Rayleigh Ritz method
Rayleigh Ritz method applied to Beams
U#1) Find the deflection at the centre using Rayleigh Ritz method for the simply supported beam subjected to Concentrated load at the centre
Take y = .
According to Rayleigh Ritz method = U – W and where π = Potential energy U = Strain energy and W is the external work done.
where yc is the deflection at the centre.
We Know that when m is not equal to n .
when m = n Hence equation 1.a becomes,
From 1 b eqn,
There fore ------------(1c)
To find out yc substitute x = l/2. in above equation (1.c)
Hence we have which is the deflection at the centre.