Is This Civil Engineering PDE Linear?

[omarxx84]

can anyone help me to solve this equation ?. is this equation linear or not?
knowing, this equation represents the equation of motion for frame members for materials which have different moduli in tension and compression (civil engineering).
"EI" ("x,t" ) ("∂" ^"4" "u" ("x,t" ))/〖"∂x" 〗^"4" "-N" ("x" ) ("∂" ^"2" "u" ("x,t" ))/〖"∂x" 〗^"2" "+m" ("x,t" ) ("∂" ^"2" "u" ("x,t" ))/〖"∂t" 〗^"2" "=0"
In which,
EI depends on a roots of cubic equation, and t depends on ("∂" ^"2" "u" )/〖"∂t" 〗^"2" (acceleration)
boundary conditions:
at x=0, u=0 and at x=L, u=0
at t=0, u=0

 

[jackmell]

That's too messy to read. Go to the "Math and Science Learning Material" sub-forum above, and look at "Introducing LaTex typesetting thread to see about formatting math for the forum. For example:

$$\frac{\partial u}{\partial t}=\frac{\partial^2 u}{\partial x^2}$$

Click on the equation to see the code used to generate it.

 

[omarxx84]

EI(x,t) (∂^4 u(x,t))/〖∂x〗^4 -N (∂^2 u(x,t))/〖∂x〗^2 +m(x,t) (∂^2 u(x,t))/〖∂t〗^2 =0
please, try to read, then help me to solve it.

 

[JJacquelin]

Yes, the PDE is linear.
Since EI(x,t) and m(x,t) are not explicit, the equation cannot be analitically solved.
Even if EI(x,t) and m(x,t) were explicit, but probably not simple formulas, the equation couldn't be analitically solved in the general case.
Probably, numerical calculus is the only way.

 

[n!kofeyn]

EI(x,t) (∂^4 u(x,t))/〖∂x〗^4 -N (∂^2 u(x,t))/〖∂x〗^2 +m(x,t) (∂^2 u(x,t))/〖∂t〗^2 =0
please, try to read, then help me to solve it.

i think when posting to a forum it is courteous to abide by their standards or requests. it reflects much better on you if you show that you've taken the time to make the question easier to read or more understandable, which will further add to people's willingness to help you.

replying to someone by saying no i won't work on making it easier to read, you should try harder, usually won't get you anywhere.

 

[omarxx84]

what is the best books or papers for solving nonlinear integro-differential equations??

 

[omarxx84]

please...What is the solution of the governing linear partial differential equation, with variable coefficients, of motion attached in the attached file. and i will be very grateful for you...