1.  

You are modeling a beam with a step discontinuity in cross-section located at x/L= 0.35. You wish to use the Rayleigh-Ritz method to approximate the first five natural frequencies of the structure. The boundary conditions of the structure are clamped at both ends. a) One of your classmates suggests the following set of shape functions to use in your model: cos(2x/L)-1, cos(3x/L)-1, cos(4x/L)-1, cos(5mx/L)-1.... Could this set of functions be used in the Rayleigh-Ritz analysis of your structure? Why or why not? b) What is the lower bound on the number of shape functions required for this analysis? c) How do you know whether you have used enough shape functions to produce reliable results?