where $X(t)$, $\zeta $, *P*, and $\omega $ are, respectively, the generalized coordinate, dissipation factor, amplitude of excitation, and excitation frequency. $K$ and $G$ are linear and nonlinear stiffness coefficients, respectively. In Eq. (A1), an overdot indicates a differentiation with respect to time *t*. Depending upon the harmonic excitation amplitude $P$, the steady-state response of the system may evolve from intrawell oscillations around one of the two stable equilibria $X*=\xb1K/G$ to interwell oscillations, which cross the unstable equilibrium $X*=0$, or evolve in the opposite trend. The harmonic balance method [49,60–62] is applied to approximately represent the steady-state dynamics of Eq. (A1) for sufficiently small damping $0<\zeta \u226a1$. As a result, the steady-state response of the oscillator is assumed as a single-term Fourier series expansion
Display Formula

(A2)$X=c(t)+a(t)cos\u2009\omega t$