Nonlinear dynamics of a Z-shaped structure with validated global analytical mode shapes

•The resonant global analytical mode shapes are obtained by considering both the axial and transverse displacements.•The analytical mode shapes are validated based on figure comparisons and MACs.•The steady-state responses of the system are solved as functions of the frequency and amplitude of the excitation.•Periodic, multiperiodic, quasiperiodic and chaotic motions are analyzed numerically.•The accuracy of the mode shapes plays an important role in determining the parametric rule of certain nonlinear phenomena.