Transient Dynamic Behavior Of Typical Elastic Components Impinging On Ideal Elastomer

The transient dynamic behaviors of typical elastic components impinging on ideal elastomer are investigated from the perspective of theory, simulation and experiment in order to reveal the distribution of energy between rigid body motion and vibration of elastic components. The research objects are classified into two types according to the characteristics of corresponding elastic components, i.e. straight elastic components and thin-wall elastic ring. The problems of straight elastic components impinging on ideal elastic spring(s) and thin-wall elastic ring impinging on ideal elastic wall are investigated respectively. For the problem of straight elastic components impinging on ideal elastic spring(s), from the mathematical problems with definitive solution of constrained-motion stage and free-motion stage, a unified analytical approach is established based on mode superposition method by repeatedly altering boundary and initial conditions between these two stages. In particular, three examples are investigated in detail, i.e., they are a straight bar impinging on an ideal elastic spring, a straight beam vertically impinging on an ideal elastic spring at the beam’s mid-point and a straight beam vertically impinging on two ideal springs with the same stiffness at the beam’s two ends. Research shows that the coefficient of restitution (COR) and the non-dimensional rebounding time (NRT) of straight components only depend on the stiffness ratio between the ideal spring(s) and the elastic components, with nothing to do with the initial velocity. Collision happens only once for the problem of straight bar impinging on ideal spring and there is an extremum value for COR at some specific stiffness ratio. However, it’s different for the problem of straight beam impinging on ideal spring, where with the increase of stiffness ratio, multiple collisions occur and COR undergoes complicated fluctuation.For the problem of thin-wall elastic ring impinging on ideal elastic wall, the corresponding non-linear and linear dynamic equations of constrained-motion stage and free-motion stage are derived through assumed modes and Lagrange equation. The whole process of impacting and rebounding is also given by repeatedly altering initial and boundary conditions. Research shows that it’s different from the problem of straight elastic components impinging on ideal elastic spring(s), the COR and NRT of thin-wall elastic ring not only depend on the stiffness ratio, but also depend on the non-dimensional initial velocity and the ratio between the thickness and radius of the ring. With the increase of stiffness ratio, multiple collisions happen and COR decreases monotonically and approaches a limited value 0.77. All the theoretical analysis results of the problems of these typical components are validated by FEA results. Moreover, for the problem of straight elastic components impinging on ideal spring(s), the influence of the springs’ mass on the rebounding behavior is demonstrated, while for the problem of thin-wall elastic ring impinging on ideal elastic wall, the existence of multiple collisions is validated experimentally.