<p>This study presents a nonlinear symmetric steady-state resonant wave system induced by circumferentially generated travelling waves. The resonant modes exhibit physical similarities with the vibration configurations of acoustic poles. By controlling the angular modulation factor, steady-state monopole, dipole, and quadrupole resonant waves are systematically simulated and investigated. A fully nonlinear Higher-Order Boundary Element Method (HOBEM) is employed in a circular numerical wave basin to resolve wave interactions in the time domain. Multidirectional wave velocity allocation is achieved through cylindrical surface-based wave sources, with an annular damping layer implemented as the outlet boundary to maintain steady resonance states. The different resonance modes exhibit distinct spatial symmetries and peak-trough distributions, all conforming to Bessel-like functions. The nodal lines, which serve as phase-reversal boundaries in the standing wave field, demarcate the resonant wave patterns. Three-dimensional interference of high-frequency waves results in significant amplification of local peaks. The results also reveal that resonance strongly excites wave nonlinearity and amplifies nonlinear coupling, leading to an increased manifestation of higher-order wave components. Strong wave nonlinearity alters the shape of the resonant waves, enhances the amplitude of the wave crests, and induces shifts in the nodal lines and peak positions.</p>