Session: Research Posters

Paper Number: 166639

Dependence of the Coefficient of Restitution on the Shape of an Impacting Body 

Introduction: The effect of the shape of an impacting body on the coefficient of restitution is addressed using the case of low velocity axial impact of axisymmetric bars. Understanding the different variables that affect the rebound velocity can assist in designing optimal shapes for impacting bodies depending on the intended rebound outcomes. This motivates the study of the effect of different cross-section variations on the coefficient of restitution of bars of the same mass and material. With identical mass and material of the body, different rebound scenarios can be obtained by reshaping the body and altering the dimensions. This work studies the influence of shape on the coefficient of restitution for the impact of axisymmetric bars.

Methodology: The impact scenario involves a variable cross-section bar travelling at a certain initial velocity and colliding with a rigid structure on one of its ends. The magnitude of the initial velocity is kept within limits to ensure that yielding does not occur. The bar’s shape is parameterised based on the cross-sectional variations using certain dimensionless shape parameters. At the onset of impact, stress waves emanating from the impacting end propagate along the length of the bar. Additionally, the contact force at the impacting end of the bar evolves over time. Furthermore, when the contact force magnitude reaches zero, the bar rebounds. The eigenvalue problem of the bars having different variations in cross-sections is solved analytically to determine the internal characteristics of the bar, such as natural frequencies and mode shapes. Furthermore, the obtained mode shapes are superimposed to determine the impact response of the variable cross-section bars. In this work, different variations in cross-sections, such as linear, exponential, sinusoidal and polynomial variations, are analysed. The theoretical solutions are compared with fully numerical solutions obtained from the impact of three-dimensional axisymmetric bars using the Finite Element Method (FEM), and a very good match is obtained in all cases considered. In each case, the deformation and restitution times are determined to calculate the coefficient of restitution (COR) using Poisson’s definition, which is compared with Newton’s definition of COR. The redistribution of the initial kinetic energy of the bar after impact in the form of gross motion of the bar and its internal motion is studied.

Preliminary Results and Conclusions: The temporal variation of the contact force at the interface of the bar and the rigid surface depends on the choice of impact end of the variable cross-section bar. In the case of variable cross-section bars, the deformation and contact time are not decided based on the corresponding wave propagation times, as observed with a uniform bar. The end of the deformation phase in a variable cross-section bar is not marked by the bar being completely at rest with the energy purely as internal strain energy, as is conventionally thought of. Furthermore, a bar with different end dimensions can have nonidentical values of the coefficient of restitution for impact at the two ends. However, special cases also exist where unequal end dimensions have identical COR for both ends. The variation in cross-section leads to the conversion of a fraction of pre-impact kinetic energy into internal motion of the bar after rebound. This fraction of the energy of internal motion depends on the dimensionless shape parameters. Moreover, it is shown that the longitudinal cross-section variation of the bar decides its rebound characteristic, which is observed by the velocity of gross motion of the bar post impact.

Presenting Author: Sukanta Patra Indian Institute of Technology, Kharagpur

Presenting Author Biography: Mr. Sukanta Patra is a Ph.D. student in the Department of Mechanical Engineering Indian Institute of Technology, Kharagpur, India. His research interests include dynamics of continuous systems, mechanical wave propagation and impact mechanics. Earlier, he has obtained his post graduate degree from National Institute of Technology, Durgapur, India in 2020.

Authors:

Sukanta Patra Indian Institute of Technology, Kharagpur
Anirvan Dasgupta Indian Institute of Technology, Kharagpur