Explicit frequency response functions of discretized structures with uncertain parameters

• Linear discretized structures with uncertain parameters are analyzed.
• A novel series expansion (RSE) of the frequency response function (FRF) is derived.
• The RSE provides an approximate explicit expression of the FRF.
• The FRF of structures with interval parameters is derived by applying the RSE.
• Explicit expressions of the bounds of the modulus of the FRF are determined.

A novel procedure for deriving approximate explicit expressions of the frequency response function (FRF) matrix of linear discretized structures with uncertain parameters is presented. The following main steps are required: (i) to decompose the deviation of the structural matrices with respect to their nominal values as sum of rank-one matrices; (ii) to derive the so-called Rational Series Expansion (RSE) which provides an approximate explicit expression of the FRF holding for any uncertainty model. The potentials of the RSE are demonstrated within the interval framework by determining the region of the modulus of the FRF of structures with uncertain-but-bounded parameters.