Linear ion traps and quadrupole mass spectrometers play vital roles in quantum technologies and classical mass spectrometry respectively. Therefore, such systems with nearly same operational principles, are very well studied both theoretically and experimentally. Despite such vast knowledge base, linear ion traps continue to be an important research topic, particularly the effect of small perturbations from ideal conditions. Here, non-degenerate nonlinear resonances of the ion dynamics in a linear three-segmented round-rod radio-frequency ion trap have been studied. Purposefully designed perturbation from an ideal 4-rod symmetric structure results in additional instabilities in the dynamics of the trapped ions. The weightage of the dodecapole potential increases by an order of magnitude in such an asymmetric setup compared to that present in usual symmetric setup of nearly equivalent geometry. The experimental results are corroborated by ion dynamics simulations with commercial software SIMION. Increased dodecapole potential in the asymmetric structure leads to resolution of the frequency of ion oscillation in two mutually perpendicular directions in the radial plane which is otherwise unresolved in a symmetric structure in absence of dc potential. Such asymmetric linear trap, in principle, finds importance in the study of Coulomb crystal, mass spectrometry and relevant trapped ion dynamics. It also opens up the possibility to remove undesired ion species (often known as dark ion) within a chain of physical qubits.