A clamped beam is shown in Fig. 1.4. It is divided into n elements, with n-1 nodes, and two fixed nodes. In some cases later in this book we use n=15 elements for simple illustration, and sometimes n=60 or n=100 elements for more sophisticated examples of beam dynamics. Each node has three degrees of freedom: horizontal displacement, x, vertical displacement, y, and in plane rotation, 6. In total it has 3(n-1) degrees of freedom. The beam is 150 cm long, with a cross-section of 1 cm2. The external (filled) nodes are clamped. The beam mass and stiffness matrices for n=15 are given in Appendix C.2.

Figure 1.4. A beam divided into n finite elements.

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