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SUMMARYThe paper lays out an exact method, using the receptance strategy, to calculate the frequency response of a modified structure. A direct inversion of the modified impedance matrix is proposed, which reduces the computation time for successive calculations of an evolving design of the structure.KEY WORDS response reanalysis; structural modifications; matrix partitioning; ShemawMorrison formula GENERAL INFORMATIONThe governing equation of motion of a mechanical system with N dof iswhere M, C and K are the N x N mass, damping and stiffness matrices, respectively, x(t) is the N-vector of generalized displacements and f ( t ) is the N-vector of generalized forces. Here, we consider the special case of a harmonic excitation. When calculating the frequency response, the forcing function is given by where f is an N-vector of constants, w the forcing frequency, t the time and the complex value j 2 = -1. The response vector is thenwhere the impedance matrix R is defined asThe matrices M, C and K depend on the structural properties of the initial structures. We are interested in the way the response x varies when the structural parameters defining M, C and K are altered. The design changes in the original structure may be modelled by changes in the mass, damping and stiffness matrices, respectively, as AM, AC and AK.

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