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Journal articles on the topic 'Singular force'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Izydorek, Marek, Joanna Janczewska, and Jean Mawhin. "Homoclinics for singular strong force Lagrangian systems." Advances in Nonlinear Analysis 9, no. 1 (2019): 644–53. http://dx.doi.org/10.1515/anona-2020-0018.

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Abstract We study the existence of homoclinic solutions for a class of Lagrangian systems $\begin{array}{} \frac{d}{dt} \end{array} $(∇Φ(u̇(t))) + ∇uV(t, u(t)) = 0, where t ∈ ℝ, Φ : ℝ2 → [0, ∞) is a G-function in the sense of Trudinger, V : ℝ × (ℝ2 ∖ {ξ}) → ℝ is a C1-smooth potential with a single well of infinite depth at a point ξ ∈ ℝ2 ∖ {0} and a unique strict global maximum 0 at the origin. Under a strong force condition around the singular point ξ, via minimization of an action integral, we will prove the existence of at least two geometrically distinct homoclinic solutions u± : ℝ → ℝ2 ∖

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2

Chen, Zhen, Lifeng Qin, Shunbo Zhao, Tommy HT Chan, and Andy Nguyen. "Toward efficacy of piecewise polynomial truncated singular value decomposition algorithm in moving force identification." Advances in Structural Engineering 22, no. 12 (2019): 2687–98. http://dx.doi.org/10.1177/1369433219849817.

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This article introduces and evaluates the piecewise polynomial truncated singular value decomposition algorithm toward an effective use for moving force identification. Suffering from numerical non-uniqueness and noise disturbance, the moving force identification is known to be associated with ill-posedness. An important method for solving this problem is the truncated singular value decomposition algorithm, but the truncated small singular values removed by truncated singular value decomposition may contain some useful information. The piecewise polynomial truncated singular value decompositi

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3

Zhang, Meirong. "A relationship between the periodic and the Dirichlet BVPs of singular differential equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 5 (1998): 1099–114. http://dx.doi.org/10.1017/s0308210500030080.

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In this paper, a relationship between the periodic and the Dirichlet boundary value problems for second-order ordinary differential equations with singularities is established. This relationship may be useful in explaining the difference between the nonresonance of singular and nonsingular differential equations. Using this relationship, we give in this paper an existence result of positive periodic solutions to singular differential equations when the singular forces satisfy some strong force condition at the singularity 0 and some linear growth condition at infinity.

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4

Anantharaman, Thomas, Murray Campbell, and Feng-hsiung Hsu. "Singular Extensions: Adding Selectivity to Brute-Force Searching1." ICGA Journal 11, no. 4 (1988): 135–43. http://dx.doi.org/10.3233/icg-1988-11402.

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5

Whiting, Bernard F. "Identifying the singular field for self-force evaluation." Classical and Quantum Gravity 22, no. 15 (2005): S661—S679. http://dx.doi.org/10.1088/0264-9381/22/15/005.

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6

Gang, Hu, and He Kai-fen. "Bistable systems subject to a singular stochastic force." Physical Review A 45, no. 8 (1992): 5447–54. http://dx.doi.org/10.1103/physreva.45.5447.

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7

Fosdick, Roger, and Gianni Royer-Carfagni. "Singular Shear-Force States in Elementary Plate Theory." Journal of Elasticity 118, no. 1 (2014): 89–99. http://dx.doi.org/10.1007/s10659-014-9480-7.

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8

Alabert, Aureli, István Gyöngy, and Istvan Gyongy. "On Stochastic Reaction-Diffusion Equations with Singular Force Term." Bernoulli 7, no. 1 (2001): 145. http://dx.doi.org/10.2307/3318606.

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9

Low, B. C. "Force-free magnetic fields with singular current-density surfaces." Astrophysical Journal 409 (June 1993): 798. http://dx.doi.org/10.1086/172710.

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10

Kono, M., and H. Sanuki. "Ponderomotive force near cyclotron resonance." Journal of Plasma Physics 38, no. 1 (1987): 43–51. http://dx.doi.org/10.1017/s0022377800012393.

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The ponderomotive force in a magnetized plasma is derived by carrying out the renormalization of wave–particle interactions based on the Vlasov equation. A significant feature of the resuit is non-singular behaviour at resonance even in the case of perpendicular propagation. This is shown to be related to the onset of the diffusive motion of particles due to the orbit instability near resonance, where the ponderomotive force is eventually small.

