Tutorial 7 for Mechanical Vibrations, Exercises of Engineering

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1. Consider the different systems shown in Figure 1 and 2. Find the relevant Equations of Motion, linearised and in matrix-vector form, for each of these systems. Leave the EOMS in symbolic form. You can assume any hinges, pivots or rollers are frictionless. my m4 “Es |" me oa cm f= ky 2 3 ™1 bw] 73 LW kg me (b)D (a) C ib) B Figure 1; Some saulli DOF systeius “| | cy ky Cae) Efe: M1, 30, - k%,- Cz, -~ k,Cx,-x,) - C,Cz,-%,) = Me, M+ Cc + bark Cx.-x,) + CC%- %,) = oO M+ Cx, ~- CX + C.m, * Kix, —bet24 Kee. = O MX. + CG Ce) % - Cote + Chye ke) 21 - be%2 = O ZF : oh xX -G Cz,-%) - k2Cx2-x,) = Me Sa MX. + C22, Cx, + bed - eX =O Max. ~ Cor + Coke — bax + kere = O Mm, Oo {% + Cl, -C, x k+ke -ke a: e - . + = O M2 lee “C, C, Xe ke ke xX O