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Academic literature on the topic 'Liapunov method'

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Published: 19 February 2023

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Journal articles on the topic "Liapunov method"

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Sharma, B. "Solving the three-dimensional findpath problem via Liapunov's method." South Pacific Journal of Natural and Applied Sciences 20, no. 1 (2002): 48. http://dx.doi.org/10.1071/sp02010.

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This paper presents a method for solving the findpath problem. Commonly known as the second or direct method of Liapunov, the method is used to solve this geometric problem of finding collision-free trajectories of moving solid objects amongst other fixed and moving solid objects. A Liapunov function is proposed for a n-point dynamical system in three-space. Computer simulations are carried out to show the effectiveness of the proposed Liapunov function-based feedback controllers.

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Tunç, Cemil. "A note on boundedness of solutions to a class of non-autonomous differential equations of second order." Applicable Analysis and Discrete Mathematics 4, no. 2 (2010): 361–72. http://dx.doi.org/10.2298/aadm100601026t.

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By defining some appropriate Liapunov functions, we discuss boundedness of solutions to a class of non-autonomous and nonlinear differential equations of second order. By this work, we prove some results established in the literature by Liapunov's second method instead of the integral test. We give six examples to illustrate the theoretical analysis in this work and effectiveness of the method utilized here.

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Ata, Atef, Salwa Elkhoga, Mohamed Shalaby, and Shihab Asfour. "Causal inverse dynamics of a flexible hub-arm system through Liapunov's second method." Robotica 14, no. 4 (July 1996): 381–89. http://dx.doi.org/10.1017/s0263574700019779.

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SUMMARYThe main objective of this work is to study the performance of a flexible single hub-arm system. The equations of motion are derived using the extended Hamilton principle. The Liapunov functional is used as a condition for the stability analysis. The Liapunov functional is considered as the sum of the internal energy of the flexible beam. The required drive torque was obtained directly through the solution of the inverse dynamic problem. Although the flexible link is nonminimum phase in nature, the use of Liapunov and the PD controller guarantee the causality for the stable case. The effects of tip mass as well as its inertia in the case of stable and asymptotic stable systems were investigated to ensure the validity of this procedure.

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Al-Bayaty, Intidhar Z. Mushete. "Modified Krasovskii's Method for Constructing Liapunov Function." Journal of Al-Nahrain University Science 14, no. 4 (December 1, 2011): 177–80. http://dx.doi.org/10.22401/jnus.14.4.25.

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RODRIGUES, HILDEBRANDO M., JIANHONG WU, and LUÍS R. A. GABRIEL. "UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS." International Journal of Bifurcation and Chaos 21, no. 02 (February 2011): 513–26. http://dx.doi.org/10.1142/s0218127411028568.

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In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

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Blot, Joël, and Philippe Michel. "On the Liapunov Second Method for Difference Equations." Journal of Difference Equations and Applications 10, no. 1 (January 2004): 41–52. http://dx.doi.org/10.1080/1023619031000148795.

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Marchelek, K., M. Pajor, and B. Powałka. "Vibrostability of the Milling Process Described by the Time-Variable Parameter Model." Journal of Vibration and Control 8, no. 4 (April 2002): 467–79. http://dx.doi.org/10.1177/107754602028158.

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This paper presents a method for vibrostability prognosis using a non-stationary model of the machine tool-cutting process system. The method employs Liapunov-Floquet theory. The method is illustrated by the example of the determination of limit cutting parameters using appropriate model reduction methods.

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Pan, Ying, and Tong Zhao. "Hybrid Control for Seismological Nonlinear Structures on Liapunov’s Theory." Applied Mechanics and Materials 166-169 (May 2012): 1237–40. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.1237.

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In this paper, the hybrid control method of earthquake excited high-raised buildings is put forword. The building is modeled as a shear-wall type structure with non-linear hysteretic restoring forces after the structure enters the period of nonlinear and plasticity. A passive base-isolation is combined with actuators applied at the basement of the structure. A candidate for Liapunov function is found out based on the theory of energy. A non-linear control law is designed following the theory of Liapunov, since small residual deformations have to be tolerated due to inelastic energy dissipation, asymptotic stability will not be required, but only stability in the sense of Liapunov has to be guaranteed. Computer simulations demonstrate the efficiency of the proposed control algorithm.

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Zhao, Jie Min. "Global Stability Analysis of Multimedia Systems." Applied Mechanics and Materials 20-23 (January 2010): 1004–8. http://dx.doi.org/10.4028/www.scientific.net/amm.20-23.1004.