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11

Mestel, Leon. "The Relativistic Force-free Equation." Publications of the Astronomical Society of Australia 18, no. 4 (2001): 384–93. http://dx.doi.org/10.1071/as01054.

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AbstractThis paper is a preliminary report on ongoing work, in collaboration with Drs S. P. Goodwyn, A. J. Mestel, and G. A. E. Wright. The non-dissipative force-free condition should be a good approximation to describe the electromagnetic field in much of the pulsar magnetosphere, but we may plausibly expect it to break down in singular domains. The detailed properties of the solutions will be affected critically by the choice of equatorial boundary condition beyond the light-cylinder.

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12

Brock, L. M., and H. P. Rossmanith. "Analysis of the Reflection of Point Force-Induced Crack Surface Waves by a Crack Edge." Journal of Applied Mechanics 52, no. 1 (1985): 57–61. http://dx.doi.org/10.1115/1.3169026.

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Dynamic stress fields near cracks follow in part from the reflection of crack surface waves by the crack edges. To gain insight into the reflection process, the problem of stationary normal and tangential point forces applied to one surface of a stationary semi-infinite crack is considered, and analytical expressions for the crack surface reflection-generated particle velocity waves presented. Study of these expressions shows that the dominant reflected wave is singular at its wave front, travels at the Rayleigh speed, and is generated by the reflection of a singular Rayleigh wave. However, th

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13

UCHIYAMA, Masaru, Yoshihiro NAKAMURA, and Kyojiro HAKOMORI. "Evaluation of robot force sensor structure using singular value decomposition." Journal of the Robotics Society of Japan 5, no. 1 (1987): 4–10. http://dx.doi.org/10.7210/jrsj.5.4.

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14

Garzón, Manuel, and Pedro J. Torres. "Periodic solutions for the Lorentz force equation with singular potentials." Nonlinear Analysis: Real World Applications 56 (December 2020): 103162. http://dx.doi.org/10.1016/j.nonrwa.2020.103162.

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15

Hu, Y. Q. "Quadrupolar Force-free Magnetic Fields with Singular Current Density Surfaces." Astrophysical Journal 454 (November 1995): 480. http://dx.doi.org/10.1086/176499.

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16

Franco, Daniel, and Pedro J. Torres. "Periodic solutions of singular systems without the strong force condition." Proceedings of the American Mathematical Society 136, no. 04 (2007): 1229–36. http://dx.doi.org/10.1090/s0002-9939-07-09226-x.

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17

Uzal, Erol, and Banu Korbahti. "Vibration control of an elastic strip by a singular force." Sadhana 35, no. 2 (2010): 233–40. http://dx.doi.org/10.1007/s12046-010-0020-2.

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18

Noda, Naoaki, Yasushi Takase, Ryohji Shirao, Jun Li, and Jun Suke Sugimoto. "Intensity of Singular Stress at the End of a Fiber under Pull-Out Force." Key Engineering Materials 353-358 (September 2007): 3100–3103. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.3100.

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In this study, singular stress fields at the ends of fibers are discussed by the use of models of rectangular and cylindrical inclusions in a semi-infinite body under pull-out force．The body force method is used to formulate those problems as a system of singular integral equations where the unknown functions are densities of the body forces distributed in a semi-infinite body having the same elastic constants as those of the matrix and inclusions.Then generalized stress intensity factors at the corner of rectangular and cylindrical inclusions are systematically calculated with varying the ela

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19

Jun, Zhang, Jun Liu, Xiao Lu Ni, Wei Li, and Rong Mu. "Dynamic Model of a Discrete-Pontoon Floating Bridge Subjected by Moving Loads." Applied Mechanics and Materials 29-32 (August 2010): 732–37. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.732.

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A discrete-pontoon floating bridge is studied based on the beam model with assumption of the bridge deck as a elastic beam with uniform section, live load such as vehicle as moving concentrate forces, and pontoons as independent mass-spring-damping systems with singular degree of freedom. The comparison results of between vehicles and moving concentrated force show that a vehicle load can be simplified as one moving concentrated force. The present model can study not only a single moving load but also multiple moving loads.

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20

Noda, Nao-Aki, and Tadatoshi Matsuo. "Singular Integral Equation Method for Interaction Between Elliptical Inclusions." Journal of Applied Mechanics 65, no. 2 (1998): 310–19. http://dx.doi.org/10.1115/1.2789056.

