I cannot transform these two coupled equations to one equation (the technique we use in Timoshenko beam).
It contains a number of operations and you could use Maple to evaluate the integrals symbolically.
I have difficulty in seeing what will result from these equations (hope and assume they are correct), have no time to look at this now and believe I had never tried one system like that.
Anyway, may be (remember I am not sure) what you are looking for can be found at work from J. R. Cannon and R. E. Ewing, e.g. "A Galerkin procedure for systems of differential equations" at https://link.springer.com/content/pdf/10.1007%2FBF02575859.pdf or more recent works.
Hope this may help or at least be a start for better literature. However, do not forget to give us some feedback on your progress.
Dear Prof. Miguel,
My problem was so simple than I thought. I was trying to use discretization on governing equations, which were 2 coupled equations. Then I realized that I can easily do it on weak statement. By the way, thanks for your attention and suggestions.
Dear Arash Imani Aria
Can you explain me how you used the discretization on copupled equation of timoshenko beam to solve.
Thank you.
Sanjeev Kumar
Yeah, actually it is pretty simple :). the point is that you should solve the weak form of the equation (the equation which includes integral). So, do not go for the differential form.
Oh yeah ! I see, thank you so much Arash Imani Aria . I was using variotional approach, After using the Hamiltonian principle it can be done.
Can i used discretization method while using virtual energy method? There is vistual displacement too.
Kindly find the attached virtual work, should i used discretization for all 6 parameter (3 real+ 3 virtual)?
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