ABSTRACT
In simple terms, modal analysis is the process that determines the properties of the normal modes that describe the dynamic response of a structure. This chapter develops the principles of analysis of discretised systems, and obtains the results for the system response at a particular location to a particular force or forces as a function of system resonance frequencies. It analyses modal damping and mode shapes applicable to the simple systems using the wave equation. The chapter develops the ideas and principles that will be of use in the analysis of multi-degree-of-freedom discrete systems. It concerns structures having many degrees of freedom. Proportional damping is a special type of damping that simplifies system analysis. The damping may be viscous or hysteretic but the damping matrix must be proportional to either or both of the mass and stiffness matrices. Although viscous damping is representative of that found in acoustic spaces, hysteretic damping is representative of the damping found in structures.
