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

Solution:

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 y_c is the deflection at the centre.

  --------(1.a)

We Know that when m is not equal to n .

 when m = n Hence equation 1.a becomes,

 --------------(1b)

From 1 b eqn, 

There fore ------------(1c)

To find out y_c substitute x = l/2. in above equation (1.c)