Softening versus hardening nonlinear energy sinks: forced vibration control and isolated resonance curves

Abstract

The nonlinear energy sink (NES) is a practical passive device for vibration control that has gained significant attention due to its ability to mitigate resonant vibrations across a wide frequency range. Conventional NES designs typically employ a hardening restoring force, which enables broad operational frequency coverage but faces limitations in the operational amplitude range, also due to the emergence of isolated resonance curves (IRCs). This study investigates a softening NES, where the restoring force characteristic is modeled as a saturating function. Analytical results demonstrate that the softening NES retains the beneficial amplitude saturation effect and strongly modulated response (SMR) observed in hardening NESs, while significantly expanding the range over which SMR occurs. Furthermore, the IRCs in the softening NES appear on the right of the resonance peak, unlike the leftward location in hardening NESs, making it advantageous for applications where excitation frequency ramps up. Notably, IRCs in the softening NES are less detrimental as they result in smaller amplitude jumps. We also identify parameter values that suppress the formation of IRCs without compromising the performance of the NES, providing a practical advantage over conventional designs. Despite these promising findings, the practical realization of the softening NES remains an open challenge, which will be the focus of future research. Overall, the softening NES exhibits superior performance compared to the hardening NES, presenting an effective alternative for vibration suppression in various engineering applications.