Relevant bibliographies by topics / Timoshenko Equation

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Academic literature on the topic 'Timoshenko Equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Timoshenko Equation"

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Lou, Menglin, Qiuhua Duan, and Genda Chen. "Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams." Shock and Vibration 12, no. 6 (2005): 425–34. http://dx.doi.org/10.1155/2005/824616.

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Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail.
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Cao, MS, W. Xu, Z. Su, W. Ostachowicz, and N. Xia. "Local coordinate systems-based method to analyze high-order modes of n-step Timoshenko beam." Journal of Vibration and Control 23, no. 1 (August 9, 2016): 89–102. http://dx.doi.org/10.1177/1077546315573919.

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High-frequency transverse vibration of stepped beams has attracted increasing attention in various industrial areas. For an n-step Timoshenko beam, the governing differential equations of transverse vibration have been well established in the literature on the basis of assembling classic Timoshenko beam equations for uniform beam segments. However, solving the governing differential equation has not been resolved well to date, manifested by a computational bottleneck: only the first k modes ( k ≤ 12) are solvable for i-step ( i ≥ 0) Timoshenko beams. This bottleneck diminishes the completeness of stepped Timoshenko beam theory. To address this problem, this study first reveals the root cause of the bottleneck in solving the governing differential equations for high-order modes, and then creates a sophisticated method, based on local coordinate systems, that can overcome the bottleneck to accomplish high-order mode shapes of an n-step Timoshenko beam. The proposed method uses a set of local coordinate systems in place of the conventional global coordinate system to characterize the transverse vibration of an n-step Timoshenko beam. With the method, the local coordinate systems can simplify the frequency equation for the vibration of an n-step Timoshenko beam, making it possible to obtain high-order modes of the beam. The accuracy, capacity, and efficiency of the method based on local coordinate systems in acquiring high-order modes are corroborated using the well-known exact dynamic stiffness method underpinned by the Wittrick-Williams algorithm as a reference. Removal of the bottlenecks in solving the governing differential equations for high-order modes contributes usefully to the completeness of stepped Timoshenko beam theory.
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Guo, Shi Wei. "Dual Variables System Analysis for Timoshenko Beam." Applied Mechanics and Materials 423-426 (September 2013): 1473–84. http://dx.doi.org/10.4028/www.scientific.net/amm.423-426.1473.

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Regarding the displacements and internal forces of Timoshenko beams as dual variables, Timoshenko beam problems were included into dual variables system. Corresponding to state transfer solution of Hamiltonian dual equation, transfer form solution of dual variables for Timoshenko beams was presented. Based on transfer form solution, element stiffness equation and the shape functions of Timoshenko beams were deduced, boundary integral equation and the fundamental solution function of Timoshenko beams were obtained, which reveal the intrinsic relationships among the finite element method, the boundary element method and dual variables system of Timoshenko beams. Based on the transfer form solution of Timoshenko beams, transfer matrix method for chain structure of Timoshenko beams was proposed. For chain beam structure problems, transfer matrix method is simple, intuitive, and has the advantages of good boundary adaptability and less calculation in solving the node variables of chain structures with recursive solution. The numerical results demonstrate the feasibility and accuracy of transfer matrix method in complex beam structure problems.
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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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White, M. W. D., and G. R. Heppler. "Vibration Modes and Frequencies of Timoshenko Beams With Attached Rigid Bodies." Journal of Applied Mechanics 62, no. 1 (March 1, 1995): 193–99. http://dx.doi.org/10.1115/1.2895902.

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The equations of motion and boundary conditions for a free-free Timoshenko beam with rigid bodies attached at the endpoints are derived. The natural boundary conditions, for an end that has an attached rigid body, that include the effects of the body mass, first moment of mass, and moment of inertia are included. The frequency equation for a free-free Timoshenko beam with rigid bodies attached at its ends which includes all the effects mentioned above is presented and given in terms of the fundamental frequency equations for Timoshenko beams that have no attached rigid bodies. It is shown how any support / rigid-body condition may be easily obtained by inspection from the reported frequency equation. The mode shapes and the orthogonality condition, which include the contribution of the rigid-body masses, first moments, and moments of inertia, are also developed. Finally, the effect of the first moment of the attached rigid bodies is considered in an illustrative example.
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Soltani, Masoumeh, and Behrouz Asgarian. "Finite Element Formulation for Linear Stability Analysis of Axially Functionally Graded Nonprismatic Timoshenko Beam." International Journal of Structural Stability and Dynamics 19, no. 02 (February 2019): 1950002. http://dx.doi.org/10.1142/s0219455419500020.

