Nonlinear Dynamic Simulation Research Articles

Nonlinear dynamic of flexible rotor supported by turbulent bearings with quadratic damping and temperature dependent viscosity

A nonlinear dynamic model of a rotor supported by the turbulent journal bearing with quadratic damping under nonlinear suspension is presented in this study, and the lubricating oil is assumed to be temperature-dependent. The bifurcation diagrams, dynamic trajectories, power spectra, Poincaré map, Lyapunov exponent, and fractal dimension are used to verify the dynamic characteristics of the rotor-bearing system, and abundant subharmonic, and even chaotic motions are found. Temperature is one of the key parameters affecting the dynamic responses of the system, and the dynamic responses will perform non-periodic or even chaotic motions with higher working temperatures of lubricant fluid, as proved in this study. Nonlinear dynamic simulation analysis results will help engineers avoid unnecessary trial and error when designing and applying rotating machinery systems.

Statement of Retraction: Nonlinear dynamics simulation of the composite reinforced annular system using harmonic differential quadrature framework

Statement of Retraction: Nonlinear dynamics simulation of the composite reinforced annular system using harmonic differential quadrature framework

Study on the 2D equivalent nonlinear dynamics simulation model related to high speed precision bearing and spindle

The stiffness and contact stress of the bearing spindle system are the key factors affecting its machining accuracy and service life under the condition of high-speed service, which will be affected by different structural parameters and service conditions. It is essential to establish an efficient and accurate computational simulation model to understand the influence of complex factors on the nonlinear dynamic characteristics of the bearing spindle system. Firstly, in the paper, a 2D axisymmetric finite element model of the bearing, aims at the relationship between stiffness and contact stress of the bearing under high-speed service, has been built based on a classical dynamic analysis model and the reversed method of material parameters of equivalent rolling balls. Additionally, for the BT30 spindle, the 2D axisymmetric finite element model of the bearing spindle system also has been built and applied in mechanical analysis of spindle under different conditions of assembly and service, based on the bearing model. The results show that the axial force of bearings decreases as the rotational speed increases, and an augmentation in speed will result in a reduction in the axial stiffness of the BT30 spindle. In addition, the maximum contact stress exhibits a slight decline as the rotational speed increases. Furthermore, with an escalating preload, the stiffness and contact stress of the spindle undergo substantial increments, however, these parameters will cease to alter once a certain threshold is reached.

Enhancing the overturning resistance capacity of high aspect ratio structure through hybrid base isolation and inter-storey isolation

The high-aspect ratio of structures is usually limited to a small range for base isolation (BI), due to the necessity of ensuring resistance to overturning. This limitation restricts the application of friction pendulum bearings (FPBs) in structures with large high-aspect ratios. This article aims to explore the application of hybrid base isolation and inter-storey isolation (BIISI) in structures with large high-aspect ratio. The theoretical basis of the BIISI was first analyzed in terms of overturning resistance. Subsequently, nonlinear dynamic numerical simulations were conducted on a building with a high aspect ratio to simulate its response subjected to typical pulse-type and non-pulse-type earthquakes. The overturning resistance of the structure and seismic dynamic responses were evaluated. A series of parametric studies were also conducted to investigate the effects of FPB properties, peak ground acceleration (PGA), the friction coefficient ratio and the radius of FPBs between inter-storey isolation storey and base isolation storey on the overturning resistance performance of isolated structures. It is demonstrated that superstructure is meticulously partitioned into two independent sliding structural elements through the BIISI, and it can significantly improve the overturning resistance of buildings with a large high-aspect ratio. PGA and FPB properties show significant differences, but the friction coefficient ratio and the radius of FPBs between the inter-storey isolation storey and base isolation storey show limited influences on the overturning resistance of the structure.

ULTRA-SR Challenge: Assessment of Ultrasound Localization and TRacking Algorithms for Super-Resolution Imaging.

