Static and dynamic behaviors of a geometrically nonlinear quasi-zero-stiffness multilayer vibration isolator with a large-stroke energy harvester

This work presents a novel tunable 𝑁 − layer low-frequency vibration isolator integrated with a large-stroke energy harvester. The proposed structure consists of multiple geometrically nonlinear layers with adjustable stiffness characteristics, enabling simultaneous vibration isolation and energy harvesting. A strongly nonlinear electromechanical model is developed and then analyzed using the harmonic balance method. The payload oscillation amplitude, displacement transmissibility, and the harvested electrical current are explored against the base excitation frequency for different system configurations. The analysis showed that the isolator dynamics can be effectively tuned through two controllable parameters, which are the structure unloaded inclination angle 𝛿 ⁢ ₀ ( 0 ≪ 𝛿 0 < 𝜋 / 2 ) and the eigen-parameter 𝛼 (that depends on the spring stiffness ratio and the isolator arm-length ratio). Also, it is found that the structure can provide a static supporting force of 𝛼 ⁢ s i n ⁡ ( 𝛿 ⁢ ₀ ) to the payload. In addition, it is demonstrated that tuning 𝛼 appropriately eliminates the isolator linear stiffness, rendering the overall stiffness purely nonlinear and proportional to c o s ⁡ ( 𝛿 ⁢ ₀ ) . Therefore, designing such a structure with a large 𝛿 ⁢ ₀ approaching ( 𝜋 / 2 ) ⁻ maximizes the supportive static force while simultaneously weakening the nonlinear dynamic stiffness, resulting in a wide quasi-zero-stiffness range. Moreover, the stiffness-like effect arising due to electromechanical coupling can be mitigated either by connecting a high-resistive load to weaken the isolator–harvester coupling or by designing the isolator with more than one layer. Increasing the number of layers enhances vibration isolation performance and maximizes harvested energy, besides reducing the electromechanical coupling effect. Finally, numerical simulations were performed and showed excellent agreement with all analytical findings.