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TASK-1 ("Warm-up" problem: basic modelling, fundamentals of the FEM)

Consider a free-free stepped beam, shown in Figure 1a. It has been modelled with four beam finite elements with total 10 degrees-of-freedom and its global mass [M] and global stiffness matrix [K] have been calculated. However, the main system to be studied is actually constrained, as shown in Figure 1b: the left end of the beam is rigidly attached (clamped) to the slider, which can freely slide along the vertical guide, and there is a pin in the middle of the beam between the FE-#2 and FE-#3. To model the main system, the method of re-adjustment of the matrices [M] and [K] is used: In order to reflect the actual boundary conditions of the main system, some of the rows and columns are to be deleted.

SHOW numbers of all of these rows and columns, which should be deleted in [M] and [K] to produce new matrices, suitable for solving eigenvalue problem for the system in Figure 1b.

Figure-1: (a) Supplementary System (free-free beam), modelled with 4 FEs; (b) Main System.