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Understanding modal interactions in non-classically damped linear oscillators with closely spaced modes

Year: 2026
Type: article
Abstract: Linear discrete coupled oscillators with closely spaced modes have been a topic of intense study since they appear often in engineering practice, e.g., in turbomachinery applications, and jointed structures with symmetries. When these systems are classically viscously damped, their vibration modes cannot interact. However, this does not hold in non-classically (non-proportionally) damped systems, which possess complex vibration modes; for such systems closely spaced vibration modes do interact. This work addresses the physics of such modal interactions. Considering an impulsively excited two-degree-of-freedom (two-DOF) system, we perform complexification-averaging analysis to show that there is a single parameter defined as a coupling versus damping non-proportionality ratio, that defines two distinct dynamical regimes. Below the critical value of this parameter, the system response possesses two distinct dissipation rates but only one (fast) frequency of oscillation, with energy being slowly exchanged between modes over a single (slow) cycle. However, above the critical parameter value, the response has a single dissipation rate but two distinct oscillation frequencies, yielding repetitive beat phenomena as energy is interchanged at a faster rate between modes. Our analytical predictions are fully validated by experimental measurements. Our findings highlight the physics of modal interactions in coupled oscillators and provide a framework for system identification and reduced-order modeling of systems with closely spaced modes.
DOI: 10.1016/j.jsv.2026.119818
Authors: Luis M ․Baldelomar Pinto, Alireza Mojahed, Sobhan Mohammadi, Keegan J. Moore, Lawrence A. Bergman, Alexander F. Vakakis
Language: English
Open Access status: hybrid
Estimated APC paid: $4,190
OpenAlex ID: W4417077345
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