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Showing 1 to 19 of 19 for “"Duffing oscillator"”.
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The Duffing Oscillator And Linearization Techniques For Its Motion Constants
… find for nonlinear dynamic systems. We chose the Duffing Oscillator as a higher order nonlinear dynamic system to have its motion constants investigated. The Duffing Oscillator was chosen because studying it gives a better view of how rigid bodies act. It forms a clear dynamic analog of the …
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Islanding Detection and Cybersecurity in Inverter-Based Microgrids Under a High-Noise Environment
… proposes an islanding detection method employing Duffing oscillators to analyze fluctuations at the point of common coupling (PCC) under a high-noise environment, focusing on decreasing detection period, zero power mismatch nondetection zone, and power quality degradation. Unlike existing methods, …
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Contributions to the Computational Analysis of Multi-Dimensional Stochastic Dynamical Systems
… civil engineering interest including hysteretic oscillators. The idea of covariance control is then generalized to the problem of response moment specification where higher order response moments are prescribed with the hope of having more authority over response extremes. The algorithm is then …
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Dynamics of Small Elastic Systems in Fluid: Tension and Nonlinearity
… modulus such that the restoring force is like a Duffing oscillator. Then, the dynamics of this virtual beam are explored in air and water, and it is demonstrated that the Duffing oscillator serves as an appropriate reduced order model for this virtual beam. To understand the stochastic dynamics …
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The mode-dependent dynamics of nonlinear nanomechanical resonators
… continuous system into one or more nonlinear oscillators. However, in many of these works, the nonlinear spring constants are estimated at the lowest order. As such, there is a clear need to more accurately characterize and scale the nonlinear coefficients for NEMS. This work considers a long …
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Passive vibration isolators with high-static-low-dynamic-stiffness
… view this allows the system to be treated as a Duffing oscillator. It is argued that for small oscillations about the static equilibrium position the mechanism behaves linearly. A lab-scale rig which reproduces the HSLDS system with magnets and springs is designed and built. The excitation level …
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Coupled oscillators near resonance
… study the dynamics of two conservative librating oscillators with perturbations from a linear displacement coupling and non-Hamiltonian forces such as damping. We examine the dynamics of these systems when they are near a resonance using secular perturbation theory. We show that near resonance a …
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Stability of nonlinear oscillatory systems with application to ship dynamics
… of the excitation. The behavior of a softening Duffing oscillator is analyzed under external and parametric excitation. The dynamics of a ship rolling in waves is also considered and three types of excitations are treated: external, parametric, and a combination of both. Analog- and …
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Intentional nonlinearity in the small scale with applications to atomic force microscopy (AFM) and mass sensing
… vibrates like a system of linearly coupled oscillators engaging simultaneously a lower, in-phase and a higher, out-of phase resonant mode. The cantilever is designed so that the 2nd mode frequency (i.e., the out-of-phase eigenfrequency) coincides with an integer multiple of the fundamental …
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State switching in multi-stable systems: control and optimisation.
… of this PD-like controller, namely: the Duffing oscillator, which is a typical smooth multistable system; the non-smooth soft-impact oscillator; and the soft-impact oscillator with a drift. A randomised triangular subdivision algorithm is proposed to reconstruct the basins of attraction …
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Advancing the theory and applications of Lagrangian Coherent Structures methods for oceanic surface flows
… the quasi-periodic Bickley jet, the Duffng oscillator and a modified, asymmetric Duffing oscillator. The applicability of this newly developed spectral clustering method, along with several common LCS approaches, such as the Finite-Time Lyapunov Exponent, is tested in several field studies. …
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Breaking the Cycle: the Rise and Fall of Conversion Cycle Limited Three-Wave Mixing
… transverse space and time. We develop a damped Duffing oscillator model that unifies the description of conventional OPA with OPAs that use linear absorption \cite{Ma:15, El-Ganainy:15, Zhong:16, Li:17, Ma:17} or SHG \cite{Flemens:21} to remove idler photons and enhance efficiency. An …
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Nonlinear stochastic vibration analysis for energy harvesting and other applications
… investigate the power dissipation of nonlinear oscillators under non-white excitation is developed by extending the Wiener series. The relatively simple first term of the series, together with the excitation spectrum, is found to completely define the power dissipated. An important property of …
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An Investigation into Nonlinear Random Vibrations based on Wiener Series Theory
… the ‘Wiener theories’. As a useful example the Duffing oscillator is investigated in this work. In many real-life applications, nonlinear systems are excited randomly so this work examines systems under white-noise excitation using the Wiener series. Equivalent Linearisation (EL) is a well-known …
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Efficient solution of the Fokker-Planck Equation via smooth particle hydrodynamics for nonlinear estimation
… state measurements, including the bi-modal Duffing oscillator that renders approaches such as the Extended Kalman Filter inconsistent. Lastly, a new method of visualizing the error of high dimensional PDFs is presented, referred to as Sub-Field Signatures (SFSs). These signatures make it …
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Robust design optimization with dynamic constraints using numerical continuation
… solutions of a linear, harmonically forced oscillator. The robust design optimization method is then applied a harmonically forced nonlinear oscillator.
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Nonlinear transverse vibrations of centrally clamped rotating circular disks
A study is presented of the instability mechanisms of a damped axisymmetric circular disk of uniform thickness rotating about its axis with constant angular velocity and subjected to various transverse space-fixed loading systems. The natural frequencies of spinning floppy disks are obtained for …