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Influence of Initial Geometric Imperfections on the Vibrations and Dynamic Stability of Elastic Shells

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Abstract

The results from studies into the vibrations and dynamic stability of thin elastic shells with initial geometric imperfections are analyzed. The corresponding dynamic problems are solved in both linear and nonlinear formulations. The influence of initial axisymmetric and nonaxisymmetric deflections on natural, forced, parametrically excited, and self-excited vibrations (flutter) is studied. The dynamic buckling of imperfect shells under short-term impulsive loading is examined. Some aspects of experimental investigation into the vibrations of shells with small geometric imperfections (deviations from the design shape) are considered

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REFERENCES

  1. V. L. Agamirov, “Review of studies into the stability of structures under impulsive loading,” in: Design of Spatial Structures [in Russian], Issue 12, Stroiizdat, Moscow (1969), pp. 186–200.

    Google Scholar 

  2. N. A. Azimov and Kh. K. Seifullaev, “Solving the equations of shallow shells of variable thickness and curvature with arbitrary boundary conditions,” Prikl. Mekh., 16, No. 10, 47–53 (1980).

    Google Scholar 

  3. I. Ya. Amiro, “Determining the critical short-term external pressure upon a spherical shell with an initial deflection,” Prikl. Mekh., 23, No. 10, 7–12 (1987).

    Google Scholar 

  4. I. Ya. Amiro, “Analyzing the influence of the dimensions of the initial dent and reinforcement characteristics on the critical short-term external pressure upon a spherical shell,” Prikl. Mekh., 26, No. 9, 29–36 (1990).

    Google Scholar 

  5. I. Ya. Amiro and V. A. Zarutskii, “Experimental and theoretical determination of the natural frequencies of reinforced cylindrical shells,” Prikl. Mekh., 13, No. 10, 6–13 (1977).

    Google Scholar 

  6. I. Ya. Amiro and V. A. Zarutskii, Theory of Ribbed Shells [in Russian], Vol. 2 of the five-volume series Methods of Shell Design, Naukova Dumka, Kiev (1980).

    Google Scholar 

  7. I. Ya. Amiro, V. A. Zarutskii, and P. S. Polyakov, Ribbed Cylindrical Shells [in Russian], Naukova Dumka, Kiev (1973).

    Google Scholar 

  8. I. Ya. Amiro, P. S. Polyakov, and V. G. Palamarchuk, “Stability of imperfect cylindrical shells,” Prikl. Mekh., 7, No. 8, 9–15 (1971).

    Google Scholar 

  9. A. A. Andronov, A. A. Vitt, and S. É. Khaikin, Theory of Vibrations [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  10. J. Arbocz and J. G. Williams, “Imperfection surveys on a 10 ft-diameter shell structure,” AIAA J., 15, No. 7, 949–956 (1977).

    Google Scholar 

  11. A. Ya. Aronson, “Influence of the disturbed median surface of a shell on its stress state,” Izv. AN SSSR, Mashinovedenie, No. 5, 37–43 (1968).

    Google Scholar 

  12. A. Ya. Aronson and F. S. Bedcher, “Determining the natural frequencies of parts, such as rods and plates, with small process-induced imperfections,” Izv. AN SSSR, Mashinovedenie, No. 5, 37–43 (1966).

    Google Scholar 

  13. A. Ya. Aronson and F. S. Bedcher, “Influence of the disturbed median surface of a shell on its natural frequencies,” in: Dynamics and Strength of Elastic and Hydroelastic Systems [in Russian], Nauka, Moscow (1975), pp. 94–99.

  14. Yu. A. Ashmarin, “Nonlinear equilibrium equations for a shell with initial imperfections,” Prikl. Mekh., 10, No. 9, 35–40 (1974).

    Google Scholar 

  15. I. Yu. Babich and N. P. Semenyuk, “Stability and initial postbuckling behavior of composite shells,” Prikl. Mekh., 34, No. 6, 3–38 (1998).

    Google Scholar 

  16. A. E. Bogdanovich, “Review of studies into the stability of cylindrical shells under dynamic axial compression. 1. Early studies and basic qualitative results; 2. Recent studies and current state of the problem,” in: Electrodynamics and Continuum Mechanics [in Russian] (1980), pp. 68–105.

