The document provides instructions to determine the deflection curve of a cantilever beam loaded as shown in a figure using the Rayleigh-Ritz method. It states to use a deflection shape of v = a1x^2 + a2x^3, where a1 and a2 are constants. It then outlines applying the method by finding the energy equation, differentiating the displacement with respect to a1 and a2, calculating parameters, substituting values into the equation, and solving the resulting matrices to determine the value of W.

1. Determine the equation of the deflection curve of the cantilever beam loaded as shown in Fig.
10.14. Use as the deflection shape of the loaded beam v = a1x^2 + a2x^3 where a1 and a2 are
constants. Apply the Rayleigh-Ritz method.
Solution
Let the displacement is
As f(x) are given in the question therefore we will replace the f(x) in the above equation.
Now first of all we have to find energy equation that is
Now for the displacement we will have the differentiation of this equation with respect to a1 and
a2 .
and we have to calculate these parameter
Now we will substitute the following values in the below eqaution
where K and M are matrices of coefficients of a1 and a2.
On solving this we have the value of W .