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Zhao, Jie Min. "On the Global Stability Problem of Multimedia Systems." Applied Mechanics and Materials 20-23 (January 2010): 1162–66. http://dx.doi.org/10.4028/www.scientific.net/amm.20-23.1162.

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Dissertations / Theses on the topic "Liapunov method"

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Lust, Alexander. "Eine hybride Methode zur Berechnung von Liapunow-Exponenten." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=98122587X.

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Bonomo, Wescley. "Sistemas dinâmicos discretos: estabilidade, comportamento assintótico e sincronização." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-01072008-164134/.

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Este trabalho é em parte baseado no livro The Stability and Control of Discrete Processes de Joseph P. LaSalle. Nós estudamos equações como x(n+1) = T(x(n)), onde T : \' R POT. m\' \' SETA\' \'R POT. m\' é uma aplicação contínua, com o sistema dinâmico associado \'PI\' (n,x) := \' T POT. n\' (x). Nós fornecemos condições suficientes para a estabilidade de equilíbrios usando o método direto de Liapunov. Também consideramos sistemas discretos da forma x(n+1)=T(n, x(n),\'lâmbda\' ) dependendo de uma parâmetro \' lâmbda\' e apresentamos resultados obtendo estimativas de atratores. Finalmente, nós apresentamos algumas simulações de sistemas acoplados como uma aplicação em sistemas de comunicação
This work is in part based on the book The Stability and Control of Discrete Processes of Joseph P. LaSalle. We studing equations as x(n+1) = T(x(n)), where T : \' R POT.m\' \' ARROW\' \' \' R POT.m\' is continuous transformation, with the associated dynamic system \'PI\' (n,x) := \' T POT.n\' (x). We provide suddicient conditions for stability of equilibria, using Liapunov direct method. We also consider nonautonomous discrete systems of the form x(n + 1) = T(n, x(n), \' lâmbda\') depending on the parameter \'lâmbda\' and present results obtaining uniform estimatives of attractors. We finally we present some simulations on synchronization of coupled systems as an application on communication systems

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DAMKE, Caíke da Rocha. "Problemas Elípticos Assintoticamente Lineares." Universidade Federal de Goiás, 2012. http://repositorio.bc.ufg.br/tede/handle/tde/1950.

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Made available in DSpace on 2014-07-29T16:02:19Z (GMT). No. of bitstreams: 1 Dissertacao Caike da R Damke.pdf: 510380 bytes, checksum: 4e479f17d8c052dd29cea88f0ca85df8 (MD5) Previous issue date: 2012-02-02
In this dissertation we analyze questions of existence and multiplicity of solutions for Dirichlet problem in the asymptotically linear case. To obtain our main results we use variational methods, such as Montain Pass Theorem and Linking Theorem.Moreover, we use the Liapunov-Schmidt reduction.
Nesta dissertação analisamos questões de existência e multiplicidade de soluções do problema de Dirichlet elíptico assintoticamente linear. Para obtermos os nossos principais resultados utilizamos métodos variacionais, tais como o Teorema do Passo da Montanha um Teorema de Linking. Além disso, utilizamos a redução de Liapunov-Schmidt.

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Maranho, Luiz Cesar. "Aplicação do método de linearização de Lyapunov na análise de uma dinâmica não linear para controle populacional do mosquito Aedes aegypti." Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/157305.

