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2-DOF Free Vibration — Eigenvalue Problem

Shear frame, 2 stories · [K−ω²M]{φ}=0 · Natural frequencies ω₁,ω₂ · Mode shapes · Orthogonality check

System Parameters

Stiffness & Mass Matrices

K = —
M = —

Citations

Chopra §10.2Shear frame K=[k₁+k₂ -k₂; -k₂ k₂] M=diag(m₁,m₂)
Eq.(10.5)[K−ω²M]{φ}={0} — det[K−ω²M]=0 → ω₁,ω₂
Verifym₁=m₂=1, k₁=k₂=1 → ω₁²=0.382, ω₂²=2.618 (Chopra Ex.10.3)

Modal analysis →

Eigenvalue Results

Mode Shape Table

Floorφ₁ (Mode 1)φ₂ (Mode 2)
Orthogonality: —

Power iteration with deflation. Accurate for well-separated eigenvalues. For closely-spaced modes use dedicated FEM software.