arXiv subjects

Keegan J. Moore

Publications and source records attributed to Keegan J. Moore.

11 recordsLinked to original sources

arXiv2026

Decomposition-based Energy-based Dual-Phase Dynamics Identification for Nonlinear MDOF Systems

System identification is an important step in modeling and evaluating vibrating structures, but many nonlinear system identification methods rely heavily on data-driven approaches that may not preserve physical consistency. This research extends the Energy-based Dual-phase Dynamics Identification (EDDI) method to multiple-degree-of-freedom (MDOF) mechanical structures undergoing nonlinear vibrations. The original EDDI framework was designed for single-degree-of-freedom (SDOF) systems and operates in two phases: the first identifies a model for internal nonconservative force, and the second captures internal conservative force. However, EDDI assumes that the potential energy is zero whenever the displacement is zero. For MDOF systems, this assumption requires all degrees of freedom (DOFs) to achieve zero displacement simultaneously, which simply occurs too infrequently in multimodal responses for direct application. To overcome this limitation, this work introduces Decomposition-based EDDI, which applies EDDI to decomposed response components to enable nonlinear system identification of MDOF systems. Wavelet-Bounded Empirical Mode Decomposition is used to extract nearly orthogonal, monochromatic intrinsic mode functions (IMFs) from the measured displacements. Each IMF is then treated as an individual SDOF oscillator and processed using EDDI to estimate its nonconservative and conservative internal forces. The IMF forces are then summed to reconstruct the total nonconservative and conservative forces acting on each physical DOF, which are used to identify the damping and stiffness models, respectively. The proposed EDDI framework is experimentally validated on a two-story tower structure with strong stiffness nonlinearity coupling the two floors. The results demonstrate the efficacy of EDDI in isolating and identifying complex, multi-modal nonlinear structural dynamics.

math.DS↗

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

Bandwidth of Linear Classically Damped Systems with Application to Experimental Model Aircraft

Bandwidth is a widely known concept and tool used in structural dynamics to measure an oscillator's capacity to dissipate energy over time, for example when used in half-power damping estimation of structural modes. Root Mean Square (RMS) Bandwidth is a generalization of bandwidth that overcomes some of the limitations encountered with conventional bandwidth, including the prerequisite of linearity, single-mode response, and light damping. However, its mathematical form does not reveal much about the physics behind it. In this paper, we extend RMS Bandwidth to multiple degree-of-freedom, linear, time-invariant, classically damped systems by deriving an Analytical Root Mean Square (ARMS) Bandwidth in terms of a system's modal parameters and initial modal energy distribution. We demonstrate that ARMS Bandwidth reliably and accurately computes a single measure for a practical structure's dissipative capacity. Also, a purely data-driven methodology for assessing the modal energy distribution is developed. We apply ARMS Bandwidth to single and multiple degree-of-freedom systems and an experimental model aircraft to demonstrate its broad applicability. Future work will address the effects of non-classical damping distribution, time-varying parameters, and nonlinearities.

physics.app-ph↗

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

Reduced-Order Modeling of Bolt Loosening: Application to a Pair of Oscillators Under Transverse Shock Excitation

The safety and integrity of engineered structures are critically dependent on maintaining sufficient preload in their bolted joints. This preload can be dynamically lost due to sustained vibrations or sudden shock that are large enough to induce slip in the threads. While high-fidelity finite element simulations and analytical methods can accurately model the loss of preload for a single, their prohibitive computational expense and complexity render them unfeasible for analyzing large-scale structures with many bolts. This creates a critical need for reduced-order models that capture the essential physics of loosening while remaining computationally efficient. This paper introduces a reduced-order modeling methodology for predicting the loosening of bolted lap joints subjected to transverse shock excitation. The core idea is to treat the bolt tension as a dynamic degree-of-freedom that governs the effective properties of the joint through tension-dependent stiffness and damping that couple the components together. The methodology is applied to a pair of oscillators coupled by with a single lap joint with a strain-sensing bolt. Three different sets of experimental measurements are used to interrogate the dynamics of the system. Mathematical models are identified for the joint stiffness and damping and the instantaneous tension, which are combined with the equations of motion for the oscillators to simulate and reproduce the experimental measurements. Ultimately, the results validate the treatment of bolt tension as a dynamic degree-of-freedom, such that the methodology provides an effective framework for predicting loosening behavior in bolted joints.

math.DS↗

arXiv2025

System Identification via Validation and Adaptation for Model Updating Applied to a Nonlinear Cantilever Beam

The recently proposed System Identification via Validation and Adaptation (SIVA) method allows system identification, uncertainty quantification, and model validation directly from data. Inspired by generative modeling, SIVA employs a neural network that converts random noise to physically meaningful parameters. The known equation of motion utilizes these parameters to generate fake accelerations, which are compared to real training data using a mean square error loss. For concurrent parameter validation, independent datasets are passed through the model, and the resulting signals are classified as real or fake by a discriminator network, which guides the parameter-generator network. In this work, we apply SIVA to simulated vibration data from a cantilever beam that contains a lumped mass and a nonlinear end attachment, demonstrating accurate parameter estimation and model updating on complex, highly nonlinear systems.

