Modal Analysis of Frames

In the previous two chapters, we obtained an exact formulation for the dynamics of continuous systems. For vibration problems, the natural frequencies and mode shapes are determined by solving a transcendental eigenvalue problem. Consequently, we found the approximate formulations easier to use because they lead to an algebraic eigenvalue problem. In this chapter, we take the approximate formulation one step further by utilizing properties of algebraic eigensystems to introduce the concept of the modal model. This model involves a transformation of the description of dynamic systems in terms of stiffness and mass to a new set of equivalent variables in terms of the structural modes of vibration. This provides a scheme for analyzing the dynamics of complicated structures in terms of more useful quantities. References [17, 50] give very readable introductions to modal analysis.