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Invariant and energy analysis of an axially retracting beam

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Chinese Journal of Aeronautics 2016年第4期29卷 952-961页

作者： Yang Xiaodong Liu Ming Zhang Wei roderick v.n.melnik Beijing Key Laboratory of nonlinear vibrations and Strength of Mechanical Engineering College of Mechanical Engineering Beijing University of Technology M2neT Laboratory The MS2Discovery Interdisciplinary Research Institute Wilfrid Laurier University

The mechanism of a retracting cantilevered beam has been investigated by the invariant and energy-based analysis. The time-varying parameter partial differential equation governing the transverse vibrations of a beam with retracting motion is derived based on the momentum theorem. The assumed-mode method is used to truncate the governing partial differential equation into a set of ordinary differential equations (ODEs) with time-dependent coefficients. It is found that if the order of truncation is not less than the order of the initial conditions, the assumed-mode method can yield accurate results. The energy transfers among assumed modes are discussed during retraction. The total energy varying with time has been investigated by numerical and analytical methods, and the results have good agreement with each other. For the transverse vibrations of the axially retracting beam, the adiabatic invariant is derived by both the averaging method and the Bessel function method. (C) 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-nC-nD license.

关键词： Adiabatic invariants Asymptotic analysis Retracting beam Time-varying systems Transient dynamics

Parametricvibration Analysis of Pipes Conveying Fluid by nonlinear normal Modes and a numerical Iterative Approach

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Advances in Applied Mathematics and Mechanics 2019年第1期11卷 38-52页

作者： Feng Liang Xiaodong Yang Wei Zhang Yingjing Qian roderick v.n.melnik College of Mechanical Engineering Yangzhou UniversityYangzhou 225127JiangsuChina Beijing Key Laboratory of nonlinear vibrations and Strength of Mechanical Engineering College of Mechanical Engineering and Applied ElectronicsBeijing University of TechnologyBeijing 100124China The MS2Discovery Interdisciplinary Research Institute M2NeT LaboratoryWilfrid Laurier University75 University Avenue WestWaterlooONCanadaN2L 3C5 BCAM–Basque Center for Applied Mathematics E48009 BilbaoSpain

nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic *** nonlinear non-autonomous governing equations are transformed into a set of pseudo-autonomous ones by employing the harmonic balance *** nonlinear normal modes are constructed by the invariant manifold method on the state space and a numerical iterative approach is adopted to obtain numerical solutions,in which two types of initial conditions for the modal coefficients are *** results show that both initial conditions can lead to fast *** frequency-amplitude responses with some modal motions in phase space are obtained by the present iterative *** phase difference and traveling waves are found in the time-domain complex modal analysis.

关键词： Gyroscopic continua pipes conveying pulsating fluid parametric vibration nonlinear normal modes iterative approach

Modeling large reversible electric-field-induced strain in ferroelectric materials using 90° orientation switching

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中国科学:技术科学 2010年第4期 450-450页

作者： roderick v.n.melnik Mathematical Modelling and Computational Sciences Wilfrid Laurier University

Reversible large electric-field-induced strain caused by reversible orientation switchings in BaTiO3 is modeled using the Landau’s theory of phase transition.A triple well free energy function is *** of its minima is associated with one of the polarization orientations *** constitutive laws accounting for reversible orientation switchings and electrostriction effects are obtained by using thermodynamic equilibrium *** dynamics of onedimensional structures is described by coupled nonlinear differential *** hysteretic loops in the electric and mechanic fields are both successfully *** reversible electrostriction is modeled as a consequence of reversible orientation switchings via electro-mechanical *** with experimental results reported in literatures are presented.

关键词： large electrostriction reversible switchings double hysteresis differential model

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热弹性动力学耦合问题的微分代数方法

应用数学和力学 2006年第9期27卷 1036-1046页

作者：王林翔 R.v.n.梅尔姆克南丹麦大学自然科学与工程学院威尔费瑞德.劳瑞尔大学耦合动力学与复杂系统研究中心

对一般的热机械问题提出了一种有效的数值方法,并对二维的热弹性问题进行了测试.该方法的基本思路是将描述热机械耦合问题的偏微分方程进行降阶,使之成为一组微分代数方程,应力应变关系被写成代数方程.所得到的微分代数系统采用全隐式... 详细信息

对一般的热机械问题提出了一种有效的数值方法,并对二维的热弹性问题进行了测试.该方法的基本思路是将描述热机械耦合问题的偏微分方程进行降阶,使之成为一组微分代数方程,应力应变关系被写成代数方程.所得到的微分代数系统采用全隐式的向后差分公式进行求解.对该方法进行了详细的说明.为了验证该方法的有效性,将其应用于一个动态非耦合的热弹性问题的求解和一个耦合的二维热弹性问题的求解.

