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Journal articles on the topic 'Equation de von Kármán'

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Published: 4 June 2021

Last updated: 8 February 2022

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1

CIARLET, PHILIPPE G., LILIANA GRATIE, and SRINIVASAN KESAVAN. "ON THE GENERALIZED VON KÁRMÁN EQUATIONS AND THEIR APPROXIMATION." Mathematical Models and Methods in Applied Sciences 17, no. 04 (April 2007): 617–33. http://dx.doi.org/10.1142/s0218202507002042.

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We consider here the "generalized von Kármán equations", which constitute a mathematical model for a nonlinearly elastic plate subjected to boundary conditions "of von Kármán type" only on a portion of its lateral face, the remaining portion being free. As already shown elsewhere, solving these equations amounts to solving a "cubic" operator equation, which generalizes an equation introduced by Berger and Fife. Two noticeable features of this equation, which are not encountered in the "classical" von Kármán equations are the lack of strict positivity of its cubic part and the lack of an associated functional. We establish here the convergence of a conforming finite element approximation to these equations. The proof relies in particular on a compactness method due to J. L. Lions and on Brouwer's fixed point theorem. This convergence proof provides in addition an existence proof for the original problem.

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2

Ciarlet, Philippe G., and Liliana Gratie. "On the Existence of Solutions to the Generalized Marguerre-von Kármán Equations." Mathematics and Mechanics of Solids 11, no. 1 (February 2006): 83–100. http://dx.doi.org/10.1177/1081286505046480.

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Using techniques from asymptotic analysis, the second author has recently identified equations that generalize the classical Marguerre-von Kármán equations for a nonlinearly elastic shallow shell by allowing more realistic boundary conditions, which may change their type along the lateral face of the shell. We first reduce these more general equations to a single “cubic” operator equation, whose sole unknown is the vertical displacement of the shell. This equation generalizes a cubic operator equation introduced by M. S. Berger and P. Fife for analyzing the von Kármán equations for a nonlinearly elastic plate. We then establish the existence of a solution to this operator equation by means of a compactness method due to J. L. Lions.

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3

PARK, JONG YEOUL, SUN HYE PARK, and YONG HAN KANG. "BILINEAR OPTIMAL CONTROL OF THE VELOCITY TERM IN A VON KÁRMÁN PLATE EQUATION." ANZIAM Journal 54, no. 4 (April 2013): 291–305. http://dx.doi.org/10.1017/s1446181113000205.

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AbstractWe consider a bilinear optimal control problem for a von Kármán plate equation. The control is a function of the spatial variables and acts as a multiplier of the velocity term. We first state the existence of solutions for the von Kármán equation and then derive optimality conditions for a given objective functional. Finally, we show the uniqueness of the optimal control.

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4

Ciarlet, Philippe G., and Liliana Gratie. "Generalized von Kármán equations." Journal de Mathématiques Pures et Appliquées 80, no. 3 (April 2001): 263–79. http://dx.doi.org/10.1016/s0021-7824(00)01198-3.

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5

Fattorusso, Luisa, and Antonio Tarsia. "Von Kármán equations inLpspaces." Applicable Analysis 92, no. 11 (November 2013): 2375–91. http://dx.doi.org/10.1080/00036811.2012.738362.

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6

Wang, Jiujiang, Xin Liu, Yuanyu Yu, Yao Li, Ching-Hsiang Cheng, Shuang Zhang, Peng-Un Mak, Mang-I. Vai, and Sio-Hang Pun. "A Review on Analytical Modeling for Collapse Mode Capacitive Micromachined Ultrasonic Transducer of the Collapse Voltage and the Static Membrane Deflections." Micromachines 12, no. 6 (June 18, 2021): 714. http://dx.doi.org/10.3390/mi12060714.

