Steady-State Responses of Pulley-Belt Systems With a One-Way Clutch and Belt Bending Stiffness

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Hu Ding ◽  
Jean W. Zu
Keyword(s):  
Time Series ◽  
Steady State ◽  
Differential Equations ◽  
Dynamic Model ◽  
Time Discretization ◽  
Bending Stiffness ◽  
Response Curves ◽  
Axially Moving ◽  
The One ◽  
Belt System

A nonlinear hybrid discrete-continuous dynamic model is established to analyze the steady-state response of a pulley-belt system with a one-way clutch and belt bending stiffness. For the first time, the translating belt spans in pulley-belt systems coupled with one-way clutches are modeled as axially moving viscoelastic beams. Moreover, the model considers the rotations of the driving pulley, the driven pulley, and the accessory. The differential quadrature and integral quadrature methods are developed for space discretization of the nonlinear integropartial-differential equations in the dynamic model. Furthermore, the four-stage Runge–Kutta algorithm is employed for time discretization of the nonlinear piecewise ordinary differential equations. The time series are numerically calculated for the driven pulley, the accessory, and the translating belt spans. Based on the time series, the fast Fourier transform is used for obtaining the natural frequencies of the nonlinear vibration. The torque-transmitting directional behavior of the one-way clutch is revealed by the steady-state of the clutch torque in the primary resonances. The frequency-response curves of the translating belt, the driven pulley, and the accessory show that the one-way clutch reduces the resonance of the pulley-belt system. Furthermore, the belt cross section's aspect ratio significantly affects the dynamic response.

Inference of gene regulatory networks based on nonlinear ordinary differential equations

2020 ◽  
Vol 36 (19) ◽  
pp. 4885-4893 ◽  
Author(s):  
Baoshan Ma ◽  
Mingkun Fang ◽  
Xiangtian Jiao
Keyword(s):  
Gene Expression ◽  
Time Series ◽  
Steady State ◽  
Differential Equations ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Time Series Data ◽  
Series Data ◽  
State Data ◽  
Gene Regulatory

Abstract Motivation Gene regulatory networks (GRNs) capture the regulatory interactions between genes, resulting from the fundamental biological process of transcription and translation. In some cases, the topology of GRNs is not known, and has to be inferred from gene expression data. Most of the existing GRNs reconstruction algorithms are either applied to time-series data or steady-state data. Although time-series data include more information about the system dynamics, steady-state data imply stability of the underlying regulatory networks. Results In this article, we propose a method for inferring GRNs from time-series and steady-state data jointly. We make use of a non-linear ordinary differential equations framework to model dynamic gene regulation and an importance measurement strategy to infer all putative regulatory links efficiently. The proposed method is evaluated extensively on the artificial DREAM4 dataset and two real gene expression datasets of yeast and Escherichia coli. Based on public benchmark datasets, the proposed method outperforms other popular inference algorithms in terms of overall score. By comparing the performance on the datasets with different scales, the results show that our method still keeps good robustness and accuracy at a low computational complexity. Availability and implementation The proposed method is written in the Python language, and is available at: https://github.com/lab319/GRNs_nonlinear_ODEs Supplementary information Supplementary data are available at Bioinformatics online.

Mechanics of Serpentine Belt Drives with Tensioner Assemblies and Belt Bending Stiffness

2004 ◽  
Vol 127 (5) ◽  
pp. 957-966 ◽  
Author(s):  
Lingyuan Kong ◽  
Robert G. Parker
Keyword(s):  
Steady State ◽  
A Priori ◽  
Bending Stiffness ◽  
Belt Drive ◽  
Creep Theory ◽  
Factors Affecting ◽  
Belt Drives ◽  
Contact Points ◽  
Serpentine Belt ◽  
Axially Moving

Steady state analysis is conducted on a multipulley serpentine belt drive with a spring-loaded tensioner assembly. Classical creep theory is extended to incorporate belt bending stiffness as well as the belt stretching and centripetal accelerations. The belt is modeled as an axially moving Euler–Bernoulli beam with nonuniform speed due to belt extensibility and variation of belt tension. The geometry of the belt-pulley contact zones and the corresponding belt tension and friction distributions are the main factors affecting belt slip. Bending stiffness introduces nontrivial span deflections, reduces the wrap angles, and makes the belt-pulley contact points unknown a priori. The free span boundary value problems (BVP) with undetermined boundaries are transformed to a fixed boundary form. A two-loop iteration method, necessitated by the tensioner assembly, is developed to find the system steady state. The effects of system parameters on serpentine drive behavior are explored in the context of an actual automotive belt drive.

Stability and Bifurcations in Three-Dimensional Analysis of Axially Moving Beams

2013 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Marco Amabili ◽  
Hamed Farokhi
Keyword(s):  
Differential Equations ◽  
Fourier Transforms ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Three Dimensional ◽  
Axially Moving Beam ◽  
Bifurcation Diagrams ◽  
Response Curves ◽  
Axially Moving

The geometrically nonlinear dynamics of a three-dimensional axially moving beam is investigated numerically for both sub and supercritical regimes. Hamilton’s principle is employed to derive the equations of motion for in-plane and out-of plane displacements. The Galerkin scheme is applied to the nonlinear partial differential equations of motion yielding a set of second-order nonlinear ordinary differential equations with coupled terms. The pseudo-arclength continuation technique is employed to solve the discretized equations numerically so as to obtain the nonlinear resonant responses; direct time integration is conducted to obtain the bifurcation diagrams of the system. The results are presented in the form of the frequency-response curves, bifurcation diagrams, time histories, phase-plane portraits, and fast Fourier transforms for different sets of system parameters.

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Primary System ◽  
Lumped Mass ◽  
Response Curves ◽  
Internal Resonances ◽  
The One

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

Stability analysis of uncertain delay differential equations

2021 ◽  
pp. 1-11
Author(s):  
Jian Wang ◽  
Yuanguo Zhu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Liu Process ◽  
Uncertain Dynamical System ◽  
Analytic Expression ◽  
Functional Differential ◽  
The One ◽  
Delay Differential

Uncertain delay differential equation is a class of functional differential equations driven by Liu process. It is an important model to describe the evolution process of uncertain dynamical system. In this paper, on the one hand, the analytic expression of a class of linear uncertain delay differential equations are investigated. On the other hand, the new sufficient conditions for uncertain delay differential equations being stable in measure and in mean are presented by using retarded-type Gronwall inequality. Several examples show that our stability conditions are superior to the existing results.

Filippov solutions of vector Dirichlet problems

2020 ◽  
Vol 70 (2) ◽  
pp. 401-416
Author(s):  
Hana Machů
Keyword(s):  
Differential Equations ◽  
The State ◽  
State Variables ◽  
Dirichlet Problems ◽  
Filippov Solutions ◽  
Natural Notion ◽  
Growth Restrictions ◽  
The One ◽  
The Right ◽  
Effective Growth

Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.

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