关键词：热弹性二维问题微分代数方法

基于内粘性哑铃模型的高分子溶液剪切流场动力学分析

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基于内粘性哑铃模型的高分子溶液剪切流场动力学分析

Modeling large reversible electric-field-induced strain in ferroelectric materials using 90° orientation switching

中国化学会、中国力学学会第九届全国流变学学术会议

作者：杨晓东 roderick v.n.melnik 沈阳航空工业学院工程力学系 Mathematical Modelling & Computational Sciences Wilfrid LaurierUniversityWaterlooOntarioCanada N2L

在科学及生物工程领域,半挠性的高分子,如 DnA 分子等的动力学分析涉及重要的工程应用。粗粒建模技术从微观高分子团的角度出发,分析高分子溶液在不同流场中的动力学行为及本构关系,它是研究聚合物溶液流变学行为的一种重要工具。同时... 详细信息

在科学及生物工程领域,半挠性的高分子,如 DnA 分子等的动力学分析涉及重要的工程应用。粗粒建模技术从微观高分子团的角度出发,分析高分子溶液在不同流场中的动力学行为及本构关系,它是研究聚合物溶液流变学行为的一种重要工具。同时高分子溶液动力学也是重要的一类多尺度问题,它既包含了溶液分子的快速运动,又包含了高分子溶剂分子的慢速变形运动。高分子团一般模型为珠簧链,这其中最简单的模型即为哑铃模型。为了解释高分子溶液的剪切变稀等宏观现象,引入粘弹性弹簧连接的哑铃模型描述微观上的分子碰撞造成的能量耗散。

关键词：高分子溶液内粘性剪切变稀物料性质

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Science China(Technological Sciences) 2009年第1期52卷 141-147页

作者： roderick v. n. melnik Mathematical Modelling and Computational Sciences Wilfrid Laurier University Waterloo 75 University Ave W Canada N2L 3C5

Reversible large electric-field-induced strain caused by reversible orientation switchings in BaTiO3 is modeled using the Landau's theory of phase transition. A triple well free energy function is constructed. Each of its minima is associated with one of the polarization orientations involved. nonlinear constitu- tive laws accounting for reversible orientation switchings and electrostriction effects are obtained by using thermodynamic equilibrium conditions. Hysteretic dynamics of one-dimensional structures is described by coupled nonlinear differential equations. Double hysteretic loops in the electric and me- chanic fields are both successfully modeled. Giant reversible electrostriction is modeled as a conse-quence of reversible orientation switchings via electro-mechanical couplings. Comparisons with ex-perimental results reported in literatures are presented.

关键词： large electrostriction reversible switchings double hysteresis differential model

DIFFEREnTIAL-ALGEBRAIC APPROACH TO COUPLED PROBLEMS OF DYnAMIC THERMOELASTICITY

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Applied Mathematics and Mechanics(English Edition) 2006年第9期27卷 1185-1196页

作者： WAnG Lin-xiang roderick v. n. melnik MCI Faculty of Science and Engineering University of Southern Denmark Sonderborg DK-6400 Denmark Center for Coupled Dynamics ＆ Complex Systems Wilfrid Laurier University 75 University Avenue West Waterloo ON Canada N2L3C5

An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations （DAEs） where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula （BDF） using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.

关键词： thermoelasticity two-dimensional differential-algebraic solvers

Component spectroscopic properties of light-harvesting complexes with DFT calculations

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BIOCELL 2020年第3期44卷 279-291页

作者： SHYAM BADU SAnJAY PRABHAKAR roderick melnik MS2Discovery Interdisciplinary Research Institute M2Net LabWilfrid Laurier UniversityWaterlooON N3L 3V6Canada Department of natural Science Gordon State CollegeBarnesvilleGA 30204USA BCAM–Basque Center for Applied Mathematics BilbaoE-48009Spain

Photosynthesis is a fundamental process in biosciences and biotechnology that influences profoundly the research in other *** this paper,we focus on the characterization of fundamental components,present in pigment-protein complexes,in terms of their spectroscopic properties such as infrared spectra,nuclear magnetic resonance,as well as nuclear quadrupole resonance,which are of critical importance for many *** components include chlorophylls and *** on the density functional theory method,we calculate the main spectroscopic characteristics of these components for the Fenna-Matthews-Olson light-harvesting complex,analyze them and compare them with available experimental *** outlook is discussed in the context of current and potential applications of the presented results.

关键词： Photosynthesis Bacteriochlorophylls Light harvesting Pigment-protein complexes Density functional theory Complex networks Photocatalysis Biosensing and bioplasmonics

Dynamic analysis of polymeric fluid in shear flow for dumbbell model with internal viscosity

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Journal of Central South University 2008年第S1期15卷 17-20页

作者：杨晓东 R.v.n.melnik Department of Engineering Mechanics Shenyang Institute of Aeronautical Engineering Mathematical Modelling and Computational Sciences Wilfrid Laurier University

The dynamic analysis of semi-flexible polymers,such as DnA molecules,is an important multiscale problem with a wide range of applications in science and *** this contribution,a dumbbell model with internal viscosity was studied in steady shear flows of polymeric *** tensors with moments other than second moment were approximated in the terms of second moment ***,the nonlinear algebraic equation of the second moment conformation tensor was calculated in closed ***,substituting the resulting conformation tensor into the Kramers equation of Hookean spring force,the constitutive equations were *** shear material properties were discussed for different internal viscosities and compared with the results of Brownian dynamics simulation.

关键词： dynamic simulation polymeric fluid internal viscosity shear thinning