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Analytical modeling of capacitive micromachined ultrasonic transducer (CMUT) is one of the commonly used modeling methods and has the advantages of intuitive understanding of the physics of CMUTs and convergent when modeling of collapse mode CMUT. This review article summarizes analytical modeling of the collapse voltage and shows that the collapse voltage of a CMUT correlates with the effective gap height and the electrode area. There are analytical expressions for the collapse voltage. Modeling of the membrane deflections are characterized by governing equations from Timoshenko, von Kármán equations and the 2D plate equation, and solved by various methods such as Galerkin’s method and perturbation method. Analytical expressions from Timoshenko’s equation can be used for small deflections, while analytical expression from von Kármán equations can be used for both small and large deflections.

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7

Hornung, Peter. "A remark on constrained von Kármán theories." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2170 (October 8, 2014): 20140346. http://dx.doi.org/10.1098/rspa.2014.0346.

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8

Wang, Yongda. "An evolution von Kármán equation modeling suspension bridges." Nonlinear Analysis 169 (April 2018): 59–78. http://dx.doi.org/10.1016/j.na.2017.12.002.

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9

Cibula, Július. "Von Kármán equations. III. Solvability of the von Kármán equations with conditions for geometry of the boundary of the domain." Applications of Mathematics 36, no. 5 (1991): 368–79. http://dx.doi.org/10.21136/am.1991.104473.

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10

Bock, I. "On Nonstationary von Kármán Equations." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 76, no. 10 (1996): 559–71. http://dx.doi.org/10.1002/zamm.19960761006.

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11

Hellinger, Petr, Andrea Verdini, Simone Landi, Luca Franci, and Lorenzo Matteini. "von Kármán–Howarth Equation for Hall Magnetohydrodynamics: Hybrid Simulations." Astrophysical Journal 857, no. 2 (April 20, 2018): L19. http://dx.doi.org/10.3847/2041-8213/aabc06.

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12

Chang, S. I. "Derivation Of The Von Kármán Equation From An Extension Of Love's Equations." Journal of Sound and Vibration 176, no. 1 (September 1994): 127–29. http://dx.doi.org/10.1006/jsvi.1994.1362.

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13

Ciarlet, Philippe G., and Liliana Gratie. "From the classical to the generalized von Kármán and Marguerre–von Kármán equations." Journal of Computational and Applied Mathematics 190, no. 1-2 (June 2006): 470–86. http://dx.doi.org/10.1016/j.cam.2005.04.008.

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14

LIU, ZENG, MARTIN OBERLACK, VLADIMIR N. GREBENEV, and SHI-JUN LIAO. "EXPLICIT SERIES SOLUTION OF A CLOSURE MODEL FOR THE VON KÁRMÁN–HOWARTH EQUATION." ANZIAM Journal 52, no. 2 (October 2010): 179–202. http://dx.doi.org/10.1017/s1446181111000678.

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AbstractThe homotopy analysis method (HAM) is applied to a nonlinear ordinary differential equation (ODE) emerging from a closure model of the von Kármán–Howarth equation which models the decay of isotropic turbulence. In the infinite Reynolds number limit, the von Kármán–Howarth equation admits a symmetry reduction leading to the aforementioned one-parameter ODE. Though the latter equation is not fully integrable, it can be integrated once for two particular parameter values and, for one of these values, the relevant boundary conditions can also be satisfied. The key result of this paper is that for the generic case, HAM is employed such that solutions for arbitrary parameter values are derived. We obtain explicit analytical solutions by recursive formulas with constant coefficients, using some transformations of variables in order to express the solutions in polynomial form. We also prove that the Loitsyansky invariant is a conservation law for the asymptotic form of the original equation.

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15

Yau, Shing-Tung, and Yang Gao. "Obstacle problem for von Kármán equations." Advances in Applied Mathematics 13, no. 2 (June 1992): 123–41. http://dx.doi.org/10.1016/0196-8858(92)90005-h.

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16

Nore, Caroline, Houda Zaidi, Frederic Bouillault, Alain Bossavit, and Jean-Luc Guermond. "Approximation of the time-dependent induction equation with advection using Whitney elements." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 35, no. 1 (January 4, 2016): 326–38. http://dx.doi.org/10.1108/compel-06-2015-0235.