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An improved approach based on the power series expansions is proposed to exactly evaluate the static and buckling stiffness matrices for the linear stability analysis of axially functionally graded (AFG) Timoshenko beams with variable cross-section and fixed–free boundary condition. Based on the Timoshenko beam theory, the equilibrium equations are derived in the context of small displacements, considering the coupling between the transverse deflection and angle of rotation. The system of stability equations is then converted into a single homogeneous differential equation in terms of bending rotation for the cantilever, which is solved numerically with the help of the power series approximation. All the mechanical properties and displacement components are thus expanded in terms of the power series of a known degree. Afterwards, the shape functions are gained by altering the deformation shape of the AFG nonprismatic Timoshenko beam in a power series form. At the end, the elastic and buckling stiffness matrices are exactly determined by the weak form of the governing equation. The precision and competency of the present procedure in stability analysis are assessed through several numerical examples of axially nonhomogeneous and homogeneous Timoshenko beams with clamped-free ends. Comparison is also made with results obtained using ANSYS and other solutions available, which indicates the correctness of the present method.
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Lárez, Hanzel, Hugo Leiva, and Darwin Mendoza. "Interior Controllability of a Timoshenko Type Equation." International Journal of Control Science and Engineering 1, no. 1 (August 31, 2012): 15–21. http://dx.doi.org/10.5923/j.control.20110101.03.

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Shou-kui, Si. "Backward wellposedness of nonuniform Timoshenko beam equation." Journal of Zhejiang University-SCIENCE A 2, no. 2 (April 2001): 161–64. http://dx.doi.org/10.1631/jzus.2001.0161.

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Esquivel-Avila, Jorge Alfredo. "Dynamic Analysis of a Nonlinear Timoshenko Equation." Abstract and Applied Analysis 2011 (2011): 1–36. http://dx.doi.org/10.1155/2011/724815.

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We characterize the global and nonglobal solutions of the Timoshenko equation in a bounded domain. We consider nonlinear dissipation and a nonlinear source term. We prove blowup of solutions as well as convergence to the zero and nonzero equilibria, and we give rates of decay to the zero equilibrium. In particular, we prove instability of the ground state. We show existence of global solutions without a uniform bound in time for the equation with nonlinear damping. We define and use a potential well and positive invariant sets.
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AROSIO, A. "ON THE NONLINEAR TIMOSHENKO-KIRCHHOFF BEAM EQUATION." Chinese Annals of Mathematics 20, no. 04 (October 1999): 495–506. http://dx.doi.org/10.1142/s0252959999000564.

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Dissertations / Theses on the topic "Timoshenko Equation"

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Acasiete, Quispe Frank Henry. "Modelagem computacional da viga de Timoshenko submetida a cargas pontuais." Laboratório Nacional de Computação Científica, 2016. https://tede.lncc.br/handle/tede/246.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
We studied the uniform stabilization of a class of Timoshenko systems with tip load at the free end of the beam. Our main result is to prove that the semigroup associated to this model is not exponentially stable. Moreover, we prove that the semigroup decays polynomially to zero. When the damping mechanism is e ective only on the boundary of the rotational angle, the solution also decays polynomially with rate depending on the coe cients of the problem.
Estudamos a estabilização uniforme para uma classe de sistemas de Timoshenko com carga pontual na extremidade livre da viga. Nosso principal resultado é provar que o semigrupo associado com este modelo não é exponencialmente estável. Além disso, provamos que o semigrupo decai polinomialmente. Quando a dissipação é eficaz apenas sobre o limite do ângulo de rotação, a solução também decai polinomialmente com taxa de decaimento dependendo dos coeficientes do problema.
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Tonzani, Giulio Maria. "Free Vibrations Analysis of Timoshenko Beams on Different Elastic Foundations via Three Alternative Models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017.

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The scope of the research is to provide a simpler and more consistent equation for the analysis of the natural frequencies of a beam with respect to the widely used one introduced by Timoshenko in 1916. To this purpose, the free vibrations of a beam resting on Winkler or/and Pasternak elastic foundations are analyzed via original Timoshenko theory as well as two of its truncated versions, which have been proposed by Elishakoff in recent years to overcome the mathematical difficulties associated with the fourth-order time derivative of the deflection. Former equation takes into account for both shear deformability and rotary inertia, while latter one is based upon incorporation of the slope inertia effect. Detailed comparisons and derivations of the three models are given for six different sets of boundary conditions stemming by the various possible combinations of three of the most typical end constraints for a beam: simply supported end, clamped end and free end. It appears that the two new theories are able to overcome the disadvantage of the original Timoshenko equation without predicting the unphysical second spectrum and to produce very good approximations for the most relevant values of natural frequencies. As a consequence, the inclusion of these simpler approaches is suggested in future works. An intriguing intermingling phenomenon is also presented for the simply supported case together with a detailed discussion about the possible existence of zero frequencies for the free–free beam and the simply supported–free beam in the context of different types of foundations.
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Bassam, Maya. "Étude de la stabilité de quelques systèmes d'équations des ondes couplées sur des domaines bornés et non bornés." Thesis, Valenciennes, 2014. http://www.theses.fr/2014VALE0034/document.