  17. A. E. Bogdanovich, Nonlinear Dynamic Problems for Cylindrical Composite Shells [in Russian], Zinatne, Riga (1987).

    Google Scholar 

  18. A. E. Bogdanovich and É. G. Feldmane, “Calculating the load-bearing capacity of cylindrical composite shells under dynamic loading,” Mekh. Komp. Mater., No. 3, 476–484 (1980).

    Google Scholar 

  19. A. E. Bogdanovich and É. G. Feldmane, “Deformation of cylindrical composite shells under compound dynamic loading,” Mekh. Komp. Mater., No. 3, 461–473 (1981).

    Google Scholar 

  20. A. E. Bogdanovich and É. G. Feldmane, “Analysis of nonaxisymmetric buckling of cylindrical shells under dynamic axial compression,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 2, 144–154 (1982).

    Google Scholar 

  21. A. E. Bogdanovich and S. P. Yushanov, “Buckling analysis of cylindrical shells with a random field of initial imperfections under dynamic axial compression,” Mekh. Komp. Mater., No. 5, 821–831 (1981).

    Google Scholar 

  22. N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Vibrations [in Russian], Nauka, Moscow (1974).

  23. V. V. Bolotin, Dynamic Stability of Elastic Systems [in Russian], Gostekhizdat, Moscow (1956).

    Google Scholar 

  24. V. V. Bolotin, Nonconservative Problems in the Theory of Elastic Stability [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  25. C. D. Babcock, Jr., “Shell stability experiments,” in: Y. C. Fung and E. E. Sechler (eds.), Thin Shell Structures: Theory, Experiment, and Design, Prentice Hall, Englewood Cliffs, N. J. (1974).

    Google Scholar 

  26. G. A. Vanin and N. P. Semenyuk, Stability of Composite Shells with Imperfections [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  27. V. Z. Vlasov, General Theory of Shells and Its Applications in Engineering [in Russian], Gostekhizdat, Moscow (1949).

    Google Scholar 

  28. A. S. Vol'mir, “Nonlinear problems in the theory of transient deformation of shells and the stability problem,” in: Applied Problems of Strength and Plasticity [in Russian], Nauka, Moscow (1967), pp. 51–66.

  29. A. S. Vol'mir, Flexible Plates and Shells [in Russian], Gostekhizdat, Moscow (1956).

    Google Scholar 

  30. A. S. Vol'mir, Stability of Deformable Systems [in Russian], Nauka, Moscow (1967).

  31. A. S. Vol'mir, Nonlinear Dynamics of Plates and Shells [in Russian], Nauka, Moscow (1972).

  32. A. S. Vol'mir and I. G. Kil'dibekov, “Nonlinear acoustic vibrations of a cylindrical shell,” Izv. AN ArmSSR, 17, No. 3, 65–70 (1964).

    Google Scholar 

  33. I. I. Vorovich, Mathematical Problems in the Nonlinear Theory of Shells [in Russian], Nauka, Moscow (1989).

  34. G. D. Gavrilenko, Stability of Ribbed Cylindrical Shells with Nonuniform Stress-Strain Distribution [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

  35. G. D. Gavrilenko, Techniques for Stability Design of Reinforced Shells [in Russian], Naukova Dumka, Kiev (1991).

    Google Scholar 

  36. G. D. Gavrilenko, “Stability and load-bearing capacity of incomplete shells,” Int. Appl. Mech., 36, No. 7, 866–887 (2000).

    Google Scholar 

  37. P. I. Galaka, V. A. Zarutskii, P. G. Kaplya et al., “Analysis of the influence of compressive forces on the frequencies and modes of ribbed cylindrical shells,” Prikl. Mekh., 11, No. 8, 41–48 (1975).

    Google Scholar 

  38. P. I. Galaka, P. S. Koval'chuk and T. S. Krasnopol'skaya, “Dynamic deformation of thin-walled cylindrical shells under longitudinal cyclic loading,” in: V. A. Kuz'menko (ed.), Ultrasonic Vibrations and Their Influence on the Mechanical Characteristics of Structural Materials (Collected Works) [in Russian], Naukova Dumka, Kiev (1986), pp. 141–146.

    Google Scholar 

  39. P. I. Galaka, P. S. Koval'chuk, V. M. Mendelutsa, and A. M. Nosachenko, “Dynamic instability of glass-fiber-reinforced plastic shells carrying concentrated masses,” Prikl. Mekh., 16, No.8, 42–47 (1980).