With the widespread interest and uptake of super-resolution ultrasound (SRUS) through localization and tracking of microbubbles, also known as ultrasound localization microscopy (ULM), many localization and tracking algorithms have been developed. ULM can image many centimeters into tissue in-vivo and track microvascular flow non-invasively with sub-diffraction resolution. In a significant community effort, we organized a challenge, Ultrasound Localization and TRacking Algorithms for Super-Resolution (ULTRA-SR). The aims of this paper are threefold: to describe the challenge organization, data generation, and winning algorithms; to present the metrics and methods for evaluating challenge entrants; and to report results and findings of the evaluation. Realistic ultrasound datasets containing microvascular flow for different clinical ultrasound frequencies were simulated, using vascular flow physics, acoustic field simulation and nonlinear bubble dynamics simulation. Based on these datasets, 38 submissions from 24 research groups were evaluated against ground truth using an evaluation framework with six metrics, three for localization and three for tracking. In-vivo mouse brain and human lymph node data were also provided, and performance assessed by an expert panel. Winning algorithms are described and discussed. The publicly available data with ground truth and the defined metrics for both localization and tracking present a valuable resource for researchers to benchmark algorithms and software, identify optimized methods/software for their data, and provide insight into the current limits of the field. In conclusion, Ultra-SR challenge has provided benchmarking data and tools as well as direct comparison and insights for a number of the state-of-the art localization and tracking algorithms.

Research on non-linear dynamic simulation model of feeding system

Abstract The automatic gun feeding system is an important mechanism for achieving continuous shooting, but due to its complex structure, there is a lot of contact during firing, and its reliability is lower. To improve the reliability of the feeding system and its dynamic characteristics, a multi rigid body dynamic simulation model of the feeding system considering contact nonlinearity was established based on nonlinear dynamics theory. The dynamic characteristics of the feeding system were analyzed for single and continuous firing. The research results indicate that the presence of contact nonlinearity increases the interaction forces between components and also increases the uncertainty of component motion.

Shared mooring system designs and cost estimates for wave energy arrays

For floating renewable energy devices to become more cost-efficient and commercially scalable, their mooring system designs must be low-cost and suited for large-scale installations. Large arrays of floating devices, such as wave energy converters (WECs), will likely be designed with an individual mooring system for each device in the array. However, new mooring technology advancements provide options to use shared mooring lines to connect adjacent devices to one another, reducing the total number of anchors in the array, thereby reducing material use and cost. This paper explores the design, modeling, and cost analysis of shared mooring systems for various sizes of arrays consisting of heaving oscillating water column (OWC) WECs. Shared mooring systems for WEC arrays sized in 2×N and N×N grid layouts are designed to meet the relevant design standards, checking their performance with a nonlinear time-domain dynamic simulation, and the costs of each are calculated and compared. Several assumptions are taken in the design process to produce efficient results, providing a preliminary optimization for guidance on design decisions rather than a full, detailed design analysis. Mooring system costs per WEC were found to decrease as the number of WECs in the array increase, up to certain array sizes. The 2 × 3 array had the lowest mooring system cost per WEC out of all arrays considered, with a 60% cost reduction relative to using individual mooring systems. The 3 × 3 and 4 × 4 arrays achieved a 50% cost per WEC reduction. In addition to these significant cost reductions, the shared mooring system designs can provide advantages through smaller mooring system footprints, lower installation times, and less seabed disturbance.

An integral of motion for a Master–Slave system of damped Duffing oscillators with variable coefficients: Nonlinear dynamics and computer simulations

In this work, a master–slave system composed by a pair of damped Duffing oscillators with variable coefficients and nonlinear coupling is investigated. An integral of motion for the system is obtained using a symmetry transformation and Noether’s theorem. Some numerical examples are presented for different cases of damping and oscillation frequency, for a varying coupling constant. The system dynamics is studied by means of space-time surfaces, time series and phase portraits. For a constant oscillation frequency, the slave presents envelopes that tend to become chaotic as the coupling constant increases. Meanwhile, as the frequency increases with time, the slave has higher amplitudes and speeds than the master oscillator.