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La thèse est portée essentiellement sur la stabilisation indirecte d’un système de deux équations des ondes couplées et sur la stabilisation frontière de poutre de Rayleigh.Dans le cas de la stabilisation d’un système d’équations d’onde couplées, le contrôle est introduit dans le système directement sur le bord du domaine d’une seule équation dans le cas d’un domaine borne ou à l’intérieur d’une seule équation mais dans le cas d’un domaine non borné. La nature du système ainsi couplé dépend du couplage des équations et de la nature arithmétique des vitesses de propagations, et ceci donne divers résultats pour la stabilisation polynomiale ainsi la non stabilité.Dans le cas de la stabilisation de poutre de Rayleigh, l’équation est considérée avec un seul contrôle force agissant sur bord du domaine. D’abord, moyennant le développement asymptotique des valeurs propres et des vecteurs propres du système non contrôlé, un résultat d’observabilité ainsi qu’un résultat de bornétude de la fonction de transfert correspondant sont obtenus. Alors, un taux de décroissance polynomial de l’énergie du système est établi. Ensuite, moyennant une étude spectrale combinée avec une méthode fréquentielle, l’optimalité du taux obtenu est assurée
The thesis is driven mainly on indirect stabilization system of two coupled wave equations and the boundary stabilization of Rayleigh beam equation. In the case of stabilization of a coupled wave equations, the Control is introduced into the system directly on the edge of the field of a single equation in the case of a bounded domain or inside a single equation but in the case of an unbounded domain. The nature of thus coupled system depends on the coupling equations and arithmetic Nature of speeds of propagation, and this gives different results for the polynomial stability and the instability. In the case of stabilization of Rayleigh beam equation, we consider an equation with one control force acting on the edge of the area. First, using the asymptotic expansion of the eigenvalues and vectors of the uncontrolled system an observability result and a result of boundedness of the transfer function are obtained. Then a polynomial decay rate of the energy of the system is established. Then through a spectral study combined with a frequency method, optimality of the rate obtained is assured
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Cao, Hongmei. "Problémes bien-posés et étude qualitative pour des équations cinétiques et des équations dissipatives." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMR044/document.