    Google Scholar 

  40. P. I. Galaka, P. S. Koval'chuk, V. M. Mendelutsa, and A. I. Telalov, “Experimental study into the nonlinear interaction of flexural modes of cylindrical shells subject to parametric excitation,” Probl. Mashinostr., 13, 50–57 (1981).

    Google Scholar 

  41. R. F. Ganiev and P. S. Koval'chuk, Dynamics of Systems of Rigid and Elastic Bodies [in Russian], Mashinostroenie, Moscow (1980).

  42. R. E. Geizenblazen, “Influence of the initial deflections on the natural frequencies and dynamic stability of closed circular cylindrical shells,” in: Studies in the Theory of Vibrations and Bridge Dynamics [in Russian], Issue 73, Tr. Dnepropetr. Inst. Inzhen. Zhel.-Dor. Transp., Dnepropetrovsk (1968), pp. 72–82.

  43. R. E. Geizenblazen, “The dynamic instability boundaries of shallow shells,” in: Studies in the Theory of Vibrations and Bridge Dynamics [in Russian], Issue 73, Tr. Dnepropetr. Inst. Inzhen. Zhel.-Dor. Transp., Dnepropetrovsk (1968), pp. 83–90.

  44. A. L. Gol'denveizer, Theory of Thin Elastic Shells [in Russian], Nauka, Moscow (1976).

  45. E. A. Gotsulyak and D. É. Prusov, “Stability of shells under nonstationary loading,” Prikl. Mekh., 33, No. 10, 59–66 (1997).

    Google Scholar 

  46. E. A. Gotsulyak and P. P. Cheverda, “Study into the self-organization phenomenon in shell dynamics,” Prikl. Mekh., 30, No. 9, 41–45 (1994).

    Google Scholar 

  47. É. I. Grigolyuk and V. V. Kabanov, “Stability of circular cylindrical shells,” in: Advances in Science: Solid Mechanics [in Russian], VINITI, Moscow (1969).

    Google Scholar 

  48. É. I. Grigolyuk and V. V. Kabanov, Stability of Shells [in Russian], Nauka, Moscow (1978).

  49. É. I. Grigolyuk and A. I. Srebrovskii, “Thin circular cylindrical shells under a pulse of external pressure,” Inzh. Zh. Mekh. Tverd. Tela, No. 3, 110–118 (1968).

    Google Scholar 

  50. N. F. Grishin and V. S. Kalinin, “Influence of initial imperfections on vibrations of plates and shells,” in: Proc. 9th All-Union Conf. on Theory of Shells and Plates [in Russian], Sudostroenie, Leningrad (1975), pp. 175–179.

    Google Scholar 

  51. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kiev (1986).

  52. A. N. Guz and I. Yu. Babich, Three-Dimensional Theory of Stability of Deformable Bodies, Vol. 4 of the six-volume series Spatial Problems in the Theory of Elasticity and Plasticity [in Russian], Naukova Dumka, Kiev (1985).

  53. A. N. Guz, V. A. Zarutskii (general editors), I. Ya. Amiro et al., Experimental Investigation of Thin-Walled Structures [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  54. I. Yu. Dedyukin and V. A. Krys'ko, “Dynamic buckling criteria for shells,” Prikl. Mekh., 30, No. 10, 56–60 (1994).

    Google Scholar 

  55. V. D. Kubenko (ed.), A. É. Babaev, E. I. Bespalova et al., Dynamics of Structural Members, Vol. 9 of the 12-volume series Mechanics of Composites [in Russian], Naukova Dumka, Kiev (1999).

    Google Scholar 

  56. L. H. Donnell, Beams, Plates, and Shells, McGraw Hill, New York (1976).

    Google Scholar 

  57. L. H. Donnell and C. C. Wan, “Effect of imperfections on buckling of thin cylinders and columns under axial compression,” J. Appl. Mech., 17, No. 1, 73–83 (1950).

    Google Scholar 

  58. D. Hui, “Large-amplitude vibrations of geometrically imperfect shallow spherical shells with structural damping,” AIAA J., 21, No. 12, 1736–1741 (1983).