A general and efficient harmonic balance method for nonlinear dynamic simulation

This paper presents a general and efficient harmonic balance (GE-HB) method to expeditiously evaluate the periodic responses of nonlinear systems. By employing the fast Fourier transform (FFT) technique, it rapidly computes harmonic expansion coefficients of the nonlinear terms and their corresponding constant tensor matrices. Notably, the nonlinear part of the Jacobian matrix is just the product of the coefficients and the constant tensor matrices, loop computations are no longer requisite for calculating the Jacobian matrix. This, facilitates accelerated determination of the nonlinear portion of the Jacobian matrix, thus obtaining the periodic responses of the system in an efficient manner. Furthermore, the constant tensor matrices are exclusively contingent upon the harmonic bases of the system's periodic response, devoid of reliance on the equation's specific formulation, facilitates obtaining the Jacobian matrix in a general manner. Simulation results on a 20-degree-of-freedom nonlinear oscillator chain system demonstrate that the efficiency of the GE-HB method is about tenfold that of the harmonic balance-alternating frequency/time domain (HB-AFT) method and twenty-fivefold that of the fourth-order Runge-Kutta (RK4) method. Further, the simulation of a 284-degree-of-freedom nonlinear rotor system exhibits the GE-HB method's computational efficiency surpassing HB-AFT method by over 500 times and Newmark method by over 3000 times. Moreover, in these two examples, the GE-HB method captures all solution branches, including unstable periodic solutions, providing comprehensive insights into periodic responses of the systems. The GE-HB method proposed here has the potential to explore dynamic characteristics for high-dimensional complex nonlinear systems in engineering.

Numerical Approach for Nonlinear Dynamics Simulation of Belt-Pulley XY Positioning Mechanism

Numerical Approach for Nonlinear Dynamics Simulation of Belt-Pulley XY Positioning Mechanism

Simulation of nonlinear system dynamics of calcium and dopamine signaling in neurons

Simulation of nonlinear system dynamics of calcium and dopamine signaling in neurons

An efficient uncertainty propagation method for nonlinear dynamics with distribution-free P-box processes

The distribution-free P-box process serves as an effective quantification model for time-varying uncertainties in dynamical systems when only imprecise probabilistic information is available. However, its application to nonlinear systems remains limited due to excessive computation. This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics. First, using the Covariance Analysis Describing Equation Technique (CADET), the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations (ODEs). These equations provide the Mean-and-Covariance (MAC) bounds of the system responses in relation to the MAC bounds of P-box-process excitations. They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps, including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs. Afterward, a Gaussian assumption of the CADET is extended to the P-box form, i.e., the responses are approximate parametric Gaussian P-box processes. As a result, the probability bounds of the responses are approximated by using the solutions of the interval ODEs. Moreover, the Chebyshev method is introduced and modified to efficiently solve the interval ODEs. The proposed method is validated based on test cases, including a duffing oscillator, a vehicle ride, and an engineering black-box problem of launch vehicle trajectory. Compared to the reference solutions based on the Monte Carlo method, with relative errors of less than 3%, the proposed method requires less than 0.2% calculation time. The proposed method also possesses the ability to handle complex black-box problems.

An assessment of crucial structural contributors of HDAC6 inhibitors through fragment-based non-linear pattern recognition and molecular dynamics simulation approaches

Amidst the Zn2+-dependant isoforms of the HDAC family, HDAC6 has emerged as a potential target associated with an array of diseases, especially cancer and neuronal disorders like Rett’s Syndrome, Alzheimer’s disease, Huntington’s disease, etc. Also, despite the availability of a handful of HDAC inhibitors in the market, their non-selective nature has restricted their use in different disease conditions. In this situation, the development of selective and potent HDAC6 inhibitors will provide efficacious therapeutic agents to treat different diseases. In this context, this study has been carried out to evaluate the potential structural contributors of quinazoline-cap-containing HDAC6 inhibitors via machine learning (ML), conventional classification-dependant QSAR, and MD simulation-based binding mode of interaction analysis toward HDAC6 binding. This combined conventional and modern molecular modeling study has revealed the significance of the quinazoline moiety, substitutions present at the quinazoline cap group, as well as the importance of molecular property, number of hydrogen bond donor-acceptor functions, carbon-chlorine distance that significantly affects the HDAC6 binding of these inhibitors, subsequently affecting their potency . Interestingly, the study also revealed that the substitutions such as the chloroethyl group, and bulky quinazolinyl cap group can affect the binding of the cap function with the amino acid residues present in the loops proximal to the catalytic site of HDAC6. Such contributions of cap groups can lead to both stabilization and destabilization of the cap function after occupying the hydrophobic catalytic site by the aryl hydroxamate linker-ZBG functions.

