On adhesive binding optimization of elastic homogeneous rod to a fixed rigid base as a control problem by coefficient

• Autorzy: Jilavyan S. H. , Khurshudyan A. Zh. , Sarkisyan A. S.
• Języki publikacji: EN

Abstrakty

EN

The problem of finite, partially glued to a fixed rigid base rod longitudinal vibrations damping by optimizing adhesive structural topology is investigated. Vibrations of the rod are caused by external load, concentrated on free end of the rod, the other end of which is elastically clamped. The problem is mathematically formulated as a boundary-value problem for onedimensional wave equation with attenuation and variable controlled coefficient. The intensity of adhesion distribution function is taken as optimality criterion to be minimized. Structure of adhesion layer, optimal in that sense, is obtained as a piecewise-constant function. Using Fourier real generalized integral transform, the problem of unknown function determination is reduced to determination of certain switching points from a system of nonlinear, in general, complex equations. Some particular cases are considered.

Słowa kluczowe

EN

topology optimization; optimal design; control by coefficient; nonlinear moments problem; adhesive binding

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2013
• Tom: Vol. 23, no. 4
• Strony: 413--425
• Opis fizyczny: Bibliogr. 10 poz., rys., wzory

Twórcy

autor

Jilavyan S. H.

• Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian street, 0025 Yerevan, Armenia

autor

Khurshudyan A. Zh.

• Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian street, 0025 Yerevan, Armenia

autor

Sarkisyan A. S.

• Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian street, 0025 Yerevan, Armenia

Bibliografia

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• [2] J. T. Betts: Practical methods of optimal control using nonlinear programming.Advances in Design and Control. SIAM, 2001.
• [3] Yu. Brychkov and A. Prudnikov: Integral transforms of generalized functions.CRC Press, 1989.
• [4] A. G. Butkovskii: Methods of control for distributed parameters systems.Moscow, Nauka Publ., 1975, (in Russian).
• [5] C. D. Chapman: Structural Topology Optimization via the Genetic Algorithm.Massachusetts Institute of Technology, 1994.
• [6] P. W. Christensen and A. Klarbring: An introduction to structural optimization.Solid Mechanics and its Applications. 153 Springer, Berlin. 2009.
• [7] A. Zh. Khurshudyan: On optimal impulsive null-finite control of nonhomogeneous rod vibrations. Proc. of Applied Math., Inform. and Mech., 7(1), (2012), 393-399, (in Russian).
• [8] A. Zh. Khurshudyan: On optimal boundary control of non-homogeneous string vibrations under impulsive concentrated perturbations with delay in controls. Math.Bull. T. Shevchenko Sci. Soc., 10 (2013), 203-209.
• [9] N. N. Krasovskii: Motion Control Theory. Moscow, Nauka Publ., 1968, (in Russian).
• [10] J. Mathews and R. Walker: Mathematical Methods of Physics. 2-nd Ed. New York-Amsterdam, W. A. Benjamin, Inc., 1970.