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Llibre Jaume - One of the best experts on this subject based on the ideXlab platform.

  • Bifurcation of Limit cycles from a 4-dimensional center in R^m in resonance 1:N
    2021
    Co-Authors: Barreira Luis, Llibre Jaume, Valls Clàudia
    Abstract:

    Agraïments: The first and third authors are partially supported by FCT through CAMGSD, Lisbon.For every positive integer N ≥ 2 we consider the linear differential center ˙x = Ax in Rm with eigenvalues ±i, ±N i and 0 with multiplicity m − 4. We perturb this linear center inside the class of all polynomial differential systems of the form linear plus a homogeneous nonlinearity of degree N, i.e. x˙ = Ax + εF(x) where every component of F(x) is a linear polynomial plus a homogeneous polynomial of degree N. When the Displacement Function of order ε of the perturbed system is not identically zero, we study the maximal number of limit cycles that can bifurcate from the periodic orbits of the linear differential center. In particular, we give explicit upper bounds for the number of limit cycles

  • Restricted independence in Displacement Function for better estimation of cyclicity
    2021
    Co-Authors: Chen Xingwu, Llibre Jaume, Wang Zhaoxia, Zhang Weinian
    Abstract:

    Agraïments: The author is partially supported by NSFC grant #11471228 (X. Chen), NSFC grant # 11501083 (Z. Wang), and NSFC grants # 11231001 and # 11221101 (W. Zhang).Since the independence of focal values is a sufficient condition to give a number of limit cycles arising from a center-focus equilibrium, in this paper we consider a restricted independence to a parametric curve, which gives a method not only to increase the lower bound for the cyclicity of the center-focus equilibrium but also to be available when those focal values are not independent. We apply the method to a nondegenerate cubic center-focus variety and prove that the cyclicity reaches its an upper bound

  • Limit cycles of discontinuous piecewise linear differential systems
    2021
    Co-Authors: Cardin, Pedro Toniol, De Carvalho Tiago, Llibre Jaume
    Abstract:

    Agraïments: The two first authors are partially supported by a FAPESP-BRAZIL grant 2007/07957-8 and grant 2007/08707-5 r espectively.We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in Rn perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) limit cycle can bifurcate up to first-order expansion of the Displacement Function with respect to the small parameter. This upper bound is reached. For proving these results, we use the averaging theory in a form where the differentiability of the system is not needed

  • On the number of limit cycles for discontinuous piecewise linear differential systems in R^2n with two zones
    2021
    Co-Authors: Llibre Jaume, Rong Feng
    Abstract:

    Agraïments: The second author is partially supported by grant 11001172 from the National Natural Science Foundation of China and grant 20100073120067 from the Research Fund for the Doctoral Program of Higher Education of China.We study the number of limit cycles of the discontinuous piecewise linear differential systems in R2n with two zones separated by a hyperplane. Our main result shows that at most (8n−6)n−1 limit cycles can bifurcate up to first-order expansion of the Displacement Function with respect to a small parameter. For proving this result we use the averaging theory in a form where the differentiability of the system is not necessary

  • On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems
    2021
    Co-Authors: Gouveia, Marcio R. A., Llibre Jaume, Novaes, Douglas D.
    Abstract:

    Agraïments: The first author is partially supported by a PROCAD-CAPES grant 88881.068 462/2014-01 and by a FAPESP grant 2013/13344-0.Agraïments: MINECO/FEDER grant UNAB13-4E-1604. The third author is partially supported by a FAPESP grant 2012/10231-7. The three authors are also supported by a CAPES CSF-PVE grant 88881.030454/2013-01 from the program CSF-PVE.In this paper we consider the linear differential center (x',y')=(-y,x) class of all discontinuous piecewise linear differential systems with two zones separated by the straight line y = 0. Using the Bendixson transformation we provide sufficient conditions to ensure the existence of a crossing limit cycle coming purely from the infinity. We also study the Displacement Function for a class of discontinuous piecewise smooth differential system

B S Kumar - One of the best experts on this subject based on the ideXlab platform.

