Vibration analysis is critical for many common mechanical systems: jet engines, bridges, pistons, and acoustic resonators are some examples of systems for which the study of vibration is crucial. Within a linear framework, one way to understand the behaviour of such oscillatory systems is by exploring their natural frequencies of oscillation in the vicinity of an equilibrium state. Such behaviour is called autonomous vibration and its analysis aids in predicting more complex behaviours of the investigated system. The analysis becomes much more challenging when the investigated mechanical system features smooth as well as nonsmooth nonlinearities: two typical examples are cubic nonlinearities capturing large displacements and impacts reflecting unilaterally constrained dynamics. Such a system, reduced to 2-degree-of-freedom vibro-impact Duffing oscillator, is numerically investigated in the light of vibration modal analysis.