Modal Analysis of Linear Dynamic Systems: Physical Interpretation

Anil K. Chopra
1996 Journal of Structural Engineering  
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
more » ... ion 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 forceexcited 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. where t = influence vector representing the displacements of the masses resulting from static application of a unit-ground displacement, u g = 1. Thus, the spatial distribution of the effective earthquake forces, (2b) is s = mt. where qn(t) = modal coordinates. A central idea of this formulation is to expand the spatial distribution s of applied forces or s = mt of the effective earthquake forces as
doi:10.1061/(asce)0733-9445(1996)122:5(517) fatcat:bl7rus63ljhknprpgiu3idmnna