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An analysis on a rigid-flexible coupling system of an oscillating massand a rotating disk

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Theoretical & Applied Mechanics Letters 2022年第5期12卷 341-348页

作者： Jian Liu Kai Zhang Zhanfang Liu College of Aerospace Engineering Chongqing UniversityChongqing 400040China CSSC Haizhuang Wind Power Co. LTDChongqing 401123China State Key Laboratory of Ultrasound in Medicine and Engineering Chongqing Medical UniversityChongqing 400016China

A mass-rod-disk system consisting of an oscillating mass attached to a rigid rotating disk by an elastic rod is designed to study rigid-flexible coupling mechanism.Suppose the rod is lightweight and has enough stiffness,the theorems of linear momentum and angular momentum are applied to the mass-rod-disk system based on the kinematic description of the system.With respect to two deflections of the mass and one angular velocity of the system,a group of nonlinear differential equations are established where the tangential inertial force,centrifugal force,Coriolis force as well as the moments of additional inertial forces take important effects on the dynamic response.For the sake of description,these three types of inertial forces mentioned before are referred to as additional inertial forces in this paper.The horizontal deflections of the mass and the angular velocity of the disk rotating about a fixed-axis are numerically solved for the prescribed external torque.The oscillating trajectory of the mass is deeply influenced by the additional inertial forces,meanwhile the dynamic fluctuations of the angular velocity and rotary inertia of the system are strongly affected by the mass oscillation.

关键词： Rigid-flexible coupling Additional inertial forces nonlinear differential equation Motion trajectory

OSCILLATORY BEHAVIOUR OF A CLASS OF nonlinear differential equationS OF THIRD ORDER

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Acta Mathematica Scientia 2001年第2期21卷 182-188页

作者： A. Tiryaki Department of Mathematics, Gazi University Faculty of Arts and Sciences Teknik Okullar, 06500 Ankara, Turkey S. (Yaman) Pasinlio■u Department of Mathematics, Hacettepe University, 06532 Beytepe, Ankara, Turkey Department of Mathematics Gazi University Faculty of Arts and Sciences Teknik Okullar 06500 Ankara Turkey Department of Mathematics Hacettepe University 06532 Beytepe Ankara Turkey

This paper investigates the oscillatory and nonoscillatory behaviour of solu- tions of a class of third order nonlinear differential equations. Results extend and improve some known results in the literature.

关键词： Oscillatory solution nonoscillatory solution behaviour of solution nonlinear differential equation

Dynamical response of hyper-elastic cylindrical shells under periodic load

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Applied Mathematics and Mechanics(English Edition) 2008年第10期29卷 1319-1327页

作者：任九生 Department of Mechanics Shanghai Institute of Applied Mathematics and Mechanics Shanghai University

Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of the nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing motion of the inner surface of the shell. Motion of the shell is nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. Solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of the dynamical solution and motion of the shell. The effects of thickness and load parameters on the critical value and oscillation of the shell are discussed.

关键词： hyper-elastic cylindrical shells nonlinear differential equation periodic oscillation quasi-periodic oscillation critical load

Scrutiny of non-linear differential equations Euler-Bernoulli beam with large rotational deviation by AGM

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Frontiers of Mechanical Engineering 2014年第4期9卷 402-408页

作者： M. R. AKBARI M. NIMAFAR D. D. GANJI M, M. AKBARZADE Department of Civil Engineering and Chemical Engineering Universityof Tehran Tehran lran Department of Mechanical and Aerospace Engineering Politecnico diTorino Turin 24-10129 Italy Department of Mechanical Engineering Babol University of Technology Babol Iran Department of Mechanical Engineering Sari Branch Islamic AzadUniversity Sari Iran

The kinematic assumptions upon which the Euler-Bernoulli beam theory is founded allow it to be extended to more advanced analysis. Simple superposition allows for three-dimensional transverse loading. Using alternative constitutive equations can allow for viscoelastic or plastic beam deformation. Euler-Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams and geometrically nonlinear beam deflection. In this study, solving the nonlinear differential equation governing the calculation of the large rotation deviation of the beam （or column） has been discussed. Previously to calculate the rotational deviation of the beam, the assumption is made that the angular deviation of the beam is small. By considering the small slope in the linearization of the governing differential equation, the solving is easy. The result of this simplifica- tion in some cases will lead to an excessive error. In this paper nonlinear differential equations governing on this system are solved analytically by Akbari-Ganji＇s method （AGM）. Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration solving. The solution of the problem can be obtained very simply and easily. Furthermore, to enhance the accuracy of the results, the Taylor expansion is notneeded in most cases via AGM manner. Also, comparisons are made between AGM and numerical method （Runge- Kutta 4th）. The results reveal that this method is very effective and simple, and can be applied for other nonlinear problems.

