The harmonically excited structure coupled with the nonlinear energy sink (NES) and a piezoelectric harvester is investigated. The complexification-averaging method is developed to analyze ordinary differential equations which also include one first order differential equation. Effects of varying parameters for the piezoelectric harvester on the saddle-node bifurcation and the Hopf bifurcation are explored. Analytical results of the amplitude–frequency response curves are verified by the numerical evidence. Global bifurcations for NES parameters are presented. Comparisons of periodic results for bifurcation diagrams are performed both numerically and analytically as well as their stable ranges. The integration of nonlinear vibration suppression and energy harvesting is discussed. The output voltage, power, displacement transmissibility, and average energy are calculated to explore the integration. Quasi-periodic responses near the resonance frequency contribute to effectively reducing the resonant amplitude and improving the bandwidth of energy harvesting, as well as targeted energy transfer. Results confirm that the integration of vibration suppression and piezoelectric energy harvesting can be enhanced by adjusting cubic nonlinearity.
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