The free-vibration solution of a two-degree-of-freedom system can be determined by solving the equations with x...
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The free-vibration solution of a two-degree-of-freedom system can be determined by solving the equations with x = [x₁ (1) x2 (1), using the initial conditions x(t = 0) = xo [m]x + [k]x = 0 = Lx10 [x₂0) and x(t = 0) = x = = 0 Jx10l Lizel If w₁ and I w2 are the natural frequencies and ₁ and 2 are the mode shapes of the system obtained from the solution of the characteristic equation [[m]s² + [k]]u (E.2) with s = = ±w₁, ±w₂ (characteristic roots), the solution of Eq. (E.1), X(t), can be found as a linear combination of different solutions as: X(t): C₁u₁e it + C₂u₁e+ e+iwit + C3u₂e-iw₂t + Cauze +int (E.1) (E.3) The free-vibration solution of a two-degree-of-freedom system can be determined by solving the equations with x = [x₁ (1) x2 (1), using the initial conditions x(t = 0) = xo [m]x + [k]x = 0 = Lx10 [x₂0) and x(t = 0) = x = = 0 Jx10l Lizel If w₁ and I w2 are the natural frequencies and ₁ and 2 are the mode shapes of the system obtained from the solution of the characteristic equation [[m]s² + [k]]u (E.2) with s = = ±w₁, ±w₂ (characteristic roots), the solution of Eq. (E.1), X(t), can be found as a linear combination of different solutions as: X(t): C₁u₁e it + C₂u₁e+ e+iwit + C3u₂e-iw₂t + Cauze +int (E.1) (E.3)
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Related Book For
Numerical Methods For Engineers
ISBN: 9780071244299
5th Edition
Authors: Steven C. Chapra, Raymond P. Canale
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