALE 1:2 a Figure 2: Trailing Arm Dimensions Figure 3: Interior view of trailing arm suspension SECTION F-F SCALE 1: 10 E
Table 1: System Parameters Parameter Trailer Body Mass* Trailer Body Radius of Gyration Tyre, wheel, hub mass* Tyre stiffness Shock Absorber Mass Shock Absorber Spring Stiffness* Shock Absorber Damping Constant* Trailing Arm Length Length from body CG to wheel CG Length from body CG to Trailing Arm Hinge Length from body CG to spring attachment Trailing Arm Box Width Trailing Arm Box Thickness Trailing Arm Connecting Rod OD* Trailing Arm Connecting Rod ID* Symbol Mb Rb Mw kt Ms ks Cs h lw b S* a t do di Value 600 kg 700 mm 14 kg 200 N mm-1 6 kg 45 N mm 4Nsmm 1 250 mm 850 mm 725 mm 760 mm 50 mm 2.5 mm 22 mm 12 mm