Abstract:

The out-of-plane buckling phenomenon, a prevalent nonlinear effect in structural mechanics, presents significant challenges for theoretical analysis. Inspired by this behavior, a novel simplified rigid dynamic model (RDM) is proposed to qualitatively capture the nonlinear vibration behavior of structures undergoing out-of-plane buckling. The approximate analytical solution and simulation model of the RDM are formulated. The approximate analytical solution is obtained through the harmonic balance method (HBM) and the arc-length continuation method (ALCM). By analyzing the stiffness variations during the buckling process, the nonlinear stiffness and potential energy characteristics of the RDM are thoroughly explored, revealing distinct softening and hardening stiffness behaviors under different parameter configurations. Two potential application scenarios for the RDM are proposed: one under quasi-zero stiffness (QZS) conditions and the other under bistable conditions. A QZS isolator is designed with two RDMs, and its effective low-frequency vibration isolation performance is confirmed through both numerical and analytical methods. Additionally, under the bistable conditions, a dynamic simulation analysis of the RDM is conducted with the ADAMS software. The consistency between the simulation results and the theoretical calculations confirms the correct implementation of the analytical and numerical frameworks. The dynamics of the RDM provide valuable insights for the design of actuators and energy harvesters. This study offers a reference for the simplified analysis of complex models involving out-of-plane bending-torsion buckling, and lays a foundation for potential applications in the structural design of flapping bistable robots and rotating QZS isolators.

Key words: nonlinear dynamics, bistable, quasi-zero stiffness (QZS), buckling, actuator, vibration isolation