The approximate methods presented at the end of the preceding chapter for the solution of the vibration problems of continuous systems are based on the assumption that the shape of the deformation of the continuous system can be described by a set of assumed functions. By using this approach, the vibration of the continuous system which has an infinite number of degrees of freedom is described by a finite number of ordinary differential equations. This approach, however, can be used in the case of structural elements with simple geometrical shapes such as rods, beams, and plates. In large-scale systems with complex geometrical shapes, difficulties may be encountered in defining the assumed shape functions. In order to overcome these problems the finite-element method has been widely used in the dynamic analysis of large-scale structural systems. The finite-element method is a numerical approach that can be used to obtain approximate solutions to a large class of engineering problems. In particular, the finite-element method is well suited for problems with complex geometries.