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Dans cette thèse, nous étudions certaines équations différentielles partielles avec mécanisme dissipatif, telles que l'équation de Boltzmann, l'équation de Landau et certains systèmes hyperboliques symétriques avec type de dissipation. L'existence globale de solutions ou les taux de dégradation optimaux des solutions pour ces systèmes sont envisagées dans les espaces de Sobolev ou de Besov. Les propriétés de lissage des solutions sont également étudiées. Dans cette thèse, nous prouvons principalement les quatre suivants résultats, voir les chapitres 3-6 pour plus de détails. Pour le premier résultat, nous étudions le problème de Cauchy pour le non linéaire inhomogène équation de Landau avec des molécules Maxwelliennes (= 0). Voir des résultats connus pour l'équation de Boltzmann et l'équation de Landau, leur existence globale de solutions est principalement prouvée dans certains espaces de Sobolev (pondérés) et nécessite un indice de régularité élevé, voir Guo [62], une série d'oeuvres d'Alexander Morimoto-Ukai-Xu-Yang [5, 6, 7, 9] et des références à ce sujet. Récemment, Duan-Liu-Xu [52] et Morimoto-Sakamoto [145] ont obtenu les résultats de l'existence globale de solutions à l'équation de Boltzmann dans l'espace critique de Besov. Motivés par leurs oeuvres, nous établissons l'existence globale de la solution dans des espaces de Besov spatialement critiques dans le cadre de perturbation. Précisément, si le datum initial est une petite perturbation de la distribution d'équilibre dans l'espace Chemin-Lerner eL 2v (B3=2 2;1 ), alors le problème de Cauchy de Landau admet qu'une solution globale appartient à eL 1t eL 2v (B3=2 2;1 ). Notre résultat améliore le résultat dans [62] et étend le résultat d'existence globale de l'équation de Boltzmann dans [52, 145] à l'équation de Landau. Deuxièmement, nous considérons le problème de Cauchy pour l'équation de Kac non-coupée spatialement inhomogène. Lerner-Morimoto-Pravda-Starov-Xu a considéré l'équation de Kac non-coupée spatialement inhomogène dans les espaces de Sobolev et a montré que le problème de Cauchy pour la fluctuation autour de la distribution maxwellienne admise S 1+ 1 2s 1+ 1 2s Propriétés de régularité Gelfand-Shilov par rapport à la variable de vélocité et propriétés de régularisation G1+ 1 2s Gevrey à la variable de position. Et les auteurs ont supposé qu'il restait encore à déterminer si les indices de régularité 1 + 1 2s étaient nets ou non. Dans cette thèse, si la donnée initiale appartient à l'espace de Besov spatialement critique, nous pouvons prouver que l'équation de Kac inhomogène est bien posée dans un cadre de perturbation. De plus, il est montré que la solution bénéficie des propriétés de régularisation de Gelfand-Shilov en ce qui concerne la variable de vitesse et des propriétés de régularisation de Gevrey en ce qui concerne la variable de position. Dans notre thèse, l'indice de régularité de Gelfand-Shilov est amélioré pour être optimal. Et ce résultat est le premier qui présente un effet de lissage pour l'équation cinétique dans les espaces de Besov. A propos du troisième résultat, nous considérons les équations de Navier-Stokes-Maxwell compressibles apparaissant dans la physique des plasmas, qui est un exemple concret de systèmes composites hyperboliques-paraboliques à dissipation non symétrique. On observe que le problème de Cauchy pour les équations de Navier-Stokes-Maxwell admet le mécanisme dissipatif de type perte de régularité. Par conséquent, une régularité plus élevée est généralement nécessaire pour obtenir le taux de dégradation optimal de L1(R3)-L2(R3) type, en comparaison avec cela pour l'existence globale dans le temps de solutions lisses
In this thesis, we study some kinetic equations and some partial differential equations with dissipative mechanism, such as Boltzmann equation, Landau equation and some non-symmetric hyperbolic systems with dissipation type. Global existence of solutions or optimal decay rates of solutions for these systems are considered in Sobolev spaces or Besov spaces. Also the smoothing properties of solutions are studied. In this thesis, we mainly prove the following four results, see Chapters 3-6 for more details. For the _rst result, we investigate the Cauchy problem for the inhomogeneous nonlinear Landau equation with Maxwellian molecules ( = 0). See from some known results for Boltzmann equation and Landau equation, their global existence of solutions are mainly proved in some (weighted) Sobolev spaces and require a high regularity index, see Guo [62], a series works of Alexandre-Morimoto-Ukai-Xu-Yang [5, 6, 7, 9] and references therein. Recently, Duan-Liu-Xu [52] and Morimoto-Sakamoto [145] obtained the global existence results of solutions to the Boltzmann equation in critical Besov spaces. Motivated by their works, we establish the global existence of solutions for Landau equation in spatially critical Besov spaces in perturbation framework. Precisely, if the initial datum is a small perturbation of the equilibrium distribution in the Chemin-Lerner space eL 2v (B3=2 2;1 ), then the Cauchy problem of Landau equation admits a global solution belongs to eL 1t eL 2v (B3=2 2;1 ). Our results improve the result in [62] and extend the global existence result for Boltzmann equation in [52, 145] to Landau equation. Secondly, we consider the Cauchy problem for the spatially nhomogeneous non-cuto_ Kac equation. Lerner-Morimoto-Pravda-Starov-Xu [117] considered the spatially inhomogeneous non-cuto_ Kac equation in Sobolev spaces and showed that the Cauchy problem for the uctuation around the Maxwellian distribution admitted S 1+ 1 2s 1+ 1 2s Gelfand-Shilov regularity properties with respect to the velocity variable and G1+ 1 2s Gevrey regularizing properties with respect to the position variable. And the authors conjectured that it remained still open to determine whether the regularity indices 1+ 1 2s is sharp or not. In this thesis, if the initial datum belongs to the spatially critical Besov space eL 2v (B1=2 2;1 ), we prove the well-posedness to the inhomogeneous Kac equation under a perturbation framework. Furthermore, it is shown that the weak solution enjoys S 3s+1 2s(s+1) 3s+1 2s(s+1) Gelfand-Shilov regularizing properties with respect to the velocity variableand G1+ 1 2s Gevrey regularizing properties with respect to the position variable. In our results, the Gelfand-Shilov regularity index is improved to be optimal. And this result is the _rst one that exhibits smoothing e_ect for the kinetic equation in Besov spaces. About the third result, we consider compressible Navier-Stokes-Maxwell equations arising in plasmas physics, which is a concrete example of hyperbolic-parabolic composite systems with non-symmetric dissipation. It is observed that the Cauchy problem for Navier-Stokes-Maxwell equations admits the dissipative mechanism of regularity-loss type. Consequently, extra higher regularity is usually needed to obtain the optimal decay rate of L1(R3)-L2(R3) type, in comparison with that for the global-in-time existence of smooth solutions
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Almeida, Junior Dilberto da Silva. "Estabilidade assintótica e numérica de sistemas dissipativos de vigas de Timoshenko e vigas de Bresse." Laboratório Nacional de Computação científica, 2009. https://tede.lncc.br/handle/tede/168.