关键词： AGM critical load of columns large deformations of beam nonlinear differential equation

MULTIPLE POSITIVE SOLUTIONS TO BVPS FOR HIGHER ORDER nonlinear differential equationS IN BANACH SPACES

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Acta Mathematicae Applicatae Sinica 2001年第2期17卷 271-278页

作者：戚仕硕 Department of Mathematics Zhengzhou University Zhengzhou China

In this article, the author employs the conical expansion and compression fixed point principle and the fixed point index theory to show that there exist at least two positive solutions for a higher order BVP.

关键词： Multiple positive solutions higher order BVP nonlinear differential equation fixed point index Banach space

OSCILLATORY AND ASYMPTOTIC BEHMIOUR OF A CLASS OF nonlinear differentialequationS OF THIRD ORDER

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Acta Mathematica Scientia 1998年第1期18卷 95-106页

作者： N. Parhi P. Das(Department of Mathematics, Berhampur University, Bechampur-760007, India)

This paper deals with oscillatory /nonoscillatory behaviour of solutions of thirdorder nonlinear differential equations of the formwhere a,b,c E C([a,oo),R) such that a(t) does not change sign, b(t) 5 0, c(t) > 0,f∈C(R, R) such that (f(y)/y) ≥ β > 0 for y ≠ 0 and γ > 0 is a quotient of odd integers.It has been shown, under certain conditions on coefficient functions, that a solution of (1)and (2) which Las a zero is oscillatory and the nonoscillatory solutions of these equationstend to zero as t → ∞. The motivation for this work came from the observation that thewhere al b, c are constants such that b≤ 0, c > 0, has an oscillatory solution if and only ifand all nonoscillatory solutions of (3) tend to zero if and only if the equation has anoscillatory solution.

关键词： Oscillatory solution nonoscillatory solution behaviour of solution nonlinear differential equation

Lyapunov-type Inequalities for a System of nonlinear differential equations

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Communications in Mathematical Research 2017年第3期33卷 205-214页

作者： wei geng-ping shi shao-yun Department of Mathematics Huaihua University Huaihua Hunan 418008 不详

This paper presents several new Lyapunov-type inequalities for a system of first-order nonlinear differential equations. Our results generalize and improve some existing ones.

关键词： Lyapunov-type inequality nonlinear differential equation Hamiltonian system

EXISTENCE　OF　SOLUTIONS　OF　nonlinear　TWO　AND　THREE－POINT　BOUNDARY　VALUE　PROBLEMS　FOR　FOURTH　ORDER　nonlinear　differential　equationS

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Applied Mathematics(A Journal of Chinese Universities) 1996年第3期11卷 335-348页

作者： GAO YONGXIN AND GAO YOU(Department of Basic Science, Northeast institute of Electric POWer,Jinn 132012.)

In this paper, the two and three-point boundary Problems (with nonlinearboundary conditions) for the general nonlinear differential equations of fourth orderare discussed. We have set some groups of the assumption con... 详细信息

关键词： nonlinear differential equation nonlinear two and three-point boundary valueproblems.

Oscillation of Solutions for a Second Order nonlinear Perturbed differential equations with Functional Arg

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Journal of Mathematical Research with Applications 1995年第3期 329-336页

作者： E.M. Elabbasy (Dept. of Math., Faculty of Science, Mansoura Univ., Mansoura, Egypt)

ＯｓｃｉｌｌａｔｉｏｎｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＳｅｃｏｎｄＯｒｄｅｒＮｏｎｌｉｎｅａｒＰｅｒｔｕｒｂｅｄＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓｗｉｔｈＦｕｎｃｔｉｏｎａｌＡｒｇｕｍｅｎｔｓＥ．Ｍ．Ｅｌａｂｂ... 详细信息

ＯｓｃｉｌｌａｔｉｏｎｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＳｅｃｏｎｄＯｒｄｅｒＮｏｎｌｉｎｅａｒＰｅｒｔｕｒｂｅｄＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓｗｉｔｈＦｕｎｃｔｉｏｎａｌＡｒｇｕｍｅｎｔｓＥ．Ｍ．Ｅｌａｂｂａｓｙ（Ｄｅｐｔ．ｏｆＭａｔｈ．，...

关键词： nonlinear differential equation oscillation continuable solution.