Modal Analysis of Linear Dynamic Systems: Physical Interpretation

The modal analysis procedure for calculating the dynamic response of classically damped linear structural systems is reformulated with the objective of developing the physical significance of the elements of the solution and defining modal contribution factors. The resulting concepts are used to develop an approach for predicting how the relative contributions of various modes to the response and the number of modes that should be included in the solution depend on the vibration properties of the system, on the response quantity of interest, and on (1) the spatial distribution and time variation of applied dynamic forces in the case of force-excited systems, or (2) the response (or design) spectrum for an earthquake excitation. To illustrate this approach, numerical results are presented for a five-story frame for a wide range of parameters and a base-isolated building.