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Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior
In this thesis we study models of plane beams governed by Timoshenko s hypothesis and models of curved beams governed by Bresse s hypothesis in the presence of dissipative mechanism, which act partially on the rotation function in the transverse section or on the transverse displacement ones. We realize an analytic study of these models and we show they are exponentially stable, if and only if, the velocities of wave propagations are equal. Such result is more interesting on the point of mathematical view whereas in the practice the velocities of wave propagations are never equal. We study in the general case the polynomial stability property and we show the dissipative systems are stable and, in these situations, the decay rate can be improved according to the regularity of the initial data. In the specific cases of the models of curved beams, the differential factor is in the mathematical techniques we use, which they are much more sophisticated. Finally we realize a numerical study of the dissipative models using semi-discrete and totally discrete models in finite differences, purposing to avoid the problem of shear locking and to we confirm the theoretical results developed here.
Neste trabalho estudamos modelos de vigas planas governados pelas hipóteses de Timoshenko e modelos de vigas curvas governados pelas hipóteses de Bresse, na presença de mecanismos dissipativos atuando parcialmente, quer sobre a função de rotação na seção transversal ou sobre a função de deslocamento transversal. Desenvolvemos um estudo analítico desses modelos e mostramos que eles são exponencialmente estáveis se, e somente se, as velocidades de propagações de ondas são iguais. Este resultado é interessante do ponto de vista matemático, visto que na prática as velocidades de propagações de ondas nunca são iguais. No caso geral, estudamos a propriedade de estabilidade polinomial e mostramos que os sistemas dissipativos são polinomialmente estáveis, com taxas de decaimento que podem ser melhoradas de acordo com a regularidade dos dados iniciais. Nos casos específficos dos modelos de vigas curvas, o fator diferencial reside nas técnicas matemáticas que aplicamos, as quais são muito mais sofisticadas. Finalmente realizamos um estudo numérico dos modelos dissipativos usando modelos semidiscretos e totalmente discretos em diferenças finitas, com a preocupação de se evitar o problema de trancamento no cortante e para comprovarmos os resultados teóricos desenvolvidos nesta tese.
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AIRES, José Fernando Leite. "Sobre existência e não-existência de soluções para problemas elípticos que envolvem um operador não-linear do tipo Timoshenko." Universidade Federal de Campina Grande, 2004. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1106.

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Capes
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Baldez, Carlos Alessandro da Costa. "Problemas de contacto transversal, estacionário e dinâmico." Laboratório Nacional de Computação Científica, 2012. https://tede.lncc.br/handle/tede/234.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes)
In this thesis we study the transverse contact problem to Timoshenko beam' to elastic and thermoelastic model, whose the vertical displacement is restricted, with Signorini's contact condition. We make the mathematical modelling and well-posed model. We consider the discrete model and we make the computational modelling to the problem. The main result this work is to model the transverse contact problem and to show the qualitative properties of solution, for example, the exponential decay for energy of the system. We obtain numeric convergence rates to numeric solutions, and that enabled us to obtain numerical and computationally properties.
Nesta tese estudamos o problema de contacto transversal de uma viga, de Timoshenko, com propriedades elástica e termoelástica, restrita ao seu movimento transversal, com condição de contacto do tipo Signorini. Fazemos a modelagem matemática do problema mostrando a boa colocação do modelo. Discretizamos o modelo e fazemos a modelagem computacional do problema. O ponto alto de nosso trabalho consiste em modelar o problema de contacto transversal e mostrar as propriedades qualitativas da solução como, por exemplo, o decaimento exponencial da energia. Obtemos taxa de convergência da solução numérica, com esse resultado, tornou-se possível obter as propriedades numéricas e computacionais.
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Youssef, Wael. "Contrôle et stabilisation de systèmes élastiques couplés." Thesis, Metz, 2009. http://www.theses.fr/2009METZ017S/document.