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Submitted by Luiz Cesar Maranho (lc-maranho@bol.com.br) on 2018-10-11T20:16:50Z No. of bitstreams: 1 Dissertação Final.pdf: 1883342 bytes, checksum: 85a25606a3113b39d6d4354dcaa161d8 (MD5)
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O mosquito Aedes aegypti é o principal vetor responsável por diversas arboviroses como a dengue, a febre amarela, o vírus zika e a febre chikungunya. Devido a sua resistência, adaptabilidade e proximidade ao homem, o Aedes aegypti é atualmente um dos maiores problemas de saúde pública no Brasil e nas Américas. Mesmo com os avanços e investimentos em pesquisas com vacinas, monitoramento, campanhas educativas e diversos tipos de controle deste vetor, ainda não existe um método eficaz para controlar e erradicar o mosquito. Portanto, esse trabalho destina-se ao auxílio na criação de estratégias para controlar esse agente transmissor, mediante a análise do espaço de estados e a estabilidade assintótica de uma dinâmica não linear para controle populacional do Aedes aegypti via a técnica de linearização de Lyapunov, além de apresentação de formas de prevenção e combate aos criadouros do mosquito. A dinâmica não linear proposta é uma dinâmica simplificada obtida de um modelo não linear existente na literatura, proposto por Esteva e Yang em 2005 e se baseia no ciclo de vida do mosquito, que é dividido em duas fases: fase imatura ou aquática (ovos, larvas e pupas) e fase alada (mosquitos adultos). Na fase adulta, os mosquitos são divididos em machos, fêmeas imaturas e fêmeas fertilizadas, sendo que a dinâmica proposta nesta dissertação de mestrado é baseada nos estudos efetuados por Reis desde 2016, obtendo um modelo simplificado no qual a soma das densidades das populações de fêmeas imaturas e fêmeas fertilizadas serão consideradas como fêmeas adultas.
The mosquito Aedes aegypti is the main vector responsible for several arboviruses such as dengue fever, yellow fever, zika virus and chikungunya fever. Due to its resistance, adaptability and proximity to humans, Aedes aegypti is currently one of the major public health problems in Brazil and the Americas. Even with the advances and investments in research with vaccines, monitoring, educational campaigns and various types of control of this vector, there is still no effective method to control and eradicate the mosquito. Therefore, this work is intended to aid in the creation of strategies to control this transmitting agent by analyzing the state space and the asymptotic stability of a nonlinear dynamics for population control of Aedes aegypti via the Lyapunov linearization technique to present ways of preventing and combating mosquito breeding sites. The proposed nonlinear dynamics is a simplified dynamics obtained from a nonlinear model existing in the literature, proposed by Esteva and Yang in 2005 and based on the life cycle of the mosquito, which is divided into two phases: immature or aquatic phase (eggs, larvae and pupae) and winged phase (adult mosquitoes). In the adult phase, mosquitoes are divided into males, immature females and fertilized females, and the dynamics proposed in this dissertation is based on studies carried out by Reis since 2016, obtaining a simplified model in which the sum of the densities of the populations of females immature and fertilized females will be considered as adult females.

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(9809531), Patrick Keleher. "Adaptive and sliding mode control of articulated robot arms using the Liapunov method incorporating constraint inequalities." Thesis, 2003. https://figshare.com/articles/thesis/Adaptive_and_sliding_mode_control_of_articulated_robot_arms_using_the_Liapunov_method_incorporating_constraint_inequalities/21721025.

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In this thesis we investigate the control of rigid robotic manipulators using robust adaptive sliding mode tracking control. Physical state constraints are incorporated using a multiplicative penalty in a Liapunov function from which we obtain analytic control laws that drive the robot's endeffector into a desired fixed target within finite time.

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Lust, Alexander [Verfasser]. "Eine hybride Methode zur Berechnung von Liapunow-Exponenten / vorgelegt von Alexander Lust." 2006. http://d-nb.info/98122587X/34.

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El, Marhomy Abd Alla M. "Dynamic stability of elastic rotor-bearing systems via Liapunov's direct method." 1987. http://catalog.hathitrust.org/api/volumes/oclc/17853037.html.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1987.
Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 192-201).

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Books on the topic "Liapunov method"

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Saad, Y. Numerical solution of large Lyapunov equations. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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Halanay, Aristide. Applications of Liapunov methods in stability. Dordrecht: Kluwer Academic Publishers, 1993.

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Halanay, A. Applications of Liapunov Methods in Stability. Dordrecht: Springer Netherlands, 1993.

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Halanay, A., and V. Răsvan. Applications of Liapunov Methods in Stability. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1600-8.

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Martyni͡uk, A. A. Stability by Liapunov's matrix function method with applications. New York: Marcel Dekker, 1998.

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Qualitative methods in nonlinear dynamics: Novel approaches to Liapunov's matrix functions. New York: Marcel Dekker, 2002.

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Liapunov-based Control of Mechanical Systems. Birkhauser Verlag AG, 2000.

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Stability Theory by Liapunov's Direct Method. Springer, 2012.

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Rouche, Nicolas, P. Habets, and M. Laloy. Stability Theory by Liapunov's Direct Method. Springer London, Limited, 2012.

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Hahn, Wolfgang. Theory and Application of Liapunov's Direct Method. Dover Publications, Incorporated, 2019.

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Book chapters on the topic "Liapunov method"

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Mei, Zhen. "Liapunov-Schmidt Method." In Numerical Bifurcation Analysis for Reaction-Diffusion Equations, 101–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04177-2_6.

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Merkin, David R. "The Direct Liapunov Method. Autonomous Systems." In Texts in Applied Mathematics, 25–74. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-4046-4_3.

