Abstract
This chapter is devoted to the analysis of one degree of freedom systems subjected to shock excitation [1, 2, Chap. 9, 3], etc. Some important concepts are discussed. among which are types of shock excitation and different approaches to the shock problem. Fourier transformation of aperiodic functions and corresponding concepts are considered and are then applied to the shock phenomenon. The spectral shock theory method and the concepts of residual and primary shock spectrums are discussed [4]. The transient vibration caused by different force and kinematic shock excitation (Heaviside step excitation, step excitation of finite duration, impulse excitation) are considered. Dynamic and transmissibility coefficients are derived and discussed in detail.
I have concluded that this question of impulse forces is very obscure, and I think that, up to the present, none of those who have treated this subject have been able to clear up its dark corners which lie almost beyond the reach of human imagination.
“Dialogues Concerning Two New Sciences” Galileo Galilei (1638)
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References
Goldsmith, W. (2014). Impact: The theory and physical behaviour of colliding solids. New York: Dover.
Harris, C. M. (Editor in Chief). (1996). Shock and vibration handbook (4th ed.). New York: McGraw-Hill.
Zukas, J. A. (1990). High velocity impact dynamics. New York: Wiley.
Ayre, R. S. (1996). Transient response to step and pulse functions. In Harris C.M. (Ed.), Shock and vibration handbook (4th ed.). New York: McGraw-Hill. Chapter 8.
Panovko, Ya. G. (1967). Fundamentals of applied theory of the vibrations and shock. Moscow: Mashinostroenie.
Lalanne, C. (2002). Mechanical vibration & shock (Vol. 1–4). New York: Hermes Penton Science.
Balandin, D. V., Bolotnik, N. N., & Pilkey, W. D. (2001). Optimal protection from impact, shock and vibration. Amsterdam: Gordon and Breach Science.
Clough, R. W., & Penzien, J. (1975). Dynamics of structures. New York: McGraw-Hill.
Fowles, G. R., & Cassiday, G. L. (1999). Analytical mechanics (6th ed.). Belmont, CA: Brooks/Cole—Thomson Learning.
Karnovsky, I. A., & Lebed, O. (2010). Advanced methods of structural analysis. New York: Springer.
Filippov, A. P. (1970). Vibration of the deformable systems. Moscow: Mashinostroenie.
Kil’chevsky, N. A. (1969). The theory of the collision of solid bodies (2nd ed.). Kiev, Ukraine: Naukova Dumka.
Lenk, A. (1977). Elektromechanische systeme. Band 2: Systeme mit verteilten parametern. Berlin: VEB Verlag Technnic.
Timoshenko, S. P., & Goodier, J. N. (1987). Theory of elasticity (Classic textbook reissue series 3rd ed.). New York: McGraw-Hill.
Rabinovich, I. M., Sinitsyn, A. P., & Terenin, B. M. (1958). Analysis of structures subjected to short-duration and impact forces. Moscow: Voenno-Inzhenernaya Akademiya (VIA).
Strelkov, S. P. (1964). Introduction to the theory of vibrations. Moscow: Nauka.
Thomson, W. T. (1981). Theory of vibration with application (2nd ed.). New York: Prentice-Hall.
Korn, G. A., & Korn, T. M. (2000). Mathematical handbook (2nd ed.). New York: McGraw-Hill Book/Dover. (Original work published 1968)
Tse, F. S., Morse, I. E., & Hinkle, R. T. (1963). Mechanical vibrations. Boston: Allyn and Bacon.
Il’insky, V. S. (1982). Protection of radio-electronic equipment and precision equipment from the dynamic excitations. Moscow: Radio.
Brown, J. W., & Churchill, R. V. (2009). Complex variables and applications—Solutions manual (8th ed.). Boston: McGraw-Hill.
Feldbaum, A. A., & Butkovsky, A. G. (1971). Methods of the theory of automatic control. Moscow: Nauka.
Karnovsky, I. A. (2012). Theory of arched structures. Strength, stability, vibration. Berlin: Springer.
Frolov, K. V. (Ed.). (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.
Ogata, K. (1992). System dynamics (2nd ed.). Englewood Cliffs, NJ: Prentice Hall Int.
Newland, D. E. (1989). Mechanical vibration analysis and computation. Harlow, England: Longman Scientific and Technical.
Crandall, S. H. (Ed.). (1963). Random vibration (Vol. 2). Cambridge, MA: MIT Press.
Lebed, E. (2009). Sparse signal recovery in a transform domain. Theory and application. Saarbrucken, Deutschland: VDM Verlag Dr.Muller, Aktiengesellschaft &Co. KG.
Biot, M. A. (1943). Analytical and experimental methods in engineering seismology. Transactions of the American Society of Civil Engineers, 108(1), 365–385.
Smallwood, D. (1981, May). An improved recursive formula for calculating shock response spectra. «The Shock and Vibration Bulletin», Bulletin No. 51, Part 2.
Lebed, E., Mackenzie, P. J., Sarunic, M. V., & Beg, M. F. (2010). Rapid volumetric OCT image acquisition using compressive sampling. Optics Express, 18(20), 21003–210012.
Lebed, E., Lee, S., Sarunic, M. V., & Beg, M. F. (2013). Rapid radial optical coherence tomography image acquisition. Journal of Biomedical Optics, 18(3), 03604–03613.
Lebed, E. (2013). Novel methods in biomedical image acquisition and analysis. PhD Thesis, Simon Fraser University, Burnaby, British Columbia, Canada.
Shabana, A. A. (1991). Theory of vibration: Vol. 2: Discrete and continuous systems. Mechanical Engineering Series. New York: Springer.
Timoshenko, S., Young, D. H., & Weaver, W., Jr. (1974). Vibration problems in engineering (4th ed.). New York: Wiley.
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Karnovsky, I.A., Lebed, E. (2016). Shock and Spectral Theory. In: Theory of Vibration Protection. Springer, Cham. https://doi.org/10.1007/978-3-319-28020-2_14
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