Moving load in a simply supported beam

[Eso7]

thread799-418661

I would like to know how to obtain the dynamic exact solution analytically

 

[Erik Panos Kostson]

I have not done anything like that for a very long time. In structural dynamics and vibrations you could typically solve this with the method of separation of variables (and with a bit of now how on Dirac functions and inner product/integrals, like shown in your post).

If you like maths , the Greens functions can be used (I think also complex analysis and Cauchy's integrals, but perhaps that is when it rests on a complex foundation).

Not that I remember how to do this anymore,

Luckily there is a thesis that covers a bit of this solution:

Link

The book below gives a full description on this:
L. Fryba ‘Vibration of Solids and Structures under Moving Loads. Groningen’, Noordhoff
International, 1972
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If you are a student read this:
Link

Link