Hi colleages. is Bernoulli-Euler theory valid in the dynamic analysis

[omarxx84]

hi colleages. is Bernoulli-Euler theory valid in the dynamic analysis as following:
M/EI=1/R
where,
M= moment
EI=stiffness
R= curvature
is this equation valid when M becomes a function of x and t, as follows:
M(x,t)/EI=1/R

 

[spacester]

Dynamics and I never really got along that well, but what you present looks a lot like a beam equation, the deflection (curvature) of a beam as a function of the local bending moment (M), material stiffness (E) and geometry (I), and that is simple enough for me to take a stab at this.

So you are asking if the equation is valid where M varies not just along the length of the beam (x) but while M varies with time (t), is that right?

First, I would say that the curvature must also be expressed as a function of x and t.

Now, if the curvature response (R) to the input M is instantaneous, the answer would be yes, and rather than a dynamics problem, you have an equation expressing the static condition at any given moment in time. A series of static moments as it were.

But I think you are correct to characterize this as a dynamics problem. In the real world I have to think there is a time delay between applying the forces that give rise to the moment and the response of the beam.

At this point in the analysis my head explodes. You will have to take it from there, FWIW.

hth