Longitudinal Air-Breathing Hypersonic Vehicle Nonlinear Dynamic Simulation with Different Control Inputs

<div>The air-breathing hypersonic vehicle (AHV) holds the potential to revolutionize global travel, enabling rapid transportation to low-Earth orbit and even space within the next few decades. This study focuses on investigating the nonlinear dynamic simulation, trim, and stability analysis of a three-degrees-of-freedom (3DOF) longitudinal model of a generic AHV for variable control surface deflection, <i>δ<sub>e</sub></i> and <i>δ<sub>r</sub></i>. A simulation is developed to analyze the burstiness of the AHV’s nonlinear longitudinal behavior, considering the complete flight envelope across a wide range of Mach numbers, from <i>M</i> = 0 to 24, for selected stable <i>M</i>. The presented simulation assesses trim analysis and explores the dynamic stability of the AHV through its flight envelope and bifurcation method analysis is carried out to gain insight and validate the dynamic stability using eigen value approach.</div>

Nonlinear dynamics simulation of the helical gear transmission system for high-speed train

Considering the bending-torsional-axial-coupled vibration of the helical gear transmission system, a 10 degrees of freedom high-speed train gear transmission system model, including motor and load, is established based on the lumped parameter method. In addition, the potential energy method based on the slicing principle is used to accurately calculate the time-varying meshing stiffness of helical gears. Furthermore, the influence of geometric parameters of helical gears on the time-varying meshing stiffness is studied, and the impact of time-varying meshing stiffness on the system is further investigated. Meanwhile, by analyzing the dynamic phenomena of the system under different parameter excitations under different parameter excitations, the influence of internal and external excitation parameters such as gear speed, wheel rail creep force, support stiffness, and support damping on the stability of high-speed train gear transmission system is deeply studied.

DESIGN AND IMPLEMENTATION OF REAL-TIME NON-LINEAR DYNAMIC SIMULATION OF FIGHTER AIRCRAFT ON MULTICORE PROCESSOR

Simulation is a system to imitate the operation of various kinds of real-world facilities or processes for training, behavior study or entertainment purposes. Some implementation of fighter aircraft simulation is done sequentially using FORTRAN and MATLAB / Simulink. On the other hand, a multicore (parallel) computer system has been in the personal computer environment, so the multicore computing paradigm should be considered. Intel Threading Building Blocks (TBB) library need to be utilized in multicore programming. This paper discusses the design and implementation of real-time nonlinear dynamic simulation of fighter aircraft on multicore processor. The aircraft model used in this study is F16 data. Implementation of the simulation code is written in C++ with Intel TBB, OpenGL, Open Scene Graph, and Open Dynamic Engine library. The testing results of non-linear dynamics simulation of fighter aircraft show that the speedup on an Intel Core 2 Duo processor is 1.1776 x for elevator doublet input (short period), while speedup on an Intel i7 is 1.5405 x for rudder doublet input (dutch roll). Key Words: multicore computing, real-time simulation, nonlinear dynamic, fighter aircraft model

Dynamical flexible inference of nonlinear latent factors and structures in neural population activity.

Modelling the spatiotemporal dynamics in the activity of neural populations while also enabling their flexible inference is hindered by the complexity and noisiness of neural observations. Here we show that the lower-dimensional nonlinear latent factors and latent structures can be computationally modelled in a manner that allows for flexible inference causally, non-causally and in the presence of missing neural observations. To enable flexible inference, we developed a neural network that separates the model into jointly trained manifold and dynamic latent factors such that nonlinearity is captured through the manifold factors and the dynamics can be modelled in tractable linear form on this nonlinear manifold. We show that the model, which we named 'DFINE' (for 'dynamical flexible inference for nonlinear embeddings') achieves flexible inference in simulations of nonlinear dynamics and across neural datasets representing a diversity of brain regions and behaviours. Compared with earlier neural-network models, DFINE enables flexible inference, better predicts neural activity and behaviour, and better captures the latent neural manifold structure. DFINE may advance the development of neurotechnology and investigations in neuroscience.

