Because of the relatively narrow bandwidth of the linear approaches, using nonlinear oscillators to harvest energy from ambient vibrations has been a primary trend in this field. Frequency response, used extensively in evaluating linear approaches, has been used as the primary metrics for nonlinear harvesters. Existing results have demonstrated that nonlinear devices may offer “broadband” performance. However, such “broadband” performance can only be obtained from a single-frequency excitation. It does not represent satisfactory performance of such devices under multi-frequency excitations because of the inapplicability of the principle of superposition. Conversely, existing nonlinear devices may perform worse than their linear counterparts for excitations with multiple dominant frequencies. This paper provides some new insights into the potential of using nonlinear systems to harvest energy from vibrations with multiple frequencies. A previous study has shown that a nonlinear harvester can achieve its maximum performance only at the so-called global resonance condition under which the properties of excitation matches those of the response. Through the global resonance mechanism, the energy can be dissipated and compensated in multiple frequencies with the maximum efficiency. A device design concept based on the matching between the potential well of the device and the characteristics of the excitation is proposed in this study. Numerical results are included to demonstrate the effectiveness of the proposed method. In this study, focus is placed on periodic response; chaos and response under random excitations are not considered.