The paper presents a new model for analyzing the behavior of a single-storey frame structure with defects, which is represented by a fifth-order nonlinear equation. The study utilizes the homotopy analysis method (HAM) to determine the vibration characteristics of the structural system. The results include frequency values and displacement functions for two cases: one with a stiffness parameter \({k}_{3}\ne 0\) and another with \({k}_{3}=0\) . The key contribution of this paper is the introduction of a new model to simulate the performance of the structure and the application of the homotopy analysis method to derive the natural frequency values and displacements of the single-degree-of-freedom structural system. The results achieved in this study show minimal errors when compared to calculations performed using numerical methods and are straightforward to apply in practical calculations.