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Cette thèse est constituée de deux parties principales. Dans la première partie on traite l'observabilité et la contrôlabilité exacte internes indirectes des systèmes hyperboliques faiblement couplés et du système de Timoshenko. La deuxième partie est consacrée à l'étude de problèmes concernant la stabilisation directe du système de Bresse par des feedbacks non linéaires en utilisant la méthode des multiplicateurs et des techniques d'inégalités intégrales, et sa stabilisation indirecte seulement par deux feedbacks localement distribués au voisinage du bord en utilisant l'approche de fréquence de domaine. On traite dans cette partie aussi la stabilisation indirecte du système de Timoshenko dans le cas d'un seul feedback localement distribué au voisinage du bord
This thesis consists of two main parts. In the fi#rst part, it treats the indirect internal observability and exact controllability of a weakly coupled hyperbolic system and of the Timoshenko system. The second part is devoted to the study of problems concerning the direct stabilization of the Bresse system by non-linear feedbacks using multiplier method and integral inequality techniques, and its indirect stabilization only by two locally distributed feedbacks at the neighborhood of the boundary using the frequency domain method. Is treated in this part also the indirect stabilization of the Timoshenko system subject to a single feedback locally distributed at the neighborhood of the boundary
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"Numerical Solutions of Wave Propagation in Beams." Master's thesis, 2016. http://hdl.handle.net/2286/R.I.38587.

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abstract: In order to verify the dispersive nature of transverse displacement in a beam, a deep understanding of the governing partial differential equation is developed. Using the finite element method and Newmark’s method, along with Fourier transforms and other methods, the aim is to obtain consistent results across each numerical technique. An analytical solution is also analyzed for the Euler-Bernoulli beam in order to gain confidence in the numerical techniques when used for more advance beam theories that do not have a known analytical solution. Three different beam theories are analyzed in this report: The Euler-Bernoulli beam theory, Rayleigh beam theory and Timoshenko beam theory. A comparison of the results show the difference between each theory and the advantages of using a more advanced beam theory for higher frequency vibrations.
Dissertation/Thesis
Masters Thesis Civil Engineering 2016
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Huang, Chien-Chih, and 黃建志. "The Equations of Motion and Steady State Solution of Three Dimensional Rotating Timoshenko Beam." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/55219132923295777137.

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碩士
國立交通大學
機械工程系
88
The objective of this paper is to derive the equations of motion and to solve the steady state axial and torsional deformations for the doubly symmetric three dimensional rotating Timoshenko beam. A co-rotational formulation combined with the rotating frame method is used here. The rotating beam is divided into several beam elements. The kinematics of beam element is defined in terms of rotating element coordinates, which are constructed at the current configuration of the beam element. The equations of motion of the beam element are derived by consistent linearization of the fully geometrically nonlinear beam theory using the d’Alembert principle and the virtual work principle in the current rotating element coordinates. The steady state equilibrium equations of the rotating beam element can be obtained from the equations of motion of the beam element. A Galerkin method is applied to the steady state equilibrium equations and an incremental iterative method based on the Newton-Raphson method is used here for the solution of the nonlinear steady state equilibrium equations. Numerical examples are studied to investigate the effect of rotating speed, setting angle, cross section of the beam and length of the beam on the steady state axial and torsional deformations for the three dimensional rotating Timoshenko beam.
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Books on the topic "Timoshenko Equation"

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Elishakoff, Isaac. Beam and Plate Theories: A New Look at Timoshenko-Ehrenfest and Uflyand-Mindlin Equations. World Scientific Publishing Co Pte Ltd, 2020.

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Book chapters on the topic "Timoshenko Equation"

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Elishakoff, Isaac. "An Equation Both More Consistent and Simpler Than the Bresse-Timoshenko Equation." In Solid Mechanics and Its Applications, 249–54. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3467-0_19.

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Öchsner, Andreas. "Timoshenko Beams." In Partial Differential Equations of Classical Structural Members, 31–46. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-35311-7_4.

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Wang, Dian-kun, and Fu-le Li. "Numerical Simulation for the Timoshenko Beam Equations with Boundary Feedback." In Communications in Computer and Information Science, 106–11. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18129-0_17.

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Avalos, George, and Daniel Toundykov. "On Stability and Trace Regularity of Solutions to Reissner-Mindlin-Timoshenko Equations." In Modern Aspects of the Theory of Partial Differential Equations, 79–91. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0069-3_5.

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Mosavi, Amir, Rami Benkreif, and Annamária R. Varkonyi-Koczy. "Comparison of Euler-Bernoulli and Timoshenko Beam Equations for Railway System Dynamics." In Advances in Intelligent Systems and Computing, 32–40. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67459-9_5.

