Example 1

Determine the frequency of vibrations of the rod system. Graphically represent the shapes of the system's natural vibrations.

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Solution

Degree of static indeterminacy

SSN=3-3=0

Number of degrees of dynamic freedom

LSSD=1
𝑚1 =𝑚















ΣMB=012+VA4=0 VA:=0.5Σy=0 VA1+VB=0 VB:=0.5Σx=0HB:=0






Dynamic delta 𝛿11:=1EI(13112+13112)=1.3331EI Vibration frequency 𝜔:=1𝑚1𝛿11𝜔:=1𝑚43𝐸𝐼𝜔:=0.866𝐸𝐼𝑚

Vibration modes