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Kolmanovskii, V., and A. Myshkis. "Applications of the Direct Liapunov Method." In Introduction to the Theory and Applications of Functional Differential Equations, 359–86. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-1965-0_9.

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Chan, Whei-Ching C., and Shui-Nee Chow. "Uniform boundness and genralized inverses in liapunov-schmidt method for subharmonics." In Lecture Notes in Mathematics, 28–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077413.

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Merkin, David R. "Application of the Direct Method of Liapunov to the Investigation of Automatic Control Systems." In Texts in Applied Mathematics, 265–87. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-4046-4_9.

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Rand, Richard H., and Dieter Armbruster. "Liapunov-Schmidt Reduction." In Perturbation Methods, Bifurcation Theory and Computer Algebra, 155–214. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-1060-3_7.

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Gandolfo, Giancarlo. "Liapunov’s Second Method." In Economic Dynamics, 407–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-06822-9_23.

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Gandolfo, Giancarlo. "Liapunov’s Second Method." In Economic Dynamics, 401–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03871-6_22.

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LaSalle, J. P. "Liapunov’s Direct Method." In The Stability and Control of Discrete Processes, 7–12. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-1076-4_2.

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Halanay, A., and V. Răsvan. "Introduction." In Applications of Liapunov Methods in Stability, 1–13. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1600-8_1.

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Conference papers on the topic "Liapunov method"

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Stroe, Ion, and Dumitru I. Caruntu. "Systems Stability Using Weight Functions Method." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80290.

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A new method for systems stability analysis is presented. This method is called weight functions method and it replaces the problem of Liapunov function finding with a problem of finding a number of functions (weight functions) equal to the number of first order differential equations describing the system. It is known that there are not general methods for finding Liapunov functions. The weight functions method is simpler than the classical method since one function at a time has to found. This method’s conditions of solution stability for linear and nonlinear systems are presented. Applications such as Lurie-Postnikov problem and controlled systems stability are presented as well.

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Mahajan, Sanjay K., and Shriram Krishnan. "A Method for State Observer Design in Bilinear Suspension Systems." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0233.

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Abstract This paper presents a simple technique of designing state observers for bilinear suspension models. A 2-DOF quarter-car automotive suspension is considered. The technique produces observer gains which dynamically depend on the control, and are obtained through observer pole placement in a time-varying system that uses Liapunov transformation. It is shown that the proposed use of this method could be effective in the design of modulated suspension systems, with certain limitations on the control law that is used.

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JUNKINS, J., Z. RAHMAN, and H. BANG. "Near-minimum-time maneuvers of flexible vehicles - A Liapunov control law design method." In 28th Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1990. http://dx.doi.org/10.2514/6.1990-663.

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Pandiyan, R., J. S. Bibb, and S. C. Sinha. "Liapunov-Floquet Transformation: Computation and Applications to Periodic Systems." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0122.

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Abstract In this paper, a new analysis technique in the study of dynamical systems with periodically varying parameters is presented. The method is based on the fact that all linear periodic systems can be replaced by similar linear time-invariant systems through a suitable periodic transformation known as the Liapunov-Floquet (L-F) transformation. A general technique for the computation of the L-F transformation matrices is suggested. In this procedure, the state vector and the periodic matrix of the linear system equations are expanded in terms of the shifted Chebyshev polynomials over the principal period. Such an expansion reduces the original differential problem to a set of linear algebraic equations from which the state transition matrix (STM) can be constructed over the period in closed form. Application of Floquet theory and eigen analysis to the resulting STM yields the L-F transformation matrix in a form suitable for algebraic manipulations. The utility of the L-F transformation in obtaining solutions of both linear and nonlinear dynamical systems with periodic coefficients is demonstrated. It is shown that the application of L-F transformation to free and harmonically forced linear periodic system directly provides the conditions for internal and combination resonances and external resonances, respectively. The application of L-F transformation to quasilinear periodic systems provides a dynamically similar quasilinear systems whose linear parts are time-invariant and the solutions of such systems can be obtained through an application of the time-dependent normal form theory. These solutions can be transformed back to the original coordinates using the inverse L-F transformation. Two dynamical systems, namely, a commutative system and a Mathieu type equation are considered to demonstrate the effectiveness of the method. It is shown that the present technique is virtually free from the small parameter restriction unlike averaging and perturbation procedures and can be used even for those systems for which the generating solutions do not exist in the classical sense. The results obtained from the proposed technique are compared with those obtained using the perturbation method and numerical solutions computed via a Runge-Kutta type algorithm. The technique is found to be very powerful in the analysis of linear and nonlinear periodic dynamical systems.

