arXiv subjects

Zhenwei Xu

Publications and source records attributed to Zhenwei Xu.

8 recordsLinked to original sources

arXiv2026

Dynamic Synchronization of Driven Self-Oscillators: Modeling and Experiment

Synchronization of self-sustained oscillators under fixed-frequency and amplitude forcing is well understood, but how time-varying forcing mangles phase locking has been much less explored. Theory predicts that slow, deterministic modulation of the drive amplitude or frequency can lead to a peculiar synchronization regime characterized by intermittent locking of the oscillation phase beyond the Arnold-tongue boundaries associated with fixed harmonic forcing. We test these predictions in a controllable aeroacoustic self oscillator, i.e, a whistle, that exhibits a robust limit cycle and is subject to external acoustic forcing with programmable frequency and amplitude modulation. Under both slowly varying frequency or amplitude of the forcing, three regimes are observed: (i) strict synchronization (ii) intermittent synchronization, characterized by alternating phase locking and brief phase slip episodes and (iii) no synchronization, with regular phase slips. Particularly in strict synchronization regime, the phase of the oscillator will follow arbitrary slowly-varying drive phase and under amplitude modulation its amplitude fluctuations are strongly suppressed.

nlin.CD↗

arXiv2024

Restricted Euler dynamics in free-surface turbulence

The small-scale velocity gradient is connected to fundamental properties of turbulence at the large scales. By neglecting the viscous and nonlocal pressure Hessian terms, we derive a restricted Euler model for the turbulent flow along an undeformed free surface and discuss the associated stable/unstable manifolds. The model is compared with the data collected by high-resolution imaging on the free surface of a turbulent water tank with negligible surface waves. The joint probability density function (PDF) of the velocity gradient invariants exhibits a distinct pattern from the one in the bulk. The restricted Euler model captures the enhanced probability along the unstable branch of the manifold and the asymmetry of the joint PDF. Significant deviations between the experiments and the prediction are evident, however, in particular concerning the compressibility of the surface flow. These results highlight the enhanced intermittency of the velocity gradient and the influence of the free surface on the energy cascade.

physics.flu-dyn↗

arXiv2024

Data-free Non-intrusive Model Reduction for Nonlinear Finite Element Models via Spectral Submanifolds

The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires explicit knowledge of nonlinear coefficients in the equations of motion, which limits their applicability to generic finite-element (FE) solvers. Here, we propose a non-intrusive algorithm for the computation of the SSMs and the associated ROMs up to arbitrary polynomial orders. This non-intrusive algorithm only requires system nonlinearity as a black box and hence, enables SSM-based model reduction via generic finite-element software. Our expressions and algorithms are valid for systems with up to cubic-order nonlinearities, including velocity-dependent nonlinear terms, asymmetric damping, and stiffness matrices, and hence work for a large class of mechanics problems. We demonstrate the effectiveness of the proposed non-intrusive approach over a variety of FE examples of increasing complexity, including a micro-resonator FE model containing more than a million degrees of freedom.

math.NA↗

arXiv2024

Data-Driven Reduction of the Finite-Element Model of a Tribomechadynamics Benchmark Problem

Bolted joints can exhibit nonsmooth and significantly nonlinear dynamics. Finite Element Models (FEMs) of this phenomenon require fine spatial discretizations, inclusion of nonlinear contact and friction laws, as well as geometric nonlinearity. Owing to the nonlinearity and high dimensionality of such models, full-order dynamic simulations are computationally expensive. In this work, we use the theory of Spectral Submanifolds (SSMs) to construct a data-driven, smoothed reduced model for a 187,920-dimensional FEM model of a broadly studied Tribomechadynamics benchmark structure with bolted joints. We train the 4-dimensional reduced model using only a few transient trajectories of the full unforced FEM model. We show that this smooth model accurately predicts the experimentally observed nonlinear forced response of the full nonsmooth benchmark problem.