eess.SY↗

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↗

arXiv2025

Structural System Identification via Validation and Adaptation

Estimating the governing equation parameter values is essential for integrating experimental data with scientific theory to understand, validate, and predict the dynamics of complex systems. In this work, we propose a new method for structural system identification (SI), uncertainty quantification, and validation directly from data. Inspired by generative modeling frameworks, a neural network maps random noise to physically meaningful parameters. These parameters are then used in the known equation of motion to obtain fake accelerations, which are compared to real training data via a mean square error loss. To simultaneously validate the learned parameters, we use independent validation datasets. The generated accelerations from these datasets are evaluated by a discriminator network, which determines whether the output is real or fake, and guides the parameter-generator network. Analytical and real experiments show the parameter estimation accuracy and model validation for different nonlinear structural systems.

math.DS↗

arXiv2024

Energy-based dual-phase dynamics identification of clearance nonlinearities

The energy-based dual-phase dynamics identification (EDDI) method is a new data-driven technique for the discovery of equations of motion (EOMs) of strongly nonlinear single-degree-of-freedom (SDOF) oscillators. This research uses the EDDI method to obtain mathematical models for SDOF systems with clearance nonlinearities. The first key aspect of the EDDI method is that it relates the kinetic energy of the system to the dissipated energy and the underlying non-conservative forces acting on the oscillator. The second key aspect is that the EOM is identified with only knowledge of the mass of the oscillator and the transient response. The first phase of the EDDI method constructs the dissipated energy from the kinetic energy, then identifies a mathematical model for the damping based on the dissipated energy. To achieve this, the moments in time when the displacements are zero, where the mechanical and kinetic energies are equal, are used to compute the energy dissipated by the damping of the system. The second phase begins by computing the conservative force acting on the oscillator from either a balance of the other forces in the system or through the Lagrange equation. Finally, the stiffness model is determined by solving a set of linear equations to construct a mathematical model for the conservative (elastic) force. The governing equations are discovered by incorporating both the damping and stiffness terms. The method is demonstrated by employing analytical and real measured responses of nonlinear SDOF systems with different clearances nonlinearities, which shows that the proposed approach is suitable for non-smooth mechanical systems as well as smooth systems.

math.DS↗

arXiv2024

Weak-form modified sparse identification of nonlinear dynamics

Identifying nonlinear dynamics and characterizing noise from data is critical across science and engineering for understanding and modeling the behavior of the systems accurately. The modified sparse identification of nonlinear dynamics (mSINDy) has emerged as an effective framework for identifying systems embedded in heavy noise; however, further improvements can expand its capabilities and robustness. By integrating the weak SINDy (WSINDy) into mSINDy, we introduce the weak mSINDy (WmSINDy) to improve the system identification and noise modeling by harnessing the strengths of both approaches. The proposed algorithm simultaneously identifies parsimonious nonlinear dynamics and extracts noise probability distributions using automatic differentiation. We evaluate WmSINDy using several nonlinear systems and it demonstrates improved accuracy and noise characterization over baselines for systems embedded in relatively strong noise.

math.DS↗

arXiv2024

A Data-Driven, Energy-based Approach for Identifying Equations of Motion in Vibrating Structures Directly from Measurements

Determining the underlying equations of motion and parameter values for vibrating structures is of great concern in science and engineering. This work introduces a new data-driven approach called the energy-based dual-phase dynamics identification (EDDI) method for identifying the nonlinear dynamics of single-degree-of-freedom oscillators. The EDDI method leverages the energies of the system to identify the governing dynamics through the forces acting on the oscillator. The approach consists of two phases: a model-dissipative and model-stiffness identification. In the first phase, the fact that kinetic and mechanical energies are equivalent when the displacement is zero is leveraged to compute the energy dissipated and a corresponding model for the nonlinear damping of the system. In the second phase, the energy dissipated is used to compute the mechanical energy (ME), which is then used to obtain a reformulated Lagrangian. The conservative forces acting on the oscillator are then computed by taking the derivative the Lagrangian, then a model for the nonlinear stiffness is identified by solving a system of linear equations. The resulting governing equations are identified by including both the nonlinear damping and stiffness terms. A key novelty of the EDDI method is that the only thing required to perform the identification is free-response measurements and the mass of the oscillator. No prior understanding of the dynamics of the system is necessary to identify the underlying dynamics, such that the EDDI method is a truly data-driven method. The method is demonstrated using simulated and measured responses of nonlinear single-degree-of-freedom systems with a variety of nonlinear mechanisms.

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