Rapid non-resonant intermodal targeted energy transfer (IMTET) caused by vibro-impact nonlinearity

M. Gzal, B. Fang, A. F. Vakakis, L. A. Bergman, O. V. Gendelman

Research output: Contribution to journalArticlepeer-review


This paper describes a rapid and efficient nonlinear non-resonance mechanism for low-to-high-frequency energy scattering, which is referred to as intermodal targeted energy transfer (IMTET). To present the IMTET mechanism in the most basic setting, a blast-excited two-DOF linear system with a single clearance is considered. The impact interactions facilitate rapid transfer of oscillation energy from an initially excited, low-frequency symmetric mode to a high-frequency antisymmetric mode with substantially higher modal dissipative capacity. Numerical exploration reveals almost immediate drastic reduction of the system response amplitude caused by nonlinear “modal energy redistribution” within its modal space. Characteristic damping time of the system exhibits a multi-fold reduction. This process requires a rather limited number of impacts; only one or two impacts are enough to cause an immediate significant suppression of the system response. The results are robust over a broad range of blast amplitudes. Matrix formalism based on eigenvalue decomposition of the state matrix is developed to obtain an implicit analytic description of the process. Then, estimations for the main characteristics of the IMTET process, such as activation threshold and expected efficiency, are obtained. The results show a rather weak dependence of the characteristic damping time of the system on the coupling strength between oscillators, and relatively strong dependence on the ratio of the clearance to the blast intensity. The findings reported in this study have potential applications for passive, rapid and efficient shock mitigation and energy absorption in engineering structures under extreme loads by redistributing the input shock energy to high-frequency structural modes.

Original languageEnglish (US)
Pages (from-to)2087-2106
Number of pages20
JournalNonlinear Dynamics
Issue number4
StatePublished - Sep 1 2020


  • Clearance
  • Impact
  • Modal energy
  • Shock mitigation
  • Targeted energy transfer

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics


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