math.DS↗

arXiv2024

Nonlinear Model Reduction to Random Spectral Submanifolds in Random Vibrations

Dynamical systems in engineering and physics are often subject to irregular excitations that are best modeled as random. Monte Carlo simulations are routinely performed on such random models to obtain statistics on their long-term response. Such simulations, however, are prohibitively expensive and time consuming for high-dimensional nonlinear systems. Here we propose to decrease this numerical burden significantly by reducing the full system to very low-dimensional, attracting, random invariant manifolds in its phase space and performing the Monte Carlo simulations on that reduced dynamical system. The random spectral submanifolds (SSMs) we construct for this purpose generalize the concept of SSMs from deterministic systems under uniformly bounded random forcing. We illustrate the accuracy and speed of random SSM reduction by computing the SSM-reduced power spectral density of the randomly forced mechanical systems that range from simple oscillator chains to finite-element models of beams and plates.

math.DS↗

arXiv2024

Data-driven modeling of the regular and chaotic dynamics of an inverted flag from experiments

We use video footage of a water tunnel experiment to construct a two-dimensional reduced-order model of the flapping dynamics of an inverted flag in uniform flow. The model is obtained as the reduced dynamics on an attracting spectral submanifold (SSM) that emanates from the two slowest modes of the unstable fixed point of the flag. Beyond an unstable fixed point and a limit cycle expected from observations, our SSM-reduced model also confirms the existence of two unstable fixed points for the flag, which were found by previous studies. Importantly, the model correctly reconstructs the dynamics from a small number of general trajectories and no further information on the system. In the chaotic flapping regime, we construct a 4D SSM-reduced model that captures the system's chaotic attractor.

physics.flu-dyn↗

arXiv2023

The effect of dataset size and the process of big data mining for investigating solar-thermal desalination by using machine learning

Machine learning's application in solar-thermal desalination is limited by data shortage and inconsistent analysis. This study develops an optimized dataset collection and analysis process for the representative solar still. By ultra-hydrophilic treatment on the condensation cover, the dataset collection process reduces the collection time by 83.3%. Over 1,000 datasets are collected, which is nearly one order of magnitude larger than up-to-date works. Then, a new interdisciplinary process flow is proposed. Some meaningful results are obtained that were not addressed by previous studies. It is found that Radom Forest might be a better choice for datasets larger than 1,000 due to both high accuracy and fast speed. Besides, the dataset range affects the quantified importance (weighted value) of factors significantly, with up to a 115% increment. Moreover, the results show that machine learning has a high accuracy on the extrapolation prediction of productivity, where the minimum mean relative prediction error is just around 4%. The results of this work not only show the necessity of the dataset characteristics' effect but also provide a standard process for studying solar-thermal desalination by machine learning, which would pave the way for interdisciplinary study.

physics.app-ph↗

arXiv2021

Improving the mass transfer rate and energy efficiency of solar still by enhancing the inner air circulation

Solar still is an eco-friendly and convenient desalination system that can provide fresh water for remote areas and emergencies. The energy efficiency and productivity of conventional solar still are unsatisfying and need improvement, which requires a deep understanding of the heat and mass transfer process in solar still. In this work, the effect of the inner air circulation on the system's heat and mass transfer performance and energy efficiency are studied theoretically and experimentally. The theoretical results reveal that a weak acceleration of the air circulation inside the SS will significantly increase its performance, due to the improved mass transfer process. By enhancing the inner air circulation, the evaporation and condensation in the solar still can reach up to the limit, and the theoretical energy efficiency reaches up to 87%, 91.5%, and 94.5%, for the input power density at 300 W/m2, 500 W/m2, and 700 W/m2, respectively. Besides, lower ambient temperature and higher ambient convective heat transfer coefficient will decrease the energy efficiency. Given the heat loss, the experimental energy efficiencies are only 3% to 6% lower than the theoretical results, which indicates that the great performance predicted by the theory can be realized in practical application. This work provides a new understanding and strategy for improving the performance of the solar still.

physics.app-ph↗