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Popov, Svilen I., and Vassil M. Vassilev. "Symmetries and Conservation Laws of a System of Timoshenko Beam Type Equations." In Advanced Computing in Industrial Mathematics, 372–80. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71616-5_33.

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Qin, Yuming, and Zhiyong Ma. "Stability for a Timoshenko-type Thermoelastic Equations of Type III with a Past History." In Global Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic Models, 73–96. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-1714-8_4.

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Chirikov, Victor A. "Approximate Solutions of Timoshenko’s Differential Equation for the Free Transverse Vibration of Stubby Beams." In Advances in Intelligent Systems and Computing, 210–19. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68324-9_23.

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"An Equation Both More Consistent and Simpler than the Bresse-Timoshenko Equation." In Carbon Nanotubes and Nanosensors, 319–24. Hoboken, NJ, USA: John Wiley & Sons, Inc, 2013. http://dx.doi.org/10.1002/9781118562000.app10.

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"Exact Solution of Timoshenko–Ehrenfest Equations." In Handbook on Timoshenko-Ehrenfest Beam and Uflyand-Mindlin Plate Theories, 107–38. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813236523_0002.

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Conference papers on the topic "Timoshenko Equation"

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Karch, Gerald, and Jörg Wauer. "Rotating, Axially Loaded Timoshenko Shaft: Modeling and Stability." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0206.

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Abstract For studying the stability of a rotating shaft subject to axial load, the derivation of correct stability equations is the essential preliminary problem. Here, the model of a uniform non-circular Timoshenko shaft under a compressive end load of constant magnitude is dealt with. Starting point is the nonlinear boundary value problem for coupled extensional-bending-torsional oscillations where a finite strain beam theory in a floating reference frame following the rigid body rotation is applied. First, the equation set describing the stationary shaft configuration is deduced. Next, the variational equations for small superimposed perturbations are derived. The only interesting stability problem for usual properties of the shaft cross section is constituted by a linear boundary value problem describing the bending vibrations. The corresponding characteristic equation is evaluated finally to find the critical buckling load also for the case of an oval shaft not considered before.
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Taskesen, Hatice, and Necat Polat. "Existence results for a nonlinear Timoshenko equation with high initial energy." In ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930449.

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Chen, Chang-New. "Dynamic Response of Timoshenko Beam Structures Solved by DQEM Using EDQ." In ASME 2002 Pressure Vessels and Piping Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/pvp2002-1290.

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The dynamic response of Timoshenko beam structures is solved by using the DQEM to the space discretization and EDQ to the time discretization. In the DQEM discretization, DQ is used to define the discrete element model. Discrete dynamic equilibrium equations defined at interior nodes in all elements, transition conditions defined on the inter-element boundary of two adjacent elements and boundary conditions at the structural boundary form a dynamic equation system at a specified time stage. The dynamic equilibrium equation system is solved by the direct time integration schemes of time-element by time-element method and stages by stages method which are developed by using EDQ and DQ. Numerical results obtained by the developed numerical algorithms are presented. They demonstrate the developed numerical solution procedure.
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Ramezani, Asghar, and Mehrdaad Ghorashi. "Nonlinear Free Vibrations of a Timoshenko Beam Using Multiple Scales Method." In ASME 7th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2004. http://dx.doi.org/10.1115/esda2004-58298.

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In this paper, the large amplitude free vibration of a cantilever Timoshenko beam is considered. To this end, first Hamilton’s principle is used in deriving the partial differential equation of the beam response under the mentioned conditions. Then, implementing the Galerkin’s method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the thick-cantilevered beam.
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Ohadi, A. R., H. Mehdigholi, and E. Esmailzadeh. "Vibration and Frequency Analysis of Non-Uniform Timoshenko Beams Subjected to Axial Forces." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-43001.

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Dynamic and stability analysis of non-uniform Timoshenko beam under axial loads is carried out. In the first case of study, the axial force is assumed to be perpendicular to the shear force, while for the second case the axial force is tangent to the axis of the beam column. For each case, a pair of differential equations coupled in terms of the flexural displacement and the angle of rotation due to bending was obtained. The parameters of the frequency equation were determined for various boundary conditions. Several illustrative examples of uniform and non-uniform beams with different boundary conditions such as clamped supported, elastically supported, and free end mass have been presented. The stability analysis, for the variation of the natural frequencies of the uniform and non-uniform beams with the axial force, has also been investigated.
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Zhu, Yang, Jean W. Zu, and Minghui Yao. "Modeling of Piezoelectric Energy Harvester: A Comparison Between Euler-Bernoulli Theory and Timoshenko Theory." In ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2011. http://dx.doi.org/10.1115/smasis2011-4995.