  • static analysis of a thick laminated circular cylindrical shell subjected to axisymmetric load
    Composite Structures, 1993
    Co-Authors: K Chandrashekhara, B S Kumar
    Abstract:

    An exact solution for a thick, transversely isotropic, simply supported, circular cylindrical shell subjected to axisymmetric load has been obtained by using a Displacement Function approach. This solution has been extended to unidirectional hybrid laminates. However, this solution in general is not applicable to cross-ply laminates. An approximate solution using an elasticity approach also has been presented for the analysis of hybrid and cross-ply laminates.The results obtained from the approximate solution have been compared with the exact solution. Numerical results have been presented for 3-ply laminates subjected to sinusoidal and band loads. To make the method computationally efficient, particularly for a laminated shell, a transfer matrix approach has been presented and the application of this has been illustrated through an example of a 10-ply laminated shell.

Song Cen - One of the best experts on this subject based on the ideXlab platform.

  • shape free polygonal hybrid Displacement Function element method for analyses of mindlin reissner plates
    Engineering With Computers, 2021
    Co-Authors: Song Cen, Yan Shang
    Abstract:

    A high-performance shape-free polygonal hybrid Displacement-Function finite-element method is proposed for analyses of Mindlin–Reissner plates. The analytical solutions of Displacement Functions are employed to construct element resultant fields, and the three-node Timoshenko’s beam formulae are adopted to simulate the boundary Displacements. Then, the element stiffness matrix is obtained by the modified principle of minimum complementary energy. With a simple division, the integration of all the necessary matrices can be performed within polygonal element region. Five new polygonal plate elements containing a mid-side node on each element edge are developed, in which element HDF-PE is for general case, while the other four, HDF-PE-SS1, HDF-PE-Free, IHDF-PE-SS1, and IHDF-PE-Free, are for the edge effects at different boundary types. Furthermore, the shapes of these new elements are quite free, i.e., there is almost no limitation on the element shape and the number of element sides. Numerical examples show that the new elements are insensitive to mesh distortions, possess excellent and much better performance and flexibility in dealing with challenging problems with edge effects, complicated loading, and material distributions.

  • two generalized conforming quadrilateral mindlin reissner plate elements based on the Displacement Function
    Finite Elements in Analysis and Design, 2015
    Co-Authors: Yan Shang, Song Cen
    Abstract:

    Abstract This work presents two 4-node, 12-DOF quadrilateral Displacement-based finite elements for analysis of the Mindlin–Reissner plate. Derived from the fundamental analytical solutions of the Displacement Function F , the deflection and rotation fields of the proposed elements satisfy a priori all related governing equations. The unknown coefficients are determined through the generalized conforming element method, a relaxed and rational conforming approach. The resulting elements perform like nonconforming elements on a coarse mesh, and with mesh refinement they converge as conforming elements. Numerical benchmarks demonstrate that the new elements are insensitive to mesh distortion and free of shear locking, and can provide satisfactory results for most cases.

Li Wang - One of the best experts on this subject based on the ideXlab platform.

  • influence of longitudinal rise of coolant temperature on the thermal strain in a cylindrical laser rod
    Optics Letters, 2009
    Co-Authors: Zhigang Li, Xiulan Huai, Li Wang
    Abstract:

    The thermal strain in a laser rod with a longitudinal temperature increase is modeled and analytically derived through the method of thermoelastic Displacement potential and the method of Love Displacement Function. The analytical results show that in the absence of external forces, the longitudinal rise of fluid temperature has an unnoticeable effect on the thermal stress profile in the laser rod. However, the thermal strain field caused by the temperature distribution under the traction free boundary condition has an evident variation in the longitudinal direction, which will considerably affect the laser transmission characteristics and the beam quality.

