We study a ball-beam impact in detail; and in particular, we study the interplay between dissipation and modal truncation. With Hertzian contact between a solid ball and an Euler–Bernoulli beam model, we find using detailed numerical simulations that many (well above 60) modes are needed before convergence occurs; that contact dissipation (either viscous or hysteretic) has only a slight effect; and that contact location plays a significant role. However, and more interestingly, we find that as little as 2% modal damping speeds up convergence of the net interaction so that only about 25 modes are needed. We offer a qualitative explanation for this effect in terms of the many subimpacts that occur in the overall single macroscopic impact. In particular, we find that in cases where the overall interaction time is long enough to damp out high modes yet short enough to leave lower modes undissipated, modal truncation at about 25 modes gives good results. In contrast, if modal damping is absent so that higher mode vibrations persist throughout the interaction, final outcomes are less regular and many more modes are needed. The regime of impact interactions studied here occurs for reasonable parameter ranges, e.g., for a 3–4 cm steel ball dropped at speeds of 0.1–1.0 m/s on a meter-long steel beam of net mass 1 kg. We are unaware of any prior similarly detailed numerical study which clearly offers the one summarizing idea that we obtain here.
Skip Nav Destination
Article navigation
November 2017
Research-Article
Interplay Between Dissipation and Modal Truncation in Ball-Beam Impact
Arindam Bhattacharjee,
Arindam Bhattacharjee
Mechanical Engineering,
Indian Institute of Technology Kanpur,
Kanpur 208016, India
Indian Institute of Technology Kanpur,
Kanpur 208016, India
Search for other works by this author on:
Anindya Chatterjee
Anindya Chatterjee
Mechanical Engineering,
Indian Institute of Technology Kanpur,
Kanpur 208016, India
Indian Institute of Technology Kanpur,
Kanpur 208016, India
Search for other works by this author on:
Arindam Bhattacharjee
Mechanical Engineering,
Indian Institute of Technology Kanpur,
Kanpur 208016, India
Indian Institute of Technology Kanpur,
Kanpur 208016, India
Anindya Chatterjee
Mechanical Engineering,
Indian Institute of Technology Kanpur,
Kanpur 208016, India
Indian Institute of Technology Kanpur,
Kanpur 208016, India
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 22, 2016; final manuscript received April 19, 2017; published online September 7, 2017. Assoc. Editor: Przemyslaw Perlikowski.
J. Comput. Nonlinear Dynam. Nov 2017, 12(6): 061018 (8 pages)
Published Online: September 7, 2017
Article history
Received:
December 22, 2016
Revised:
April 19, 2017
Citation
Bhattacharjee, A., and Chatterjee, A. (September 7, 2017). "Interplay Between Dissipation and Modal Truncation in Ball-Beam Impact." ASME. J. Comput. Nonlinear Dynam. November 2017; 12(6): 061018. https://doi.org/10.1115/1.4036830
Download citation file:
Get Email Alerts
Cited By
Investigation of Gear Meshing Vibration and Meshing Impact Resonance Intensity Assessment
J. Comput. Nonlinear Dynam (May 2024)
Hand Vibration Reduction Using Nonlinear Vibration Absorber for the Vibro-Impact Hammer Model
J. Comput. Nonlinear Dynam
Irrational Nonlinearity Enhances the Targeted Energy Transfer in a Rotary Nonlinear Energy Sink
J. Comput. Nonlinear Dynam
On a Nonlinear Locally Resonant Metamaterial With Resistance-Inductance Shunt
J. Comput. Nonlinear Dynam (May 2024)
Related Articles
Analytical and Numerical Investigations of Stable Periodic Solutions of the Impacting Oscillator With a Moving Base and Two Fenders
J. Comput. Nonlinear Dynam (November,2017)
An Improved Mathematical Model of Galton Board With Velocity-Dependent Restitution
J. Comput. Nonlinear Dynam (November,2017)
A Direct Simulation Monte Carlo Approach for the Analysis of Granular Damping
J. Comput. Nonlinear Dynam (April,2007)
Energy Dissipation in
Normal Elastoplastic Impact Between Two Spheres
J. Appl. Mech (November,2009)
Related Proceedings Papers
Related Chapters
Fundamentals of Structural Dynamics
Flow Induced Vibration of Power and Process Plant Components: A Practical Workbook
Design and Simulation of Heat Dissipation System for HV Power House of the Seafloor Junction Box
International Conference on Mechanical and Electrical Technology 2009 (ICMET 2009)
Testing, Simulation, and Interpretation of Materials Impact Characteristics
Instrumented Impact Testing of Plastics and Composite Materials