arXiv subjects

Sobhan Mohammadi

Publications and source records attributed to Sobhan Mohammadi.

3 recordsLinked to original sources

arXiv2026

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

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.

math.DS↗

arXiv2025

Understanding Modal Interactions in Non-classically Damped Linear Oscillators with Closely Spaced Modes

This work addresses non-classically damped coupled oscillators with closely spaced modes focusing on the physics of modal interactions. Considering the simplest representative example in the form of an impulsively excited two-degree-of-freedom (two-DOF) system, we show that there is a single parameter defined as a coupling versus damping non-proportionality ratio, that separates two different dynamical regimes. Based on complexification-averaging analysis, we show that, below the critical value of this parameter, the system response possesses two distinct dissipation rates but only one frequency of oscillation; as a result, energy is slowly exchanged between modes in a single beat phenomenon. However, above the critical parameter value, the response has a single dissipation rate but two distinct oscillation frequencies; this yields an infinity of 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.

physics.class-ph↗

arXiv2025

Mixed Mode Oscillations and Bifurcation Mechanism in a Nonlinear Beam-Elastic Foundation Under Parametric and External Excitations

This paper aims to study existence condition of possible bursting oscillations generated by low frequency excitation of a nonlinear vibratory system in the presence of parametric excitation. Slow-fast dissection technique and numerical bifurcation analysis are employed to extract qualitative changes in system response originated from its nonlinear dynamics. Role of all parameters of elastic foundation and excitation model are studies and it is shown that the system exhibits the phenomena of folding, cusp and Bogdanov-Takens bifurcations which are potentially routes to bi-stability and chaos. It can be found that slow excitation of the nonlinear foundation is the main generating factor of fold bifurcation and stiffness of elastic foundation has a remarkable effect on stability region of the beam. In addition, the base excitation of an elastic foundation in form of a traveling wave, adds multi-frequency excitation and parametric resonances necessarily to the system. This study showed investigating nonlinear oscillator under low frequency excitations in framework of slow-fast plays an invaluable role in understanding instabilities in systems that are not captured by standard methods.

math.DS↗