The nonsmooth modal analysis of a simple one-dimensional bar of constant cross-section has already been successfully performed using a Finite Volume formulation and the Frequency-Domain Boundary Element Method (FD-BEM). Both strategies took advantage of the existence of d'Alembert solution for such problem. The present contribution extends the previous works to a bar of non-constant cross-section for which the d'Alembert solution no longer exists. The proposed scheme combines the finite element method in space to the harmonic balance technique in time. The solution satisfies the unilateral contact condition along with an energy-preserving implicit impact law in a weighted-residual sense. The partial backbone curve of the first mode shows the existence of internal resonances.