Modal combination methods in deterministic and stochastic dynamics

The role played by the modal analysis in the framework of structural dynamics is fundamental from both deterministic and stochastic point of view. However the accuracy obtained by means of the classical modal analysis is not always satisfactory. Therefore it is clear the importance of methods able to correct the modal response in such a way to obtain the required accuracy. Many methods have been proposed in the last years but they are meaningful only when the forcing function is expressed by an analytical function. It follows that they cannot be adopted for seismic analysis where the forcing function is a piecewise linear one. Moreover in stochastic analysis they fail for white noise excitation. In the paper a method able to give a very accurate response for both deterministic and stochastic input is presented. This method is based upon the use of Ritz vectors together with the classical modal analysis and it can be considered as an extension of the DCM correction method. Numerical applications for a primary-secondary composed structure show the great accuracy of the proposed method.