Generalized mode acceleration methods and modal truncation augmentation

When computing the dynamic response of structures, modal superposition methods are often used to reduce the number of unknowns and thereby to represent the dynamical behavior by a small number of vibration modes. In order for the accuracy of mode superposition methods to be acceptable, quasi-static corrections must usually be added such as in the Mode Acceleration Method. This method can be extended to include higher order static corrections. A approach similar to the Mode Acceleration Method consists in using the static correction as a Ritz vector to represent the dynamical behavior. This method, known as Modal Truncation Augmentation method is extended here to include higher order static corrections. An example is presented to demonstrate the high accuracy that can be obtained by this Generalized Modal Truncation Augmentation approach. It is also shown that, compared to the Generalized Mode Acceleration Method, the proposed procedure retains its accuracy over a wide frequency range.