The nonlinear energy interactions are an intriguing aspect of nonlinear oscillators, such as vibro-impacting cantilevers (VICs). Despite extensive research, the domain of energy interactions in nonlinear oscillators still requires further exploration. The motivation arises from the complex and captivating dynamics as well as the vast array of potential applications. This paper presents a comprehensive investigation of various energy interaction mechanisms within the resonance realms of the first and second mode resonance frequencies of harmonically base-excited VICs. These energy interactions are of paramount importance as they give rise to the captivating response of the VIC, characterized by multi- and quasi-periodicity, energy amplification, combination resonances, amplitude modulation, and other intriguing features. This paper introduces the phenomenon termed “Harmonic Resonance Energy Stimulation (HRES)” and extensively investigates its role in generating the secondary jump in the frequency response. Moreover, the present study discovers and reports the non-resonant energy interactions and resulting modulating, quasi-periodic response in the VIC. Various illustrative plots obtained from the theoretical investigation, relying on the mathematical model, have been utilized to facilitate a comprehensive investigation. The results hold immense significance as they contribute valuable knowledge to the nonlinear dynamics of VIC, which is of great importance in research advancements and practical applications.
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