Theory of Modal Analysis

Abstract

As shown in the preceding chapter, the motion of a dynamic structure or system may be represented by a set of simultaneous differential equations using some discretization scheme, such as the finite element method, if necessary. The dynamic characteristics (dynamic responses, strains, stresses, etc.) of the system can be obtained from these equations using the direct integration methods (finite difference method, Newmark method, for example) in the time domain. Alternatively, these coupled equations of motion may be solved by transforming them into a set of independent (uncoupled) equations by means of a modal matrix. This procedure is the classic meaning of modal analysis. Actually, the procedure of determining the system’s modal parameters, including natural frequency, natural mode, damping factor, modal scaling, etc., is also referred to as modal analysis. The determination of these modal parameters may be by the way of either a theoretical (analytical or numerical) approach or an experimental approach and termed theoretical modal analysis and experimental modal analysis, respectively.