Novel twisted cosine beam design for quasi-zero stiffness vibration isolator

Conventional quasi-zero stiffness (QZS) vibration isolators, typically constructed using positive and negative stiffness elements, often involve relatively complex structural parameter designs. Cosine beams provide a more compact configuration for achieving QZS, but their performance is constrained by the apex height-to-thickness ratio. This study proposes a novel twisted cosine beam (TCB) structure, aiming to overcome the limitation of the apex height-to-thickness ratio of conventional cosine beams to achieve QZS. Static characteristics of the TCB are derived using a theoretical framework based on a chained-beam constraint model and validated through numerical simulations and experiments. The width and twisting angle of the TCB are identified as critical parameters for stiffness tuning to achieve QZS. The beam length primarily governs the QZS range and load-bearing capacity. Based on these principles, both single-layer and double-layer isolators are designed, and their dynamic responses are analysed using a harmonic balance method in combination with numerical simulations. Particular attention is given to the role of fractional derivative (FD) damping, which arises from the intrinsic properties of thermoplastic polyurethane. For the single-layer isolator, reducing the FD damping first induces a slight decrease in the initial isolation frequency, followed by a pronounced increase. Moreover, as the fractional order decreases from 1 to 0.2, the initial isolation frequency increases by approximately 65 %. For the double-layer isolator with distinct structural parameters in each layer, the lower-layer QZS configuration performs better at low frequencies, whereas the upper-layer configuration is more effective at high frequencies. Experimental evaluations further confirm that positioning the supported mass at the QZS location minimises the initial isolation frequency, thereby enhancing isolation efficiency. Thus, this study offers a compact and versatile approach to designing QZS vibration isolators, providing enhanced flexibility in parameter tuning.