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Purpose – The purpose of this paper is to present a new formulation for taking into account the convective term due to an imposed velocity field in the induction equation in a code based on Whitney elements called DOLMEN. Different Whitney forms are used to approximate the dependent variables. The authors study the kinematic dynamo action in a von Kármán configuration and obtain results in good agreement with those provided by another well validated code called SFEMaNS. DOLMEN is developed to investigate the dynamo action in non-axisymmetric domains like the impeller driven flow of the von Kármán Sodium (VKS) experiment. The authors show that a 3D magnetic field dominated by an axisymmetric vertical dipole can grow in a kinematic dynamo configuration using an analytical velocity field. Design/methodology/approach – Different Whitney forms are used to approximate the dependent variables. The vector potential is discretized using first-order edge elements of the first family. The velocity is approximated by using the first-order Raviart-Thomas elements. The time stepping is done by using the Crank-Nicolson scheme. Findings – The authors study the kinematic dynamo action in a von Kármán configuration and obtain results in good agreement with those provided by another well validated code called SFEMaNS. The authors show that a 3D magnetic field dominated by an axisymmetric vertical dipole can grow in a kinematic dynamo configuration using an analytical velocity field. Originality/value – The findings offer a basis to a scenario for the VKS dynamo.

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17

Alon Tzezana, Gali, and Kenneth S. Breuer. "Thrust, drag and wake structure in flapping compliant membrane wings." Journal of Fluid Mechanics 862 (January 15, 2019): 871–88. http://dx.doi.org/10.1017/jfm.2018.966.

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We present a theoretical framework to characterize the steady and unsteady aeroelastic behaviour of compliant membrane wings under different conditions. We develop an analytic model based on thin airfoil theory coupled with a membrane equation. Adopting a numerical solution to the model equations, we study the effects of wing compliance, inertia and flapping kinematics on aerodynamic performance. The effects of added mass and fluid damping on a flapping membrane are quantified using a simple damped oscillator model. As the flapping frequency is increased, membranes go through a transition from thrust to drag around the resonant frequency, and this transition is earlier for more compliant membranes. The wake also undergoes a transition from a reverse von Kármán wake to a traditional von Kármán wake. The wake transition frequency is predicted to be higher than the thrust–drag transition frequency for highly compliant wings.

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18

Khabirov, S. V., and G. Ünal. "Group analysis of the von Kármán–Howarth equation. Part I. Submodels." Communications in Nonlinear Science and Numerical Simulation 7, no. 1-2 (May 2002): 3–18. http://dx.doi.org/10.1016/s1007-5704(02)00003-5.

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19

Feireisl, Eduard. "Dynamic von Kármán equations involving nonlinear damping: Time-periodic solutions." Applications of Mathematics 34, no. 1 (1989): 46–56. http://dx.doi.org/10.21136/am.1989.104333.

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20

Brilla, Igor. "Bifurcations of generalized von Kármán equations for circular viscoelastic plates." Applications of Mathematics 35, no. 4 (1990): 302–14. http://dx.doi.org/10.21136/am.1990.104412.

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21

Cibula, Július. "Von Kármán equations. II. Approximation of the solution." Applications of Mathematics 30, no. 1 (1985): 1–10. http://dx.doi.org/10.21136/am.1985.104123.

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22

Puel, Jean-Pierre, and Marius Tucsnak. "Boundary Stabilization for the von Kármán Equations." SIAM Journal on Control and Optimization 33, no. 1 (January 1995): 255–73. http://dx.doi.org/10.1137/s0363012992228350.

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23

Quintela Estévez, P. "Perturbed bifurcation in the von Kármán equations." Asymptotic Analysis 8, no. 2 (1994): 161–84. http://dx.doi.org/10.3233/asy-1994-8203.

