A combined method for computing frequency responses of proportionally damped systems

• An new method is proposed for computing frequency responses of proportionally damped systems.
• It combines the modal superposition with a model order reduction method.
• Only the modes corresponding to a frequency range of interest are used for modal superposition.
• Basis vectors of the model order reduction method are obtained by applying PCG method.
• The existing factored stiffness matrix from an iterative eigensolution is utilized as preconditioner.

Frequency response analysis requires the evaluation of an associated function for a typically large number of frequencies. Direct method for performing these calculations is time-consuming. In this paper, a method is proposed for solving frequency responses of a mechanical system with proportional damping. The method combines modal superposition with a model order reduction. Only the modes corresponding to a frequency range which is a little bigger than that of interest are used for modal superposition. Complementary part of contribution of computed modes for frequency response is calculated by a model order reduction method. Basis vectors are obtained by applying preconditioned conjugate gradient method to a modified undamped system at the highest frequency of interest. The existing factorized stiffness matrix developed for partial eigensolutions is used as preconditioner. This computational methodology is illustrated by its applications to two frequency response problems. It is shown that the present method can remarkably reduce the CPU time required by the direct method to frequency response analysis.