Nonsmooth Modal Analysis of a unilaterally constrained one-dimensional bar with constant cross-sectional area was recently proposed. The corresponding formulation took advantage of the d'Alembert solution available for such systems and does not require any space semi-discretization of the governing equations. However, it is unable to cope with non-constant cross-sectional area bars, for instance. The present work suggests a formulation relying on various space semi-discretization methodologies (such as finite elements, Rayleigh-Ritz techniques, component mode synthesis, modal superposition and reduced-order models) where the complementarity Signorini condition, reflecting the unilateral contact constraint, is enforced in a weighted residual sense in time through the Harmonic Balance Method. Importantly, the Newton impact law, classically required for uniqueness purposes in a dynamics framework, is here explicitly ignored in the formulation and attendant solution strategy and is, instead, implicitly satisfied in a weighted residual sense. It corresponds to a restitution coefficient e=1 as required for energy preservation and existence of periodic solutions. Periodic responses are investigated in the form of classical energy-frequency backbone curves along with the associated displacement fields. It is found that for the constant cross-section benchmark system, the results compare well with existing works and the proposed methodology stands as a viable option in the field of interest when semi-discretization in space is required.