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24

Chien, C. S., and M. S. Chen. "Multiple Bifurcation in the von Kármán Equations." SIAM Journal on Scientific Computing 18, no. 6 (November 1997): 1737–66. http://dx.doi.org/10.1137/s106482759427364x.

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25

Chien, C. S., S. Y. Gong, and Z. Mei. "Mode Jumping In The Von Kármán Equations." SIAM Journal on Scientific Computing 22, no. 4 (January 2000): 1354–85. http://dx.doi.org/10.1137/s1064827596307324.

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26

Rao, Bopeng. "Marguerre-Von Kármán equations and membrane model." Nonlinear Analysis: Theory, Methods & Applications 24, no. 8 (April 1995): 1131–40. http://dx.doi.org/10.1016/0362-546x(94)00226-8.

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27

Menzala, G. Perla, and E. Zuazua. "Timoshenko's beam equation as limit of a nonlinear one-dimensional von Kármán system." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 4 (August 2000): 855–75. http://dx.doi.org/10.1017/s0308210500000470.

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We consider a dynamical one-dimensional nonlinear von Kármán model depending on one parameter ε > 0 and study its weak limit as ε → 0. We analyse various boundary conditions and prove that the nature of the limit system is very sensitive to them. We prove that, depending on the type of boundary condition we consider, the nonlinearity of Timoshenko's model may vanish.

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28

Brilla, Igor. "Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates." Applications of Mathematics 35, no. 3 (1990): 237–51. http://dx.doi.org/10.21136/am.1990.104408.

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29

Root, Robert G. "Boundary value problems for degenerate von Kármán equations." Quarterly of Applied Mathematics 57, no. 1 (March 1, 1999): 1–17. http://dx.doi.org/10.1090/qam/1672163.

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30

Ciarlet, Philippe G., Liliana Gratie, and Srinivasan Kesavan. "Numerical analysis of the generalized von Kármán equations." Comptes Rendus Mathematique 341, no. 11 (December 2005): 695–99. http://dx.doi.org/10.1016/j.crma.2005.09.031.

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31

Jin, Rongrong, and Guangcun Lu. "Variational study of bifurcations in von Kármán equations." Frontiers of Mathematics in China 14, no. 3 (April 29, 2019): 567–90. http://dx.doi.org/10.1007/s11464-019-0766-8.

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32

Lai, C. Y., K. R. Rajagopal, and A. Z. Szeri. "Asymmetric flow above a rotating disk." Journal of Fluid Mechanics 157 (August 1985): 471–92. http://dx.doi.org/10.1017/s0022112085002452.

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In this paper we generalize the von Kármán solution for flow above a single rotating disk, to include non-axisymmetric solutions. These solutions contain an arbitrary parameter; for zero value of the parameter the asymmetric flow degenerates into the classical von Kármán solution. Thus the classical solution is never isolated when considered within the scope of the full Navier–Stokes equations; there are asymmetric solutions in every neighbourhood of the von Kármán solution. Calculations are reported here for s = 0, 0.02 and 0.06, where s represents the ratio of angular velocity of the fluid at infinity to the angular velocity of the disk. A subset of the solutions obtained here corresponds to flow induced by the rotation of a disk when the latter is placed in a fluid that is moving with a constant uniform velocity.

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33

Khabirov, S. V., and G. Ünal. "Group analysis of the von Kármán–Howarth equation. Part II. Physical invariant solutions." Communications in Nonlinear Science and Numerical Simulation 7, no. 1-2 (May 2002): 19–30. http://dx.doi.org/10.1016/s1007-5704(02)00012-6.

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34

Liu, Zeng, Martin Oberlack, Vladimir N. Grebenev, and Shijun Liao. "Explicit series solution of a closure model for the von Kármán-Howarth equation." ANZIAM Journal 52 (September 3, 2011): 179. http://dx.doi.org/10.21914/anziamj.v52i0.3215.

