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Soft-impact dynamics of deformable bodies

Continuum Mechanics and Thermodynamics volume 25, pages 375–398 (2013)Cite this article

Abstract

Systems constituted by impacting beams and rods of non-negligible mass are often encountered in many applications of engineering practice. The impact between two rigid bodies is an intrinsically indeterminate problem due to the arbitrariness of the velocities after the instantaneous impact and implicates an infinite value of the contact force. The arbitrariness of after-impact velocities is solved by releasing the impenetrability condition as an internal constraint of the bodies and by allowing for elastic deformations at contact during an impact of finite duration. In this paper, the latter goal is achieved by interposing a concentrate spring between a beam and a rod at their contact point, simulating the deformability of impacting bodies at the interaction zones. A reliable and convenient method for determining impact forces is also presented. An example of engineering interest is carried out: a flexible beam that impacts on an axially deformable strut. The solution of motion under a harmonic excitation of the beam built-in base is found in terms of transverse and axial displacements of the beam and rod, respectively, by superimposition of a finite number of modal contributions. Numerical investigations are performed in order to examine the influence of the rigidity of the contact spring and of the ratio between the first natural frequencies of the beam and the rod, respectively, on the system response, namely impact velocity, maximum displacement, spring stretching and contact force. Impact velocity diagrams, nonlinear resonance curves and phase portraits are presented to determine regions of periodic motion with impacts and the appearance of chaotic solutions, and parameter ranges where the functionality of the non-structural element is at risk.

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Author notes

  1. Ugo Andreaus

    Present address: , Via Eudossiana, 18 00184, Rome, Italy

  2. Bernardino Chiaia

    Present address: , Corso Duca degli Abruzzi, 24, 10129, Turin, Italy

  3. Luca Placidi

    Present address: , C.so Vittorio Emanuele II, 39, 00186, Rome, Italy

Authors and Affiliations

  1. Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma La Sapienza, Rome, Italy

    Ugo Andreaus

  2. Dipartimento di Ingegneria Strutturale e Geotecnica, Politecnico di Torino, Turin, Italy

    Bernardino Chiaia

  3. International Telematic University Uninettuno, Rome, Italy

    Luca Placidi

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  1. Ugo Andreaus
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  2. Bernardino Chiaia
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  3. Luca Placidi
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Correspondence to Luca Placidi.

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Communicated by Francesco dell’Isola and Samuel Forest.

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Andreaus, U., Chiaia, B. & Placidi, L. Soft-impact dynamics of deformable bodies. Continuum Mech. Thermodyn. 25, 375–398 (2013). https://doi.org/10.1007/s00161-012-0266-5

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  • DOI: https://doi.org/10.1007/s00161-012-0266-5

Keywords

  • Nonlinear dynamics
  • Impact mechanics
  • Chaotic solutions