    Google Scholar 

  59. V. A. Zarutskii, “Features of the buckling of ribbed shells,” Int. Appl. Mech., 36, No. 5, 559–585 (2000).

    Google Scholar 

  60. V. A. Zarutskii and V. F. Sivak, “A technique for processing experimental data from stability tests on cylindrical shells under axial compression,” Prikl. Mekh., 30, No. 4, 45–50 (1994).

    Google Scholar 

  61. V. A. Zarutskii and V. F. Sivak, “An empirical formula for stability design of shells,” Prikl. Mekh., 33, No. 7, 25–30 (1997).

    Google Scholar 

  62. V. A. Zarutskii and V. F. Sivak, “Experimental investigation of the dynamics of shells of revolution,” Int. Appl. Mech., 35, No. 3, 217–224 (1999).

    Google Scholar 

  63. V. A. Zarutskii and A. I. Telalov, “Vibration of thin-walled structures with design features. A review of experimental studies,” Prikl. Mekh., 27, No. 4, 3–9 (1991).

    Google Scholar 

  64. J. Singer, “Vibrations and buckling of imperfect stiffened shells—recent developments,” in: Collapse: The Buckling of Structures in Theory and Practice, Cambridge Univ. Press (1983), pp. 443–481.

  65. F. S. Isanbaeva, “Experimental study into the stability of circular cylindrical shells under external uniform pressure,” Izv. Kazan. Filiala AN SSSR, Ser. Fiz.-Mat. Nauk, No. 14, 47–54 (1960).

    Google Scholar 

  66. V. O. Kononenko, A. A. Bondarenko, P. I. Galaka et al., Vibration Analysis of Glass-Fiber-Reinforced Plastic Shells [in Russian], Naukova Dumka, Kiev (1974).

    Google Scholar 

  67. A. Kaplan, “Buckling of spherical shells,” in: Y. C. Fung and E. E. Sechler (eds.), Thin Shell Structures: Theory, Experiment, and Design, Prentice Hall, Englewood Cliffs, N. J. (1974).

    Google Scholar 

  68. I. G. Kil'dibekov, “Nonlinear natural vibrations of a circular cylindrical shell,” in: Proc. 8th All-Union Conf. on the Theory of Shells and Plates [in Russian], Nauka, Moscow (1973), pp. 488–491.

  69. I. G. Kil'dibekov, “Study into the nonlinear natural vibrations of a cylindrical shell,” Prikl. Mekh., 13, No. 11, 46–52 (1977).

    Google Scholar 

  70. I. G. Kil'dibekov, “Study into nonlinear vibrations and buckling of a cylindrical shell under intensive acoustic forces,” Prikl. Mekh., 14, No. 7, 43–48 (1978).

    Google Scholar 

  71. P. S. Koval'chuk and S. V. Kozlov, “Features of the dynamic deformation of thin-walled cylindrical shells,” Probl. Prochn., No. 7, 36–42 (1987).

    Google Scholar 

  72. P. S. Koval'chuk, S. V. Kozlov, and T. S. Krasnopol'skaya, “Resonant phenomena in full-scale cylindrical shells under nonlinear vibrations,” in: Abstracts of Papers Read at Conf. on Problems of Nonlinear Vibrations of Mechanical Systems [in Russian], Naukova Dumka, Kiev (1978).

    Google Scholar 

  73. P. S. Koval'chuk and T. S. Krasnopol'skaya, “Dynamic instability of imperfect cylindrical shells,” in: Stability of Spatial Structures [in Russian], Izd. Kiev. Inzh.-Stroit. Inst., Kiev (1978), pp. 69–74.

  74. P. S. Koval'chuk and T. S. Krasnopol'skaya, “Resonant phenomena in cylindrical shells with initial imperfections under nonlinear vibrations,” Prikl. Mekh., 15, No. 9, 13–20 (1979).

    Google Scholar 

  75. P. S. Koval'chuk and T. S. Krasnopol'skaya, “Resonant vibrations of a cylindrical shell under compound periodic loading,” Prikl. Mekh., 23, No. 4, 115–119 (1987).

    Google Scholar 

  76. P. S. Koval'chuk and T. S. Krasnopol'skaya, “Wave modes of motion of cylindrical composite shells under periodic forces,” Mekh. Komp. Mater., No. 2, 305–311 (1985).