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35

Park, Jong Yeoul, Sun Hye Park, and Yong Han Kang. "Bilinear optimal control of the velocity term in a von Kármán plate equation." ANZIAM Journal 54 (July 29, 2013): 291. http://dx.doi.org/10.21914/anziamj.v54i0.7130.

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36

Perla Menzala, G., and E. Zuazua. "Timoshenko's plate equation as a singular limit of the dynamical von Kármán system." Journal de Mathématiques Pures et Appliquées 79, no. 1 (January 2000): 73–94. http://dx.doi.org/10.1016/s0021-7824(00)00149-5.

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37

Kang, Jum-Ran. "Exponential Decay for Nonlinear von Kármán Equations with Memory." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/484596.

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We consider the nonlinear von Kármán equations with memory term. We show the exponential decay result of solutions. Our result is established without imposing the usual relation betweengand its derivative. This result improves on earlier ones concerning the exponential decay.

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38

Wang, Chun-Yan. "Asymptotic analysis to Von Kármán swirling-flow problem." Modern Physics Letters B 33, no. 25 (September 10, 2019): 1950298. http://dx.doi.org/10.1142/s0217984919502981.

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In this paper, we consider the Von Kármán swirling-flow problem, which is described by an ordinary equations system. The explicit asymptotic solutions are given by applying the homotopy renormalization method. Furthermore, the numerical simulations verify that our asymptotic solutions have high precision and the absolute errors are less than 0.03, which means that the results obtained are truly valid and can be used practically.

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39

Menzala, G. P., and A. F. Pazoto. "Uniform boundary stabilization of the dynamical von Kármán and Timoshenko equations for plates." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 2 (April 2006): 385–413. http://dx.doi.org/10.1017/s0308210500004625.

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The full nonlinear dynamic von Kárm´n system depending on a small parameter ε > 0 is considered. We study the asymptotic behaviour of the total energy associated with the model for large t and ε → 0. Introducing appropriate boundary feedback, we show that the total energy of a solution of the corresponding damped model decays exponentially as t → +∞, uniformly with respect to the parameter ε > 0. As ε → 0, we obtain a damped plate model for which the energy also tends to zero exponentially. The limit system can be viewed as new variant of the so-called Timoshenko model. It consists of a second-order hyperbolic equation for transversal vibrations of the plate coupled with a first-order ordinary differential equation whose solution appears as coefficient of the plate model and takes into account (when ε → 0) the contribution of the tangential components.

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40

Bock, I. "On Integro-Differential von Kármán Equations for Viscoelastic Plates." PAMM 1, no. 1 (March 2002): 131. http://dx.doi.org/10.1002/1617-7061(200203)1:1<131::aid-pamm131>3.0.co;2-z.

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41

Kang, Jum-Ran. "Exponential decay for a von Kármán equations with memory." Journal of Mathematical Physics 54, no. 3 (March 2013): 033501. http://dx.doi.org/10.1063/1.4791694.

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42

Chien, C. S., Y. J. Kuo, and Z. Mei. "Symmetry and scaling properties of the von Kármán equations." Zeitschrift für angewandte Mathematik und Physik 49, no. 5 (September 1998): 710–29. http://dx.doi.org/10.1007/pl00001487.

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43

Mallik, Gouranga, and Neela Nataraj. "Conforming finite element methods for the von Kármán equations." Advances in Computational Mathematics 42, no. 5 (February 6, 2016): 1031–54. http://dx.doi.org/10.1007/s10444-016-9452-5.

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44

Lovadina, Carlo, David Mora, and Iván Velásquez. "A virtual element method for the von Kármán equations." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 2 (March 2021): 533–60. http://dx.doi.org/10.1051/m2an/2020085.

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In this article we propose and analyze a Virtual Element Method (VEM) to approximate the isolated solutions of the von Kármán equations, which describe the deformation of very thin elastic plates. We consider a variational formulation in terms of two variables: the transverse displacement of the plate and the Airy stress function. The VEM scheme is conforming inH2for both variables and has the advantages of supporting general polygonal meshes and is simple in terms of coding aspects. We prove that the discrete problem is well posed forhsmall enough and optimal error estimates are obtained. Finally, numerical experiments are reported illustrating the behavior of the virtual scheme on different families of meshes.

