Galerkin procedure for resonance analysis of the forced Van der Pol-Duffing-Helmholtz oscillator

This investigation centers on the resonance analysis of the forced Van der Pol-Duffing-Helmholtz oscillator (VdP-DH). Employing an equivalent linearization method on this forced-damped nonlinear oscillator yields a linear solution, albeit one not conducive to resonance response analysis. To address this, an advanced approach was adopted to derive a solution akin to the conventional one. Utilizing the Galerkin method facilitated the examination of resonance occurrence and the establishment of stability conditions for both resonance and non-resonance states. Numerical comparisons confirm the derived solution aligns with the advanced solution. The resonance region, interspersed within the stability domain, and mirrors the influence of all physical parameters, showcasing the nuanced interplay of forces within the system.