Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support

This study analytically and numerically modeled the dynamics of a gyroscopic rigid rotor with linear and nonlinear cubic damping and nonlinear cubic stiffness of an elastic support. It has been shown that (i) joint linear and nonlinear cubic damping significantly suppresses the vibration amplitude (including the maximum) in the resonant velocity region and beyond it, and (ii) joint linear and nonlinear cubic damping more effectively affects the boundaries of the bistability region by its narrowing than linear damping. A methodology is proposed for determining and identifying the coefficients of nonlinear stiffness, linear damping, and nonlinear cubic damping of the support material, where jump-like effects are eliminated. Damping also affects the stability of motion; if linear damping shifts the left boundary of the instability region towards large amplitudes and speeds of rotation of the shaft, then nonlinear cubic damping can completely eliminate it. The varying amplitude (VAM) method is used to determine the nature of the system response, supplemented with the concept of “slow” time, which allows us to investigate and analyze the effect of nonlinear cubic damping and nonlinear rigidity of cubic order on the frequency response at a nonstationary resonant transition.

Design of 3D printable prosthetic foot to implement nonlinear stiffness behavior of human toe joint based on finite element analysis

Toe joint is known as one of the critical factors in designing a prosthetic foot due to its nonlinear stiffness characteristic. This stiffness characteristic provides a general feeling of springiness in the toe-off and it also affects the ankle kinetics. In this study, the toe part of the prosthetic foot was designed to improve walking performance. The toe joint was implemented as a single part suitable for 3D printing. The various shape factors such as curved shape, bending space, auxetic structure, and bending zone were applied to mimic human foot characteristics. The finite element analysis (FEA) was conducted to simulate terminal stance (from heel-off to toe-off) using the designed prosthetic foot. To find the structure with characteristics similar to the human foot, the optimization was performed based on the toe joint geometries. As a result, the optimized foot showed good agreement with human foot behavior in the toe torque-angle curve. Finally, the simulation conditions were validated by comparing with human walking data and it was confirmed that the designed prosthetic foot structure can implement the human foot function.