Dynamic equilibrium of vibrated beam-column member

AI Thread Summary
The equation presented describes the dynamic equilibrium of a vibrated beam-column member under specific boundary conditions. It incorporates the dynamic moment, shear force at one end, external dynamic loading, and inertia force due to mass and acceleration. The integral term accounts for the distribution of forces along the length of the member. The discussion seeks validation of the equation's accuracy in representing the dynamic behavior of the system. Overall, it emphasizes the importance of understanding these dynamics in structural analysis.
omarxx84
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hi colleages...is the equation below represent a dynamic equilibrium of vibrated beam-column member and simple boundary conditions?

M(x,t)=Q(0,t)*x+integral{q(x,t)-mass*acceleration(x,t)}*(L-x)dx

where

M(x,t)= dynamic moment.
Q(0,t)=shear at x=0.
q(x,t)= external dynamic loading.
mass*accel.(x,t)= inertia force.
 
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hi colleages...is the equation below represent a dynamic equilibrium of vibrated beam-column member and simple boundary conditions?

M(x,t)=Q(0,t)*x+integral{q(x,t)-mass*acceleration(x,t)}*(L-x)dx

where

M(x,t)= dynamic moment.
Q(0,t)=shear at x=0.
q(x,t)= external dynamic loading.
mass*accel.(x,t)= inertia force.
 
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