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This paper deals with numerical solutions of singular integral equations in interaction problems of elliptical inclusions under general loading conditions. The stress and displacement fields due to a point force in infinite plates are used as fundamental solutions. Then, the problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the unknowns are the body force densities distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. To determine the unknown body force densities to sati

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21

KITRON-BELINKOV, MYRA, AMY NOVICK-COHEN, and NADAV LIRON. "A SLIP CONDITION BASED ON MINIMAL ENERGY DISSIPATION." Mathematical Models and Methods in Applied Sciences 06, no. 04 (1996): 467–80. http://dx.doi.org/10.1142/s0218202596000171.

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An intrinsic difficulty arises when solving Stokes equations in Ω ⊂ ℝ2 when the boundary conditions on the velocity are discontinuous: the solution is physically unacceptable since the force exerted by the fluid on the boundary is logarithmically singular. To illustrate this phenomena, we present an explicit solution in which the logarithmic singularity appears in a particularly simple form. A common method of avoiding the appearance of these singular forces is via an alteration of the boundary velocity profile in the vicinity of the discontinuity. However, there is no obvious physical criteri

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22

Carroll, M. M., and F. J. Rooney. "Singular Solutions in Second-Order Elasticity." Journal of Applied Mechanics 66, no. 4 (1999): 867–71. http://dx.doi.org/10.1115/1.2791790.

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The problems of a concentrated point force in an infinite medium (Kelvin's problem), or applied normal to the boundary of a half-space (Boussinesq's problem), as well as the corresponding problems for a concentrated couple, are solved to second order for incompressible isotropic elastic solids. The solutions are based on a simplified form of the second-order equations, obtained previously, and use of the Love's function representation for axisymmetric problems in the linear theory.

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23

Polonyi, Janos. "The Abraham–Lorentz force and electrodynamics at the classical electron radius." International Journal of Modern Physics A 34, no. 15 (2019): 1950077. http://dx.doi.org/10.1142/s0217751x19500775.

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The Abraham–Lorentz force is a finite remnant of the UV singular structure of the self-interaction of a point charge with its own field. The satisfactory description of such an interaction needs a relativistic regulator. This turns out to be a problematic point because the energy of regulated relativistic cutoff theories is unbounded from below. However, one can construct point-splitting regulators which keep the Abraham–Lorentz force stable. The classical language can be reconciled with QED by pointing out that the effective quantum theory for the electric charge supports a saddle point produ

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24

Liao, Yi. "New Periodic Solutions for the Singular Hamiltonian System." Abstract and Applied Analysis 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/703539.

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By use of the Cerami-Palais-Smale condition, we generalize the classical Weierstrass minimizing theorem to the singular case by allowing functions which attain infinity at some values. As an application, we study certain singular second-order Hamiltonian systems with strong force potential at the origin and show the existence of new periodic solutions with fixed periods.

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25

Uchiyama, Masaru, Yoshihiro Nakamura, and Kyojiro Hakomori. "Evaluation of the robot force sensor structure using singular value decomposition." Advanced Robotics 5, no. 1 (1990): 39–52. http://dx.doi.org/10.1163/156855391x00052.

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26

Kim, Hyea-Hyun. "A REGULARIZED CORRECTION METHOD FOR ELLIPTIC PROBLEMS WITH A SINGULAR FORCE." Journal of the Korean Mathematical Society 49, no. 5 (2012): 927–45. http://dx.doi.org/10.4134/jkms.2012.49.5.927.

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27

Antabli, Mohamed, and Morched Boughariou. "Homoclinic solutions for singular Hamiltonian systems without the strong force condition." Journal of Mathematical Analysis and Applications 472, no. 1 (2019): 352–71. http://dx.doi.org/10.1016/j.jmaa.2018.11.028.

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28

NODA, Nao-Aki, Dong CHEN, Rei TAKAKI, Guowei CHANG, Yoshikazu SANO, and Yasushi TAKASE. "Intensity of Singular Stress Fields of Fiber under Pull-out Force." Proceedings of the Materials and Mechanics Conference 2019 (2019): OS1412. http://dx.doi.org/10.1299/jsmemm.2019.os1412.

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29

Kim, Nam-Il, Seunghye Lee, Namshik Ahn, and Jaehong Lee. "Damage Identification of Truss Structures Based on Force Method." Advances in Applied Mathematics and Mechanics 7, no. 2 (2015): 229–44. http://dx.doi.org/10.4208/aamm.2013.m377.

