Figure 4 show a two storey (MDOF) shear building with masses (mi, m2) and total storey...

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Figure 4 show a two storey (MDOF) shear building with masses (mi, m2) and total storey stiffness (k₁, k₂) given in the same figure. Assume that the damping ratio is 5% for all modes. The structure is subjected to a sinusoidal force at the second level. Answer the following problems. a) Determine the mode shapes and modal frequencies via eigenvalue analysis. b) Decouple the MDOF equation of motion to two SDOF equations using the orthogonality conditions of mode shapes. c) Determine the expression of displacement U(x) of the shear building using modal superposition. m₂ = 300 kg m₁ = 500 kg 242 P₂ (t) = p. sin ut k₂ = 7000 N/m U₁ k₁ = 10000 N/m where Po = 500 N @= 3 rad/s {₁ = {₂ = 5% U(t) = [] Figure 4 show a two storey (MDOF) shear building with masses (mi, m2) and total storey stiffness (k₁, k₂) given in the same figure. Assume that the damping ratio is 5% for all modes. The structure is subjected to a sinusoidal force at the second level. Answer the following problems. a) Determine the mode shapes and modal frequencies via eigenvalue analysis. b) Decouple the MDOF equation of motion to two SDOF equations using the orthogonality conditions of mode shapes. c) Determine the expression of displacement U(x) of the shear building using modal superposition. m₂ = 300 kg m₁ = 500 kg 242 P₂ (t) = p. sin ut k₂ = 7000 N/m U₁ k₁ = 10000 N/m where Po = 500 N @= 3 rad/s {₁ = {₂ = 5% U(t) = []

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Answer I The mode shapes and modal ... View the full answer