In this paper a new free interface modal synthesis method for the dynamic analysis of linear structures by the finite element method is developed. The technique is based on the so called higher order modal combination methods. In particular, the second force derivative method is used to accurately include the effect of the higher truncated modes in the representation of the substructures’ response. It is shown that the method is capable of providing very accurate estimates of the nature frequencies of the combined structure as well as the associated modes of vibration and elastic forces.

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