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AbstractAn computationally efficient damage identification technique for the planar and space truss structures is presented based on the force method and the micro genetic algorithm. For this purpose, the general equilibrium equations and the kinematic relations in which the reaction forces and the displacements at nodes are take into account, respectively, are formulated. The compatibility equations in terms of forces are explicitly presented using the singular value decomposition (SVD) technique. Then governing equations with unknown reaction forces and initial elongations are derived. Next,

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30

Lane, Nick. "Life force: why energy shapes evolution." Biochemist 37, no. 5 (2015): 6–11. http://dx.doi.org/10.1042/bio03705006.

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Life on earth began some 4 billion years ago, but then got stuck at the level of bacteria for more than 2 billion years. The complex ‘eukaryotic’ cell arose abruptly in a singular event around 1.5–2 billion years ago. All eukaryotes share a long list of complex traits, from the nucleus to sex and senescence, which are all but unknown in bacteria. Why are humans so similar to mushrooms at the level of cells, even though we live so differently? Why did evolution follow such a peculiar trajectory? The answers might lie in the equally strange mechanism by which all cells generate ATP: chemiosmotic

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31

Juang, Jer-Nan, and J. R. Wright. "A Multi-Point Force Appropriation Method Based Upon a Singular Value Decomposition Approach." Journal of Vibration and Acoustics 113, no. 2 (1991): 176–81. http://dx.doi.org/10.1115/1.2930166.

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Force appropriation methods aim to provide an estimate for the force pattern required to excite a “pure” normal mode in a vibration test where multiple exciters are available. In this paper, a new method based upon a Singular Value Decomposition approach is presented. The appropriated force vector which minimizes the in-phase response components while maximizing the required quadrature components is found, subject to a fixed force norm. The method can accommodate more transducers than exciters and also more exciters than effective degrees of freedom. The method is demonstrated upon a six degre

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32

DOUBLIEZ, PAUL-FRANÇOIS, OLIVIER BRUNEAU, and FETHI BEN OUEZDOU. "FORCE CONTROL OF THE REDUNDANT LEG OF A BIPED ROBOT TO PRODUCE LARGE INERTIAL EFFECTS FOR CROSSING OBSTACLES." International Journal of Humanoid Robotics 09, no. 01 (2012): 1250003. http://dx.doi.org/10.1142/s021984361250003x.

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This paper proposes an energy control method for dynamic obstacle crossing by a planar biped. This approach was tested in a simulation where it was found to enable the biped robot to cross obstacles of different heights, due to inertial forces, by leaning with the front foot on the obstacles. The propulsion energy of the system is produced by the rear leg, which is endowed with four actuated degrees-of-freedom (hip, knee, ankle, toes), and is controlled by force control with four degrees-of-freedom in the non-singular case, and three degrees-of-freedom in the singular case. This paper identifi

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33

Hao, S., and L. M. Keer. "Rolling Contact Between Rigid Cylinder and Semi-Infinite Elastic Body With Sliding and Adhesion." Journal of Tribology 129, no. 3 (2007): 481–94. http://dx.doi.org/10.1115/1.2736431.

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Based on a hybrid superposition of an indentation contact and a rolling contact an analytical procedure is developed to evaluate the effects of surface adhesion during steady-state rolling contact, whereby two analytic solutions have been obtained. The first solution is a Hertz-type rolling contact between a rigid cylinder and a plane strain semi-infinite elastic substrate with finite adhesion, which is a JKR-type rolling contact but without singular adhesive traction at the edges of the contact zone. The second solution is of a rolling contact with JKR singular adhesive traction. The theoreti

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34

Li, Xin You, and W. Y. Chen. "Singularity Analysis of Limited-DOF Parallel Manipulator Based on Jacobian Matrixes." Applied Mechanics and Materials 141 (November 2011): 488–92. http://dx.doi.org/10.4028/www.scientific.net/amm.141.488.

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To analyze effects of singularity on parallel manipulator, the Jacobian matrixes were introduced as the indexes for analyzing the 3UPS/S parallel machine. The relationship between the velocity Jacobian matrix and the force-transformation matrix was established, and their equivalence was verified through the determinant and condition number’ reciprocal of the matrixes. Effects of singularity on motion accuracy, actuator forces and constrained forces were investigated within the nutation angle’range. The result showed that velocity analysis and mechanical analysis were consistent for 3UPS/S para

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35

Oda, Kazuhiro, and Naoaki Noda. "An Iterative Algorithm of Hypersingular Integral Equations for Crack Problems." Key Engineering Materials 385-387 (July 2008): 793–96. http://dx.doi.org/10.4028/www.scientific.net/kem.385-387.793.

