Example 2-20 Write the differential equation of the system. 1 Establish the generalized coordinate of the system This is a three-degree-of-freedom system. Generalized coordinates: x₁, x₂, and x3 (direction and origin). 2 Calculate the stiffness coefficients 91+ 1 1₂ m₁ WWW m₂ 으라 Suppose that x₁=1 and x₂=x3=0, The force is need at mass m, is F₁=1X (k₁+k₂), i.e. k₁₁= k₁+k₂ ; The force is need at mass m₂ is F₂=-k₂ X 1=-k₂, i.e. k₂₁=-k₂ ; The force is need at mass m3 is F3-0, i.e. k31-0. k3 033 m3

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Theory of vibration exercise
Example 2-20 Write the differential equation of the system.
1 Establish the generalized coordinate of the system
This is a three-degree-of-freedom system.
Generalized coordinates: x₁, x₂, and x3 (direction and origin).
2 Calculate the stiffness coefficients
4₁
k₂
www₁wHM₂
Suppose that x₁=1 and x₂-x3=0,
The force is need at mass m, is F₁=1×(k₁+k₂), i.e. k₁₁= k₁+k₂ ;
The force is need at mass m₂ is F₂=-k₂ × 1 =-k₂, i.e. k₂1--k₂;
The force is need
at mass m3 is F3-0, i.e. k31-0.
2 03
k3
W M3
Transcribed Image Text:Example 2-20 Write the differential equation of the system. 1 Establish the generalized coordinate of the system This is a three-degree-of-freedom system. Generalized coordinates: x₁, x₂, and x3 (direction and origin). 2 Calculate the stiffness coefficients 4₁ k₂ www₁wHM₂ Suppose that x₁=1 and x₂-x3=0, The force is need at mass m, is F₁=1×(k₁+k₂), i.e. k₁₁= k₁+k₂ ; The force is need at mass m₂ is F₂=-k₂ × 1 =-k₂, i.e. k₂1--k₂; The force is need at mass m3 is F3-0, i.e. k31-0. 2 03 k3 W M3
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