Abstract
Modern theory of automatic control of dynamical systems contains in its arsenal an extremely valuable tool. We are talking about the structural representation of an arbitrary dynamical system. Such representation allows us to divert attention from the physical nature of a process (thermal, vibrational, diffusion, etc) to the physical nature of the elements (mechanical, pneumatic, etc). In the context of structural representation of a mechanical system, we can explore diverse aspects of dynamic processes (controllability, invariance, stability, etc.) [1–3]. The theory of vibration protection is a very attractive application area of structural theory for several reasons. First, many fundamental aspects and concepts of control theory in general and the theory of vibration protection coincide; these include input–output concepts, transfer function, etc. Second, a vibration protection system consists of pronounced blocks and can be represented in symbolic form by a functional block diagram. Successful attempts that consider the problems of vibration protection in terms of the structural theory have been performed by Kolovsky [4, 5], Eliseev [6], and Bozhko et al. [7]. Systematic exposition of the structural theory to systems with distributed parameters was presented by Butkovsky [8]. Structural representation of the system in conjunction with the vibration protection device is a common way of describing complex dynamical systems with lumped and distributed parameters. Structural theory allows us to easily introduce changes into a vibration protection system of the object and find a relationship between any coordinates of a system, while the differential equation of the system assumes a fixed input–output. The Simulink (MATLAB) package has a full set of blocks that allows us to implement just about any structural model.
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References
Solodovnikov, V. V. (Ed.). (1967). Technical cybernetics (Vol. 1–4). Moscow: Mashinostroenie.
Athans, M., & Falb, P. L. (2006). Optimal control: An introduction to the theory and its applications. New York: McGraw-Hill/Dover. (Original work published 1966)
D’Azzo, J. J., & Houpis, C. H. (1995). Linear control systems. Analysis and design (4th ed.). New York: McGraw Hill.
Kolovsky, M. Z. (1999). Nonlinear dynamics of active and passive systems of vibration protection. Berlin: Springer.
Kolovsky, M. Z. (1976). Automatic control by systems of vibration protection. Moscow: Nauka.
Eliseev, S. V. (1978). Structural theory of vibration protection systems. Novosibirsk, Russia: Nauka.
Bozhko, A. E., Gal’, A. F., Gurov, A. P., Nerubenko, G. P., Rozen, I. V., & Tkachenko, V. A. (1988). Passive and active vibration protection of ship machinery. Leningrad, Russia: Sudostroenie.
Butkovsky, A. G. (1983). Structural theory of distributed systems. New York: Wiley.
Newland, D. E. (1989). Mechanical vibration analysis and computation. Harlow, England: Longman Scientific and Technical.
Chelomey, V. N. (Editor in Chief). (1978–1981). Vibrations in engineering. Handbook: Vols. 1–6. Moscow: Mashinostroenie.
Inman, D. J. (2006). Vibration, with control. New York: Wiley.
Harris, C. M. (Editor in Chief). (1996). Shock and vibration handbook (4th ed.). McGraw-Hill.
Bishop, R. E. D., & Johnson, D. C. (1960). The mechanics of vibration. London: Cambridge University Press.
Feldbaum, A. A., & Butkovsky, A. G. (1971). Methods of the theory of automatic control. Moscow: Nauka.
Shearer, J. L., Murphy, A. T., & Richardson, H. H. (1971). Introduction to system dynamics. Reading, MA: Addison-Wesley.
Ogata, K. (1992). System dynamics (2nd ed.). Englewood Cliffs, NJ: Prentice Hall Int.
Lenk, A. (1977). Elektromechanische systeme. Band 2: Systeme mit verteilten parametern. Berlin: VEB Verlag Technnic.
Butkovskiy, A. G., & Pustyl’nikov, L. M. (1993). Characteristics of distributed-parameter systems: Handbook of equations of mathematical physics and distributed-parameter systems. New York: Springer.
Nowacki, W. (1963). Dynamics of elastic systems. New York: Wiley.
Butkovsky, A. G. (1969). Distributed control systems. New York: Elsevier.
Shinners, S. M. (1978). Modern control system theory and application. Reading, MA: Addison Wesley. (Original work published 1972)
Timoshenko, S., Young, D. H., & Weaver, W., Jr. (1974). Vibration problems in engineering (4th ed.). New York: Wiley.
Karnovsky, I. A. (1973). Pontryagin’s principle in the eigenvalues problems. Strength of materials and theory of structures: Vol. 19, Kiev, Budivel’nik.
Iskra, V. S., & Karnovsky, I. A. (1975). The stress-strain state of the bar systems with variable structure. Strength of materials and theory of structures: Vol. 25. Kiev, Budivel’nik.
Tse, F. S., Morse, I. E., & Hinkle, R. T. (1963). Mechanical vibrations. Boston: Allyn and Bacon.
Alabuzhev, P., Gritchin, A., Kim, L., Migirenko, G., Chon, V., & Stepanov, P. (1989). Vibration protecting and measuring systems with quasi-zero stiffness (Applications of Vibration Series). New York: Hemisphere Publishing/Taylor & Francis Group.
Frolov, K. V. (Editor). (1981). Protection against vibrations and shocks. vol. 6. In Handbook: Chelomey, V.N. (Editor in Chief) (1978–1981) Vibration in engineering, vols. 1–6, Moscow: Mashinostroenie.
Frolov, K. V. (Ed.). (1982). Dynamic properties of linear vibration protection systems. Moscow: Nauka.
Hsu, J. C., & Meyer, A. U. (1968). Modern control principles and application. New York: McGraw-Hill.
Fuller, C. R., Elliott, S. J., & Nelson, P. A. (1996). Active control of vibration. London: Academic Press.
Karnovsky, I. A. (1977). Stabilization of the motion of a cylindrical panel. Sov. Applied Mechanics, 13(5).
Genkin, M. D., Elezov, V. G., & Yablonsky, V. V. (1985). Methods of controlled vibration protection of machines. Moscow: Nauka.
Petrov, B. N. (1961). The invariance Principle and the conditions for its application during the calculation of linear and nonlinear systems. Proc. Intern. Federation Autom. Control Congr., Moscow, vol. 2, pp. 1123–1128, 1960. Published by Butterworth & Co. London.
Zakora, A. L., Karnovsky, I. A., Lebed, V. V., & Tarasenko, V. P. (1989). Self-adapting dynamic vibration absorber. Soviet Union Patent 1477870.
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Karnovsky, I.A., Lebed, E. (2016). Structural Theory of Vibration Protection Systems. In: Theory of Vibration Protection. Springer, Cham. https://doi.org/10.1007/978-3-319-28020-2_12
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