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Crack problems are reducible to singular integral equations with strongly singular kernels by means of the body force method. In the ordinary method, the integral equations are reduced to a system of linear algebraic equations. In this paper, an iterative method for the numerical solution of the hypersingular integral equations of the body force method is proposed. This method is based on the Gauss- Chebyshev numerical integration rule and is very simple to program. The solution is achieved without solving the system of linear algebraic equations. The proposed method is applied to some plane e

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36

Lin, C.-C., and W.-T. Chang. "The force transmissibility of planar multiloop linkages." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 217, no. 11 (2003): 1259–70. http://dx.doi.org/10.1243/095440603771665278.

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A procedure for analysing the force transmissibility of. planar multiloop linkage mechanisms is introduced. The procedure considers the power flow paths in a multiloop linkage. By using a normalized force transmission index based on the ‘gain per unit cost’ concept, the force transmission performance of multiloop linkages can be characterized and measured quantitatively. The result shows that a multiloop mechanism may transmit effective force to the output link when it is at a singularity of motion. In such a condition, the power can reach the output link without passing through the singular-r

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37

Chadwick, Edmund, and Ali Hatam. "The physical interpretation of the lift discrepancy in Lanchester–Prandtl lifting wing theory for Euler flow, leading to the proposal of an alternative model in Oseen flow." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2085 (2007): 2257–75. http://dx.doi.org/10.1098/rspa.2007.1870.

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Consider uniform, steady potential and incompressible flow past a fixed thin wing inclined at a small angle to the flow. An investigation is conducted into the physical interpretation and consequences of the revision by Chadwick (Chadwick 2005 Proc. R. Soc. A 461 , 1–18) of the Lanchester–Prandtl lifting wing theory in Euler flow. In the present paper, the lift is evaluated from the pressure distribution over the top and bottom surfaces together with a contribution across the trailing edge of the wing. It is shown that this contribution across the trailing edge has previously been erroneously

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38

Zhang, Jun, Ming Kang Gou, Chuan Liang, Xiao Lu Ni, and Zi Wen Zhou. "Singular Function Models of a Simply Continuous Beam Bridge under a Moving Load." Applied Mechanics and Materials 204-208 (October 2012): 2240–43. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.2240.

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The system of a simply continuous beam was looked on as one span beam with several internal elastic supports of inexhaustible stiffness. There were two types of models such as the dynamic models by a moving concentrated force and by a moving mass. A three-span beam was introduced as example solved with the present model by a moving concentrated force and FEM, which verified that the present model was correct. Two cases of the example bridge by a moving concentrated force and by a moving mass were considered. The results indicate that mass of the moving load has little influence over the dynami

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39

Kowser, Md Arefin, Yoshio Arai, and Wakako Araki. "Asymptotic Analysis for the Singular Stress Behaviour around an Interface Edge of Dissimilar Power-Law Hardening Materials Joint." Key Engineering Materials 462-463 (January 2011): 1290–95. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.1290.

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An asymptotic analysis for singular stress fields around an interface-edge of dissimilar power-law hardening materials joint has been presented under plane strain condition and J2 deformation plasticity theory. Both the balance of force and the continuity of displacement are satisfied on the interface. In the higher order approximation, the nonlinear effective stress term was expanded by Taylor series. An iteration method is proposed for the determination of singular fields around interface edge. Multiple stress singular terms exist for in the higher order approximation. The order of stress si

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40

Lin, A. C. Y., and Y. G. Tsuei. "The Prediction of Substructure and System Modes by the Extended Complex Mode Indication Function." Journal of Vibration and Acoustics 120, no. 3 (1998): 671–77. http://dx.doi.org/10.1115/1.2893882.