  • an analytical solution to the thermal stress and thermal strain in a cylindrical laser rod with longitudinal temperature rise
    Volume 10: Heat Transfer Fluid Flows and Thermal Systems Parts A B and C, 2008
    Co-Authors: Zhigang Li, Xiulan Huai, Li Wang
    Abstract:

    In this paper, a mathematical model of the thermal stress and thermal strain in the laser medium was presented. An analytical solution was further derived for the thermal stress and thermal strain in the laser rod through the method of Thermoelastic Displacement Potential and the method of Love Displacement Function. The analytical solution results show that under the traction free boundary conditions, the longitudinal rise of fluid temperature has little effect on the thermal stress profile in the laser rod. However, the thermal strain field caused by both the temperature and the thermal stress fields has an evident variation in the longitudinal direction, which will affect the laser transmission characteristics and the beam quality.Copyright © 2008 by ASME

Weiqiu Chen - One of the best experts on this subject based on the ideXlab platform.

  • a unified solution for an anisotropic Functionally graded piezoelectric beam subject to sinusoidal transverse loads
    Journal of Intelligent Material Systems and Structures, 2009
    Co-Authors: D.j. Huang, H.j. Ding, Weiqiu Chen
    Abstract:

    The behavior of anisotropic Functionally graded piezoelectric beams subject to sinusoidal transverse loads is investigated based on the equations for a generalized plane stress problem. Both the stress Function and electric Displacement Function are assumed to consist of two parts. One corresponds to a product of a trigonometric Function of the longitudinal coordinate (x) and an undetermined Function of the thickness coordinate (z). The other is represented by a linear polynomial of x with unknown coefficients also depending on z. The equations governing these z-dependent Functions are presented. The expressions for stresses, electric Displacements, resultant forces, Displacements, and electric potential are then deduced, in which the integral constants are determined from the boundary conditions. Analytical solution is derived in the case that material coefficients vary exponentially along the thickness of the beam. Semi-analytical solution is also suggested along with the sub-layer approximation when th...

  • Analysis of Functionally graded and laminated piezoelectric cantilever actuators subjected to constant voltage
    Smart Materials and Structures, 2008
    Co-Authors: D.j. Huang, H.j. Ding, Weiqiu Chen
    Abstract:

    Functionally graded and laminated piezoelectric cantilever actuators are investigated. Each material parameter of the Functionally graded actuator can be an arbitrary continuous Function of the thickness coordinate of the beam, while the property of each layer in the laminated actuator is uniform. Piezoelectricity solutions for the two actuators subjected to a constant electric potential difference are presented. Firstly, the partial differential equations for the plane problem of Functionally graded piezoelectric materials, which govern the stress Function and electric Displacement Function, are derived. Secondly, the stress Function is assumed to be an undetermined Function of the thickness coordinate, and the electric Displacement Function is assumed as a linear Function of the longitudinal coordinate. In such a case, the stress and electric Displacement Function can be acquired through successive integrations. The analytical expressions of axial force, bending moment, shear force, Displacements, electric Displacements and electric potential are then deduced. The analytical solutions are finally obtained, with the integral constants completely determined from the boundary conditions. Comparisons of the present analytical solutions with beam theory, finite element method and experiments indicate that the analytical solutions are effective and exact, while certain deviations of the beam theory can be found.

  • green s Functions for a two phase infinite piezoelectric plane
    Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1997
    Co-Authors: Haojiang Ding, G Q Wang, Weiqiu Chen
    Abstract:

    First, on the basis of the governing equations of piezoelectric materials, a Displacement Function is introduced and the general solutions are derived. Second, by employing the generalized Almansi's theorem, these solutions are further simplified, i.e. all physical quantities are expressed in three Displacement Functions i (i = 1,2,3), which satisfy, respectively, three similar harmonic secondorder partial differential equations. Then the Green's Functions for point forces and point charge acting in the interior of a twophase infinite piezoelectric plane are given using the method of mirror image source. The paper is concluded by a discussion of some special cases, in which the point force and charge solutions for an infinite uniform piezoelectric plane and for a halfplane with free or fixed straight boundary are given.