Time evolution of Einstein-Maxwell-scalar black holes after a thermal quench

We employ the holographic quench technique to drive Einstein-Maxwell-scalar (EMs) black holes out of equilibrium and study the real-time dynamics therein. From the fully nonlinear dynamical simulations, a dynamically unstable Reissner-Nordström anti-de Sitter (RN-AdS) black hole can be scalarized spontaneously after an arbitrarily small quench. On the other hand, a dynamically stable scalarized black hole can be descalarized after a quench of sufficient strength. Interestingly, on the way to descalarization, the scalarized black hole behaves like a holographic superfluid, undergoing a dynamical transition from oscillatory to non-oscillatory decay. Such behaviors are related to the spectrums of quasi-normal modes of scalarized black holes, where the dominant mode migrates toward the imaginary axis with increasing quench strength. In addition, due to the ℤ2-symmetry preserved by the model, the ground state is degenerate. We find that there exists a threshold for the quench strength that induces a dynamical transition of the gravitational system from one degenerate ground state to the other. Near the threshold, the gravitational system is attracted to an excited state, that is, a RN-AdS black hole with dynamical instability.

Open NASA Blade Models for Nonlinear Dynamics Simulations

Abstract This contribution presents a catalogue of open turbomachinery blade models dedicated to nonlinear dynamics simulations. Based on a specifically developed in-house computer code, three-dimensional computer-aided design (CAD) models and finite element (FE) models of multiple-circular-arc (MCA) NASA airfoils are generated. Both the in-house code and the models are made freely accessible online. To cover a wide range of geometries, 39 blades are considered from different stages and with different aspect ratios. It is expected that this blade catalogue will provide an opportunity for the direct comparison of recently developed methodologies relative to nonlinear vibration phenomena in turbomachines, including rubbing events and blade-tip/casing contacts. To this end, the paper also contains original results for some of the most emblematic NASA blades, with an emphasis on nonlinear interaction maps and a detailed presentation of redesign operations to mitigate high amplitude of vibrations when blade-tip/casing contacts occur.

Simulation‐based characterization of the variability of earthquake risk to buildings in the near‐field

AbstractRecent advancements in high performance computing platforms and computational workflow for regional‐scale simulations are enabling unprecedented modeling of fault‐to‐structure earthquake processes. Regional simulations resolving ground motions at frequencies relevant to engineered systems are becoming computationally viable and provide a new capability to improve understanding of the geographical distribution and intensity of risk to buildings and critical infrastructure. As computational capabilities advance, it is essential to move beyond illustrative single rupture realizations for scenario earthquake events towards the development of a full suite of rupture realizations that appropriately characterize the range of risk to building systems. The work described in this article investigates the application of a suite of fault rupture realizations with the objective of assessing near‐fault, site‐specific seismic demand variability for building structures. A representative high‐performance regional‐scale computational model is utilized to execute ground motion and building response simulations based on 18 kinematic rupture realizations of an M7 strike‐slip scenario earthquake. The fault rupture models for the scenario earthquake are created by systematically perturbing the hypocenter location and stochastically generating rupture parameters (slip, rise time, rake angle) to represent a breadth of ground motion intensities resulting from the spatial and temporal variabilities of an earthquake rupture process. The resulting seismic demand variability for three‐story (short period) and forty‐story (long period) steel moment‐resisting frame buildings is characterized in terms of the median and distribution of peak inter‐story drift ratio for a range of near‐fault sites. The full suite of 18 fault rupture realizations and approximately 280,000 nonlinear dynamic building simulations indicate that the three‐story building undergoes higher median seismic demand and significantly greater variability of demand at a given site than the forty‐story building, which has important implications for the level of certainty in predicting building performance during an earthquake. The simulations performed provide deeper insight into the relationship between fault rupture parameterization and building response, which is essential information for developing a representative suite of rupture realizations for specific earthquake scenarios.