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Dobov'ek, Igor. "An Application of the Direct Method of Liapunov in Stability Analysis of Semilinear Systems." In 2015 International Conference on Modeling, Simulation and Applied Mathematics. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/msam-15.2015.45.

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Dale, Sanda, Helga Maria Silaghi, and Claudiu Costea. "Procedural and software development of a Liapunov-based stability analysis method for interpolative-type control systems." In 2013 17th International Conference on System Theory, Control and Computing (ICSTCC). IEEE, 2013. http://dx.doi.org/10.1109/icstcc.2013.6688952.

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Butcher, Eric A., and S. C. Sinha. "Canonical Perturbation of a Fast Time-Periodic Hamiltonian via Liapunov-Floquet Transformation." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4107.

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Abstract In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic, the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent canonical perturbation theory may be successfully applied. For this purpose, the Liapunov-Floquet (L-F) transformation and its inverse associated with the unperturbed time-periodic quadratic Hamiltonian are computed using a recently developed technique. Action-angle variables and time-dependent canonical perturbation theory are then utilized to find the solution in the original coordinates. The results are compared for accuracy with solutions obtained by both numerical integration and by the classical method of directly applying the time-dependent perturbation theory in which the time-periodic quadratic part is treated as another perturbation term. A strongly excited Mathieu-Hill quadratic Hamiltonian with a cubic perturbation and a nonlinear time-periodic Hamiltonian without a constant quadratic part serve as illustrative examples. It is shown that, unlike the classical method in which the internal excitation must be weak, the proposed formulation provides accurate solutions for an arbitrarily large internal excitation.

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Guttalu, Ramesh S., and Henryk Flashner. "A Comparison of Analytical Methods for Studying a Single-DOF Nonlinear System." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4023.

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Abstract Qualitative analysis of periodic nonlinear dynamical systems is often carried out using perturbation and averaging methods. Important topics of study for this class of systems are determination of periodic solutions, their stability analysis and their bifurcation characteristics. Since perturbation and averaging methods rely on expanding the solution in terms of a small parameter, important questions such as convergence and accuracy of the solution arise which are often difficult to answer. This paper presents a preliminary study of the comparison of the method of averaging, Liapunov-Floquet transformation, and point mapping. The methods are applied for the analysis of a damped pendulum subjected to periodic support motion. To evaluate the accuracy of various methods, the results of stability analysis are compared with direct numerical solution for different parameter values of the system.

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Shiau, Ting Nung, Jon Li Hwang, and Yuan Bin Chang. "A Study on Stability and Response Analysis of a Nonlinear Rotor System With Mass Unbalance and Side Load." In ASME 1992 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/92-gt-007.

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The stability of steady state synchronous and nonsynchronous response of a nonlinear rotor system supported by squeeze-film dampers is investigated. The nonlinear differential equations which govern the motion of rotor bearing system are obtained by using the Generalized Polynomial Expansion Method. The steady state response of system is obtained by using the hybrid numerical method which combines the merits of the harmonic balance and collocation methods. The stability of system response is examined using Floquet-Liapunov theory. Using the theory, the performance may be evaluated with the calculation of derivatives of nonlinear hydrodynamic forces of the squeeze-film damper with respect to displacement and velocity of the journal center. In some cases, these derivatives can be expressed in closed form and the prediction of the dynamic characteristic of the nonlinear rotor system will be more effective. The stability results are compared to those using a direct numerical integration method and both are in good agreement.

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Shiau, T. N., J. S. Rao, Y. D. Yu, and S. T. Choi. "Steady State Response and Stability of Rotating Composite Blades With Frictional Damping." In ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-469.

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Abstract:

Friction dampers are widely used to improve the performance of rotating blades. This paper is concerned with the steady stale response and stability analysis of ratating composite plates in the presence of non linear friction damping. Direct Integration Method (DIM) and Harmonic Balance Method (HBM) are used to determine the steady state response due to periodic lateral external forces. In addition, an alternate procedure, Hybrid Method (HM) is proposed for this analysis to substantiate the results from DIM and HBM. The analysis shows that the steady state response is a function of friction damping magnitude as well as its location besides the excitation frequency and the rotational speed. A stability analysis of the composite blades is also made by including periodic in-plane excitation using Floquet-Liapunov theory.

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Reports on the topic "Liapunov method"

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Grossberg, Stephen. Content-Addressable Memory Storage by Neural Networks: A General Model and Global Liapunov Method,. Fort Belvoir, VA: Defense Technical Information Center, March 1988. http://dx.doi.org/10.21236/ada192716.

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