Forced harmonic vibrations of duffing oscillator with cubic-quintic spring nonlinearity

The modified Duffing oscillator with cubic-quintic nonlinearity at harmonic force excitations is analysed. Several phenomena are observed, including (i) the possibility for the presence of triple wells in the potential energy; (ii) the finding of a relation between the roots of the potential and nonlinear elastic moduli; (ii) the appearance of two chaotic regimes split by a regular regime; (iii) the occurrence of harmonic and superharmonic oscillations in the regular regime; and (iv) a significant topological difference in the Poincaré sections associated with these chaotic regimes. These observations open the possibility of creating a new type of vibration isolation devices free from viscous or dry friction elements. The analysis is based on constructing potential and solving the equations of motion by the finite difference method in combination with the multiprecision package for long-mantissa computations, enabling stable computations over large time intervals. • The Duffing oscillator with cubic-quintic nonlinearity is analysed; • An analytical expression for the triple well potential is constructed; • It is found that between two chaotic regimes, one regular regime with harmonic and superharmonic oscillations appears; • Two analysis of the Poincaré sections reveals that two chaotic regimes have different strange attractors; • The transformation of the Poincaré sections is analysed.