A Closed-Form Solution of Drop Test on an Elastic Bar: Benchmarking Force Response of the Restrained Bar to Impact

EasyChair Preprint no. 5868

Abstract

The behaviour of an elastic bar; restrained at one end and subjected to a rigid impactor at the other end is evaluated in this analytical work. In the original work on this problem, duration of impact is only considered up to four-times of the time taken by compressive stress wave to travel from end struck to the bottom support and back. The current work revisits the closed-form solution provided in the literature in terms of the set of first four compressive stresses, then formulates these terms in programming language. The code is then utilised to derive arbitrary number of higher-order stress intervals depending on mass ratio of the system to complete the whole impact process. Compressive stress at the end struck and its corresponding load are then formulated for each stress interval by the current and previous compressive stress formula; a process which provides force history at the end struck for the whole impact duration. Parametric study is then performed on the number of selected input parameters in the stress equations e.g. mass ratio, drop height (or initial velocity), elastic modulus and length of the elastic bar; revealing proportional relations to apparent output variables obtained from force history, namely number of intervals, initial compressive stress, pulse width, peak load and interval frequency. These proportionalities and their corresponding mathematical relations are useful in explaining and correlating respective output variable-parameter relationships obtained via experimental or numerical works. The closed-form solution provided in this work serves as a benchmark to numerical or experimental impact problems assuming homogeneous and isotropic bar behaving linear elastically.

Keyphrases: Elastic bar, Force at end struck, impact, Mathematical relations, Stress intervals

@Booklet{EasyChair:5868,
  author = {Adib Hamdani and Pankaj Pankaj},
  title = {A Closed-Form Solution of Drop Test on an Elastic Bar: Benchmarking Force Response of the Restrained Bar to Impact},
  howpublished = {EasyChair Preprint no. 5868},

  year = {EasyChair, 2021}}