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Yee and Tsuei (1989) developed the Modal Force Technique (MFT) as a tool for component synthesis. The approach utilizes the frequency response functions at connecting joints to predict the dynamical behavior of a synthesized system. The main difference between the MFT and the traditional impedance modeling approach is that no inversion of the frequency response functions is required for the MFT, which makes the Model Force Technique more efficient. The other major feature is that the Modal Force matrix of the synthesized system equation contains the information of both the substructure and the

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41

Ran, Zhi Hong, Jun Tong Qu, Fei He, and Sheng Miao. "Singular Perturbation Method for Solving Non-Linear Vibration of Stay Cable (II) - Engineering Application." Applied Mechanics and Materials 147 (December 2011): 117–21. http://dx.doi.org/10.4028/www.scientific.net/amm.147.117.

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According to vibration characteristic of cable in cable-stayed bridges, the non-linear dynamic model of cables was set up. The vibration differential equation is deduced using the singular perturbation method. The stiffness and coupling boundary conditions of simple and fixed are introduced in the cable force analysis. The useful formulation of measuring techniques for cable force using frequency method is advanced. Results of analyses indicate that the formulation is high in accuracy and convenient in practice. The formulation was used to the cable-stayed construction control of Nanjing Yangt

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42

Bibikov, Yu N., V. R. Bukaty, and A. A. Dorodenkov. "Regular and singular periodic perturbations of an oscillator with cubic restoring force." Vestnik St. Petersburg University: Mathematics 43, no. 2 (2010): 82–91. http://dx.doi.org/10.3103/s1063454110020044.

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43

Hu, You-qiu, and Lin Li. "Force-free magnetic fields with singular current density surfaces and their stability." Chinese Astronomy and Astrophysics 26, no. 4 (2002): 451–57. http://dx.doi.org/10.1016/s0275-1062(02)00096-6.

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44

NODA, Nao-Aki, Ryohji SHIRAO, Jun LI, and Jun-Suke SUGIMOTO. "A14 Intensity of Singular Stress for a Fiber under Pull-out Force." Proceedings of Conference of Kyushu Branch 2006.59 (2006): 15–16. http://dx.doi.org/10.1299/jsmekyushu.2006.59.15.

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45

Briot, Sébastien, and Vigen Arakelian. "Optimal Force Generation in Parallel Manipulators for Passing through the Singular Positions." International Journal of Robotics Research 27, no. 8 (2008): 967–83. http://dx.doi.org/10.1177/0278364908094403.

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46

Lu, Jian-Fei, and Andrzej Hanyga. "Wave field simulation for heterogeneous porous media with singular memory drag force." Journal of Computational Physics 208, no. 2 (2005): 651–74. http://dx.doi.org/10.1016/j.jcp.2005.03.008.

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47

Izydorek, Marek, and Joanna Janczewska. "Two families of infinitely many homoclinics for singular strong force Hamiltonian systems." Journal of Fixed Point Theory and Applications 16, no. 1-2 (2014): 301–11. http://dx.doi.org/10.1007/s11784-015-0212-9.

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48

Wu, Qin, Jian Jun Yang, and Chun Li Lei. "Modeling and Simulation for the Feed System of CNC Machine." Applied Mechanics and Materials 496-500 (January 2014): 1024–27. http://dx.doi.org/10.4028/www.scientific.net/amm.496-500.1024.

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Study the linear and nonlinear stiffness dynamic characteristics of ball screw in feed system. According to the structure and the stiffness of ball screw, considering the influence of damping force, elastic force, friction force, driving force and load, establish the dynamic model of feed system. Use Linz Ted- Poincare (L-P) Method of singular perturbation to solve the model, obtain the quadratic approximate solution of the free vibration, analyze the multiple solution phenomenon of the model, and also conduct the numerical simulation analysis for the model.

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49

Kevin Jui, C. K., and Qiao Sun. "Path Tracking of Parallel Manipulators in the Presence of Force Singularity." Journal of Dynamic Systems, Measurement, and Control 127, no. 4 (2005): 550–63. http://dx.doi.org/10.1115/1.2098893.

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Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel ma

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Alawneh, A. D., and N. T. Shawagfeh. "Singularity methods for magnetohydrodynamics." International Journal of Mathematics and Mathematical Sciences 9, no. 1 (1986): 111–22. http://dx.doi.org/10.1155/s0161171286000145.

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Abstract:

Singular solutions for linearized MHD equations based on Oseen approximations have been obtained such as Oseenslet. Oseenrotlet, mass source, etc. By suitably distributing these singular solutions along the axes of symmetry of an axially symmetric bodies, we derive the approximate values for the velocity fields, the force and the momentum for the case of translational and rotational motions of such bodies in a steady flow of an incompressible viscous and magnetized fluid.

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