Wuhan University of Technology8.2 Generalized properties: assemblages ofrigid bodiesThismaybewritteninthesimplifiedformm*Z(t)+c*Z(t)+h*Z(t) =p*(t)44j2m*matm239a299k*1691cC1+ C21616p*(t)-paf(t)=8-11
8-11 Wuhan University of Technology 8.2 Generalized properties: assemblages of rigid bodies This may be written in the simplified form
Wuhan Universityof Technology8.2 Generalized properties: assemblages ofrigid bodiesExampleE82.Asasecondexampleoftheformulationoftheeguationsofmotionforarigidbodyassemblage,thesystemshowninFig.E84willbeconsidered.ThesmallamplitudemotionofthissystemcanbecharacterizedbythedownwarddisplacementoftheloadpointZ(t),andall thesystemforcesresisting this motion can be expressed in terms of it:mass(uniform)areakf,(t)5000f,(t)+M,(t)bfobzt+p(t)8-12
8-12 Wuhan University of Technology 8.2 Generalized properties: assemblages of rigid bodies Example E82. As a second example of the formulation of the equations of motion for a rigidbody assemblage, the system shown in Fig. E84 will be considered. The smallamplitude motion of this system can be characterized by the downward displacement of the load point Z(t), and all the system forces resisting this motion can be expressed in terms of it:
Wuhan Universityof Technology8.2 Generalized properties: assemblages ofrigid bodiesThedownwarddisplacement of theloadpointZ(t),and all the systemforcesresistingthismotioncanbeexpressedintermsofit:hf,(t) =abz(t)fs(t) =k = z(t)0a2+62b Z(t)M,(t)=ab12(t)fi,(t) =ab122aaThe equation of motion for this simple system can be written directly byexpressing the equilibrium of moments about the plate hinge:60fs(t)b + fi,(t)M,(t) = p(t) a+ fi,(t)+-2262621Z(t) +kZ(t) = p(t)a0244a28-13
8-13 Wuhan University of Technology 8.2 Generalized properties: assemblages of rigid bodies The downward displacement of the load point Z(t), and all the system forces resisting this motion can be expressed in terms of it: The equation of motion for this simple system can be written directly by expressing the equilibrium of moments about the plate hinge:
Wuhan University of Technology8.2 Generalized properties: assemblages ofrigid bodiesmass(uniform)上areakfs(t)1000fi(t)+M,(t)-bfi,(t)b3Z(t)0p(t)3m* Z(t)+ k* Z(t) =p*(t)6262yabk*=kmp*(t) =p(t)a23a28-14
8-14 Wuhan University of Technology 8.2 Generalized properties: assemblages of rigid bodies
Wuhan Universityof Technology8.3 Generalized properties: distributed flexibilityNZ(O)-Se(t)w(a,t) =b(a)z(t)U(x.n)5(2) = 2(z,t)v(x,t)Perr(x,t)=-m(x)i,(t)erraaraZ(t)m(x)SWE=SWEI(x)(b)(a)8-15
8-15 Wuhan University of Technology 8.3 Generalized properties: distributed flexibility