An innovative methodology in analyzing two-degrees-of-freedom of coupled dynamical system

Analyzing two-degrees-of-freedom (2DOF) coupled dynamical systems is crucial in understanding complex interactions in mechanical, structural, and aerospace engineering. Advanced analytical and numerical methods elucidate complicated behavior relevant to bio-inspired systems, smart materials, and vibration control. Consequently, the present topic centers on a recognized benchmark challenge in the field of a cart-pendulum system. The non-perturbative approach (NPA) underlies the unique analysis. The principal aim of the NPA is to convert weakly nonlinear oscillators of ordinary differential equations (ODEs) into linear forms. The swift evaluation of the frequency-amplitude correlation is essential in acquiring successive approximations of responses to parametric nonlinear fluctuations. The influence of several parameters on the stability of steady states is examined. The results demonstrated that the suggested technique is exceptionally intuitive, extremely effective, and firmly established. The alteration of bifurcation parameters influences the configuration of the bifurcation curve. The Lyapunov exponent (LE) curves are additionally illustrated.