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45

Yongsheng, Ren, Du Chenggang, and Shi Yuyan. "Nonlinear Free and Forced Vibration Behavior of Shear-Deformable Composite Beams with Shape Memory Alloy Fibers." Shock and Vibration 2016 (2016): 1–16. http://dx.doi.org/10.1155/2016/1056087.

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The nonlinear free and forced vibration of the composite beams embedded with shape memory alloy (SMA) fibers are investigated based on first-order shear deformation beam theory and the von Kármán type nonlinear strain-displacement equation. A thermomechanical constitutive equation of SMA proposed by Brinson is used to calculate the recovery stress of the constrained SMA fibers. The equations of motion are derived by using Hamilton’s principle. The approximate solution is obtained for vibration analysis of the composite beams based on the Galerkin approach. The parametric study is carried out to display the effect of the actuation temperature, the volume fraction, the initial strain of SMA fibers, and the length-to-thickness ratio. The shear deformation is shown to have a significant contribution to nonlinear vibration behavior of the composite beams with SMA fibers.

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46

Guo, Yong. "Fluid-Induced Nonlinear Vibration of a Cantilevered Microtube with Symmetric Motion Constraints." Shock and Vibration 2020 (August 12, 2020): 1–14. http://dx.doi.org/10.1155/2020/8852357.

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This paper investigates the dynamic behavior of a cantilevered microtube conveying fluid, undergoing large motions and subjected to motion-limiting constraints. Based on the modified couple stress theory and the von Kármán relationship, the strain energy of the microtube can be deduced and then the governing equation of motion is derived by using the Hamilton principle. The Galerkin method is applied to produce a set of ordinary differential equations. The effect of the internal material length scale parameter on the critical flow velocity is investigated. By using the projection method, the Hopf bifurcation is demonstrated. The results show that size effect on the vibration properties is significant.

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47

Younis, Mohammad I., and Ali H. Nayfeh. "Simulation of Squeeze-Film Damping of Microplates Actuated by Large Electrostatic Load." Journal of Computational and Nonlinear Dynamics 2, no. 3 (January 7, 2007): 232–41. http://dx.doi.org/10.1115/1.2727491.

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We present a new method for simulating squeeze-film damping of microplates actuated by large electrostatic loads. The method enables the prediction of the quality factors of microplates under a limited range of gas pressures and applied electrostatic loads up to the pull-in instability. The method utilizes the nonlinear Euler-Bernoulli beam equation, the von Kármán plate equations, and the compressible Reynolds equation. The static deflection of the microplate is calculated using the beam model. Analytical expressions are derived for the pressure distribution in terms of the plate mode shapes around the deflected position using perturbation techniques. The static deflection and the analytical expressions are substituted into the plate equations, which are solved using a finite-element method. Several results are presented showing the effect of the pressure and the electrostatic force on the structural mode shapes, the pressure distributions, the natural frequencies, and the quality factors.

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48

Perla Menzala, G., and E. Zuazua. "The beam equation as a limit of a 1-D nonlinear von Kármán model." Applied Mathematics Letters 12, no. 1 (January 1999): 47–52. http://dx.doi.org/10.1016/s0893-9659(98)00125-6.

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49

Abels, Helmut, Maria Giovanna Mora, and Stefan Müller. "The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity." Calculus of Variations and Partial Differential Equations 41, no. 1-2 (August 15, 2010): 241–59. http://dx.doi.org/10.1007/s00526-010-0360-0.

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50

Hui-chuan, Shen. "The relation of von Kármán equation for elastic large deflection problem and Schrödinger equation for quantum eigenalues problem." Applied Mathematics and Mechanics 6, no. 8 (August 1985): 761–75. http://dx.doi.org/10.1007/bf03250496.

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