Rapid non-resonant intermodal targeted energy transfer (IMTET) caused by vibro-impact nonlinearity
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ORIGINAL PAPER
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
Received: 23 June 2020 / Accepted: 20 August 2020 Ó Springer Nature B.V. 2020
Abstract This paper describes a rapid and efficient nonlinear non-resonance mechanism for low-to-highfrequency 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
M. Gzal O. V. Gendelman (&) Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, Israel e-mail: [email protected] B. Fang A. F. Vakakis Department of Mechanical Science and Engineering, University of Illinois, Urbana, USA B. Fang Key Laboratory of the Ministry of Education Ministry for Modern Design and Rotor-Bearing Systems, Xi’an Jiaotong University, Xi’an, People’s Republic of China L. A. Bergman Department of Aerospace Engineering, University of Illinois, Urbana, USA
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. Keywords Shock mitigation Targeted energy transfer Impact Clearance Modal energy
1 Introduction Passive energy management in structures subjected to extreme loads, i.e., high-energy, often short-duration
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transient excitations such as shock, blast and earthquakes, is a common and challenging problem. One of most important issues here is rather limited suppression achieved for the first few (but most intensive and d
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