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A generalized oscillator model for nonlinear vibration analysis of various mechanical systems was proposed and solved using the quasi-static cubication method. The proposed generalized oscillator model is useful for introducing and discussing the nonlinear vibration models of several oscillatory systems. To establish the accuracy of the quasi-static cubication method for the generalized oscillator model, a number of simulations were carried out for the nonlinear vibration models of common mechanical systems derived from the generalized oscillator model. The results obtained were found to be in good agreement with exact solutions and other approximate solutions found in the literature. Furthermore, the quasi-static cubication method was found to be accurate for a wide range of oscillation amplitudes. A significant feature of the quasi-static cubication method is its simplicity and accuracy; hence, it is considered an efficient technique for nonlinear vibration analysis in undergraduate and post-graduate courses on dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we derive the exact analytical solution for the periodic oscillations of a nonlinear mechanical oscillator that is capable of describing phase transition phenomenon with spatially inhomogeneous distribution of the order parameter. The exact analytical solution was derived in terms of the elliptic integral of the third kind and covers the cases where the physical variable influencing the order parameter is negative or positive. The conditions for obtaining periodic oscillations for the two cases were discussed, and results were simulated for small‐ and large‐amplitude nonlinear oscillations. The results also cover periodic responses with bistable oscillations, which indicate the existence of bifurcation in phase transition. Furthermore, the error of the numerical solution and other published approximate analytical solutions were analyzed and discussed. The present study can be viewed as a benchmark solution for the mechanical oscillator for phase transition and can be used to verify the accuracy of existing and future approximate solutions. [ABSTRACT FROM AUTHOR]