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Harvesting vibration energy using piezoelectric materials has gained considerable attention over the past few years. Typically, a piezoelectric energy harvester is a unimorph or bimorph cantilevered beam which undergoes base vibration. The focus of this paper is to compare the Euler-Bernoulli model and the Timoshenko model, which are both used for modeling the vibration-based energy harvester. Procedures of deriving the electro-mechanical equation of motion are provided, following exact expressions for the electrical output in two models. Parametric case studies are carried out in order to compare the frequency response of two models. Simulation results show that there is a great difference between Euler-Bernoulli model and Timoshenko model at low length-to-thickness aspect ratio. Such difference diminishes and becomes negligible as aspect ratio increases. It is shown that for the design of piezoelectric energy harvester with small aspect ratio, Timoshenko model can be more accurate than Euler-Bernoulli model in predicting the system behavior.
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Chen, Chang-New. "Influence of Axial Force on the Deflection of Timoshenko Beam Structures Solved by DQEM." In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26032.

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The influence of axial force on the deflection of Timoshenko beam structures is analyzed by differential quadrature element method (DQEM). The DQEM uses the differential quadrature to discretize the governing differential equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.
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Ghoneim, H., and D. J. Lawrie. "Dynamic Analysis of a Hyperbolic Composite Coupling." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79558.

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A novel hyperbolic composite coupling is proposed. In addition to enjoying the advantages of composite materials, the proposed coupling can be readily integrated with composite drive shaft into a single unit. A mathematical model of the coupling is developed based on the Timoshenko beam theory using the energy approach and the extended Lagrange’s equations. The corresponding discrete equation of vibration is obtained using the finite element method and solved for the natural frequencies using MATLAB. The dynamic characteristics of the coupling (Axial, torsional and bending natural frequencies) are studied in order to assess the merits and potential of the proposed coupling.
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Xue, M. D., D. F. Li, and K. C. Hwang. "A Thin Shell Theoretical Solution for Two Intersecting Cylindrical Shells Due to External Branch Pipe Moments." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-2597.

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Two intersecting cylindrical shells subjected to internal pressure and external moment are of common occurrence in pressure vessel and piping industry. The highest stress intensity occurring in the vicinity of junction, which is a complex space curve when the diameter ratio d/D increases. As the new process of theoretical solution and design criteria research developed by the authors, the stress analysis based on the theory of thin shell is carried out for cylindrical shells with normally intersecting nozzles subjected to three kinds of external branch pipe moments. The thin shell theoretical solution for the main shell with cutout, on which a moment is applied, is obtained by superposing a particular solution on the homogeneous solution. The double trigonometric series solution of cylindrical shell subjected to arbitrary distributed normal and tangential forces based on Timoshenko equation is used for the particular solution and the Xue et al.’s solution, for the homogeneous solution based on the modified Morley equation instead of the Donnell shallow shell equation. The displacement function solution for the nozzle with a nonplanar end is obtained on the basis of the Goldenveizer equation instead of Timoshenko’s. The presented results are in good agreement with those obtained by experiments and by three-dimensional finite element method. The present analytical results are in good agreement with WRC Bulletin 297 when d/D is small. The theoretical solution can be applied to d/D ≤ 0.8, λ = d/DT ≤ 8 and d/D ≤ t/T ≤ 2 successfully.
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Ganguly, Krishanu, Pradeep Nahak, and Haraprasad Roy. "Dynamics of Cracked Viscoelastic Beam: An Operator Based Finite Element Approach." In ASME 2017 Gas Turbine India Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gtindia2017-4616.

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The presence of crack introduces local flexibilities and changes physical characteristics of a structure which in turn alter its dynamic behavior. Crack depth, location, orientation and number of cracks are the main parameters that greatly influence the dynamics. Therefore, it is necessary to understand dynamics of cracked structures. Predominantly, every material may be treated as viscoelastic and most of the time material damping facilitates to suppress vibration. Thus present study concentrates on exploring the dynamic behavior of damped cantilever beam with single open crack. Operator based constitutive relationship is used to develop the general time domain, linear viscoelastic model. Higher order equation of motion is obtained based on Euler-Bernoulli and Timoshenko beam theory. Finite element method is utilized to discretize the continuum. Higher order equation is further converted to state space form for Eigen analysis. From the numerical results, it is observed that the appearance of crack decreases the natural frequency of vibration when compared to an uncracked viscoelastic beam. Under cracked conditions, the viscoelastic Timoshenko beam tends to give lower frequency values when compared to viscoelastic Euler-Bernoulli beam due to shear effect.
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