arXiv subjects

Alireza Mojahed

Publications and source records attributed to Alireza Mojahed.

7 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↗

arXiv2023

Assessing the Dissipative Capacity of Particle Impact Dampers Based on their Nonlinear Bandwidth Characteristics

The dissipative capacity as quantified by the nonlinear bandwidth measure of impulsively loaded primary structures (PSs) coupled to particle impact dampers (PIDs) is assessed. The considered PIDs are designed by initially placing different numbers of spherical, linearly viscoelastic granules at different 2D initial topologies and clearances. The strongly nonlinear and highly discontinuous dynamics of the PIDs are simulated via the discrete element method taking Hertzian interactions, slipping friction and granular rotations into account. The general definition of nonlinear bandwidth is used to evaluate the energy dissipation capacity of the integrated PS-PID systems. Moreover, the effect of the dynamics of the PIDs on the time-bandwidth product of these systems is studied, as a measure of their capacity to store or dissipate vibration energy. It is found that the initial topologies of the granules in the PID drastically affect the time-bandwidth product, which, depending on shock intensity, may break the classical limit of unity which holds for linear time-invariant dissipative resonators. The optimal PS-PID systems composed of multiple granules produce large nonlinear bandwidths, indicating strong dissipative capacity of broadband input energy by the PIDs. Additionally, in the optimal configurations, the time-bandwidth product, i.e., the measure of the frequency bandwidth of the input shock that is stored in the PS-PID system, in tandem with the amount of time it takes for the system to dissipate (1/e) of the initial energy, can be tuned either above or below unity by varying the applied shock intensity. The implications of these findings on the dissipative capacity of the system considered are discussed, showing that it can be predictively assessed so that PIDs can act as highly effective nonlinear energy sinks capable of rapid and efficient suppression of vibration induced by shocks.

math.OC↗

arXiv2023

Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems

Machine learning methods for the construction of data-driven reduced order model models are used in an increasing variety of engineering domains, especially as a supplement to expensive computational fluid dynamics for design problems. An important check on the reliability of surrogate models is Uncertainty Quantification (UQ), a self assessed estimate of the model error. Accurate UQ allows for cost savings by reducing both the required size of training data sets and the required safety factors, while poor UQ prevents users from confidently relying on model predictions. We examine several machine learning techniques, including both Gaussian processes and a family UQ-augmented neural networks: Ensemble neural networks (ENN), Bayesian neural networks (BNN), Dropout neural networks (D-NN), and Gaussian neural networks (G-NN). We evaluate UQ accuracy (distinct from model accuracy) using two metrics: the distribution of normalized residuals on validation data, and the distribution of estimated uncertainties. We apply these metrics to two model data sets, representative of complex dynamical systems: an ocean engineering problem in which a ship traverses irregular wave episodes, and a dispersive wave turbulence system with extreme events, the Majda-McLaughlin-Tabak model. We present conclusions concerning model architecture and hyperparameter tuning.

stat.ML↗

arXiv2021

Generalization of the Concept of Bandwidth

In the sciences and engineering, the concept of bandwidth is often subject to interpretation depending upon context and the requirements of a specific community. The focus of this work is to formulate this concept for a general class of passive oscillatory dynamical systems, including but not limited to mechanical, structural, acoustic, electrical, and optical. Typically, the bandwidth of these systems is determined by the half-power (-3 dB) method, and the result is often referred to as half-power bandwidth. The fundamental assumption underlying this definition is that the system performance degrades once its power decreases by 50%; moreover, there are restrictive conditions that are rarely met. Here the concept of root mean square bandwidth is considered, justified by the Fourier uncertainty principle, to generalize the definition of bandwidth to encompass linear and nonlinear, single and multi-mode, low and high loss and time-varying and invariant oscillating systems. By tying the bandwidth of an oscillatory dynamical system directly to its dissipative capacity, one can formulate a definition based solely on its transient energy evolution, effectively circumventing the previous restrictions. Further, applications are given that highlight the limitations of the traditional half-power bandwidth; including a Duffing oscillator with hardening nonlinearity, and a geometrically nonlinear oscillator with tunable hardening or softening nonlinearity. The resulting energy-dependent bandwidth computations are compatible with the nonlinear dynamics of these systems, since at low energies they recover the half-power bandwidth, whereas at high energies they accurately capture the nonlinear physics. Moreover, the bandwidth computation is directly tied to nonlinear harmonic generation in the transient dynamics.

physics.gen-ph↗

arXiv2021

Exceeding the Classical Time-bandwidth Product in Nonlinear Time-invariant Systems

The classical 'time-bandwidth' limit for linear time-invariant (LTI) devices asserts that it is impossible to store broadband waves (large Δω's) for long times (large Δt's). For standing waves, i.e., vibrations, in particular, this limit takes on a simple form, Δt Δω = 1, where Δω is the bandwidth over which localization occurs, and Δt is the storage time. It remains a fundamental challenge in classical wave physics and vibration engineering to try to find ways to overcome this limit, not least because that would allow for storing broadband waves for long times, or achieve broadband resonance for low damping. Recent theoretical studies have suggested that such a feat might be possible in LTI terminated unidirectional waveguides or LTI topological 'rainbow trapping' devices, although an experimental confirmation of either concept is still lacking. In this work, we consider a nonlinear but time-invariant mechanical system and demonstrate experimentally that its time-bandwidth product can exceed the classical time-bandwidth limit, thus achieving values, both, above and below unity, in an energy-tunable way. Our proposed structure consists of a single degree-of-freedom nonlinear oscillator, rigidly coupled to a nondispersive waveguide. Upon developing the full theoretical framework for this class of nonlinear systems, we show how one may control the nonlinear flow of energy in the frequency domain, thereby managing to disproportionally decrease (increase) Δt, the storage time in the resonator, as compared with an increase (decrease) of the system's bandwidth Δω. Our results pave the way to conceiving and harnessing hitherto unattainable broadband and simultaneously low-loss wave-storage devices, both linear and nonlinear, for a host of key applications in wave physics and engineering.

physics.app-ph↗

arXiv2020

Acoustic Steering of Active Spherical Carriers

Following the novel introduced concept of the active carriers, this paper brings forward a technique toward the manipulability of an internally piezo-equipped active spherical carrier subjected to the progressive acoustic plane waves as the handling contactless asset. It is assumed that the piezoelectric part of the active carrier may be actuated as a bi-sectional body (i.e., two continuous hemispherical parts), with prescribed phase difference, and the polar position of the imaginary separating plane may be altered. This issue brings about an asymmetry in the dynamics of the problem which leads to emergence of position/frequency dependent acoustic radiation torque. It is obtained that as the carrier is excited by imposing harmonic voltage with the same amplitude and a $π$-radians phase difference,the zero-radiation force situation is obtained for a specific amplitude and phase of voltage as a function of frequency. This situation is treated as a criterion to determine the optimal amplitude of operation voltage. It is shown that the net force's direction exerted on the activated carrier may be steered along any desired orientation, assuming the fixed direction of the incident wave field. The explained method of excitation and controllability of the spatial position of the divisor plane can possibly be a breakthrough in acoustic handling of active carriers. Noticeably, by this new technique, the single beam acoustic based contact-free methods and their applications in association with the concept of active carriers are now one step forward.

physics.app-ph↗