Dynamic equilibrium of vibrated beam-column member

In summary, the equation provided represents a dynamic equilibrium for a vibrated beam-column member with simple boundary conditions. The equation includes terms for dynamic moment, shear at x=0, external dynamic loading, and inertia force.
  • #1
omarxx84
28
0
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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  • #2


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.
 

1. What is dynamic equilibrium of vibrated beam-column member?

Dynamic equilibrium of vibrated beam-column member refers to the state where the external forces acting on the member are balanced by the internal forces generated within the member, resulting in a stable and steady motion under the influence of vibration.

2. How is dynamic equilibrium achieved in a vibrated beam-column member?

Dynamic equilibrium is achieved in a vibrated beam-column member through the balancing of inertial forces, such as gravity and vibration-induced forces, with the structural stiffness and damping of the member. This results in a continuous motion without any net acceleration or deformation.

3. What factors affect the dynamic equilibrium of a vibrated beam-column member?

The dynamic equilibrium of a vibrated beam-column member can be affected by various factors such as the amplitude and frequency of the applied vibration, the structural properties of the member (e.g. stiffness, damping), and the type and magnitude of external loads.

4. How can dynamic equilibrium be analyzed in a vibrated beam-column member?

Dynamic equilibrium can be analyzed in a vibrated beam-column member using mathematical and computational methods such as finite element analysis, which takes into account the structural properties and external loads to determine the equilibrium state of the member.

5. What are the practical applications of understanding dynamic equilibrium in vibrated beam-column members?

Understanding dynamic equilibrium in vibrated beam-column members is important for the design and analysis of structures such as bridges, tall buildings, and other civil engineering structures that are subjected to vibrational forces. It also has applications in the study of earthquake-resistant design and vibration control techniques.

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