Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2604.00427

Time-bandwidth Study of Non-classically Damped, Linear, Time-invariant Coupled Oscillators with Closely Spaced Modes

Luis M. Baldelomar Pinto·Alireza Mojahed·Sobhan Mohammadi·Keegan J. Moore·Lawrence A. Bergman·Alexander F. Vakakis
View original source ↗Read source document ↗Export metadata ↓

Abstract

In dynamics and vibrations, the concept of bandwidth for linear time-invariant systems is widely recognized as a measure of the dispersion of frequency content around resonance. Similarly, the time constant is associated with the rate of energy decay in the time domain. Notably, the time-bandwidth limit for such systems is unity, indicating that achieving sharp frequency localization while simultaneously maintaining a slow energy decay is not feasible, nor is it possible to achieve a broad frequency spread while preserving a rapid energy decay. However, the time-bandwidth concept does not have a well-defined application to multi-degree of freedom systems characterized by strong modal interactions. This research aims to develop a comprehensive time and bandwidth concept for a linear two-DOF system with significant modal interactions. We focus on a non-classically damped system, which facilitates complex mode interactions, and we investigate how the definition of bandwidth and time constant can be applied to account for the slow dynamics observed in energy decay. By examining this system under various parameters, we gain insights into the energy decay behavior at specific time-bandwidth product regimes. Our analytical results are validated through experiments. Our findings elucidate the implications of the time-bandwidth product for a linear multi-DOF system's response and provide valuable insights into the influence of modal interactions on energy decay.

Explore related subjects

math.DSmath-phmath.MPphysics.class-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Luis M. Baldelomar Pinto, Alireza Mojahed, Sobhan Mohammadi, Keegan J. Moore, Lawrence A. Bergman, Alexander F. Vakakis. 2026-04-01. Time-bandwidth Study of Non-classically Damped, Linear, Time-invariant Coupled Oscillators with Closely Spaced Modes. https://arxiv.org/abs/2604.00427

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive H\"older class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-H\"older continuity of the integrated density of states for the associated quasiperiodic Schr\"odinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS↗
arXiv2026

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS↗
arXiv2026

Ergodicity of dynamical systems without uniqueness of orbits

Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.

math.DS↗