(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to crudely approximately the distance individual masonry units fly when a blast load impacts a masonry wall. I'm a structures guy so I can calculate when the wall will failure, but I am having trouble with the calculus associated with the equation of motion.

My structure is subjected to a linearly decreasing blast loading,

F(t)=A*Po*(1-t/td) when 0<t<td

F(t)=0 when t>td

where td is the duration of the load

The drag force exerted on the units is given by

Fd=0.5*Cd*A*rho*(u')^2

2. Relevant equations

The equation of motion, introducing constants A and B to simplify the equation, is:

u'' + A*(u')^2 = B*F(t)

The acceleration, u'', and velocity, u', as well as the load F(t), are all a function of time

3. The attempt at a solution

The equation has derivatives of u, so I introduced v=u', v'=u'', so the equation of motion becomes:

v'+A*(v^2)=B*F(t) which is now first order and should be easier to solve....

v'=B*F(t)-A*(v^2) but I am not sure how to proceed.

Any ideas on how to continue with this analysis?

Thanks!

-EJ

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# Homework Help: Equation of motion with drag and external forces

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