<p>This paper presents an integrated model that considers the spatial inertia of drill-string and the non-uniform distribution (NUD) of drill-bit blades, aiming to research the nonlinear dynamics of rotary drilling. Unlike most studies that overlook the interplay between different modes of vibrations and focus on a limited number of nonlinearities, this model comprehensively addresses these aspects. The proposed model incorporates various nonlinear behaviours resulting from the interaction between NUD drill-bit and rock, including dry friction, regenerative effect, and loss of contact. The spatial discretization of the drill-string is conducted through finite element (FE) method, and the predictive capabilities of the resultant FE model is validated using field data. Linear stability analysis reveals that both NUD of blades and the addition of extra blades can expand stable drilling region. Numerical simulations capture several types of self-excited vibrations, notably stick–slip and bit-bounce. Considering rate-of-penetration as a variable parameter, system states will undergo qualitative changes, evolving from periodic to quasi-periodic dynamics, and further leading to chaos through period-doubling bifurcation. A sliding mode controller is designed to suppress drill-string vibrations, and its effectiveness in nonlinear drilling system, both with and without the presence of stick–slip and bit-bounce, is numerically validated.</p>