    Google Scholar 

  77. P. S. Koval'chuk, T. S. Krasnopol'skaya, and N. P. Podchasov, “Dynamic instability of circular cylindrical shells with initial deflections,” Prikl. Mekh., 18, No. 3, 28–33 (1982).

    Google Scholar 

  78. P. S. Koval'chuk, T. S. Krasnopol'skaya, and N. P. Podchasov, “Determining the damping characteristics of the vibrations of cylindrical shells with initial imperfections,” in: Energy Dissipation in Mechanical Systems under Vibrations [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

  79. P. S. Koval'chuk, T. S. Krasnopol'skaya, and A. I. Telalov, “Influence of damping on the dynamic instability of a cylindrical shell with initial imperfections,” in: Energy Dissipation in Mechanical Systems under Vibrations [in Russian], Naukova Dumka, Kiev (1982), pp. 25–30.

    Google Scholar 

  80. P. S. Koval'chuk and L. A. Kruk, “Nonlinear energy interchange between the natural modes of freely vibrating circular cylindrical shells filled with liquid,” Int. Appl. Mech., 36, No. 1, 103–110 (2000).

    Google Scholar 

  81. P. S. Koval'chuk and V. D. Kubenko, “Interaction of vibrating cylindrical shells with the fluid they contain,” in: A. N. Guz (ed.), S. Markus, L. Pust et al., Dynamics of Bodies Interacting with a Medium [in Russian], Naukova Dumka, Kiev (1991), pp. 168–214.

  82. P. S. Koval'chuk and V. D. Lakiza, “Experimental studies into forced large-deflection vibrations of glass-fiber-reinforced plastic shells of revolution,” Prikl. Mekh., 31, No.11, 63–69 (1995).

    Google Scholar 

  83. P. S. Koval'chuk, V. S. Pavlovskii, and V. G. Filin, “Stability analysis of resonant nonlinear vibrations of liquid-filled cylindrical shells subject to longitudinal and transverse periodic excitation,” Dokl. NAN Ukrainy, No. 4, 56–61 (2000).

    Google Scholar 

  84. I. Ya. Amiro (ed.), V. A. Zarutskii, V. N. Revutskii et al., Vibrations of Ribbed Shells of Revolution [in Russian], Naukova Dumka, Kiev (1988).

  85. V. O. Kononenko, Vibrating Systems with Limited Excitation [in Russian], Nauka, Moscow (1964).

  86. V. O. Kononenko and P. S. Koval'chuk, “Interaction of the vibration-generation mechanisms in mechanical systems,” in: V. O. Kononenko, Nonlinear Vibrations of Mechanical Systems (Selected Works) [in Russian], Naukova Dumka, Kiev (1980), pp. 317–362.

    Google Scholar 

  87. V. M. Kots and D. E. Lipovskii, “Experimental study into the stability of cylindrical shells with initial imperfections,” in: Trans. 6th All-Union Conf. on the Theory of Shells and Plates [in Russian], Nauka, Moscow (1966), pp. 142–146.

  88. V. D. Kubenko and P. S. Koval'chuk, “Wave buckling modes of orthotropic cylindrical shells under axial dynamic compression,” Prikl. Mekh., 31, No. 12, 17–24 (1995).

    Google Scholar 

  89. V. D. Kubenko and P. S. Koval'chuk, “Resonant vibrations of orthotropic cylindrical shells with initial imperfections,” in: V. D. Kubenko (ed.), Dynamics of Structural Members, Vol. 9 of the 12-volume series Mechanics of Composites [in Russian], A.S.K., Kiev (1999), pp. 174–201.

    Google Scholar 

  90. V. D. Kubenko and P. S. Koval'chuk, “Dynamic instability of shells under axial loading,” in: V. D. Kubenko (ed.), Dynamics of Structural Members, Vol. 9 of the 12-volume series Mechanics of Composites [in Russian], A.S.K., Kiev (1999), pp. 202–223.

    Google Scholar 

  91. V. D. Kubenko, P. S. Koval'chuk, L. G. Boyarshina et al., Nonlinear Dynamics of Axisymmetric Bodies Filled with Liquid [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  92. V. D. Kubenko, P. S. Koval'chuk, and T. S. Krasnopol'skaya, “Influence of the initial deflection on nonlinear natural vibrations of cylindrical shells,” Prikl. Mekh., 18, No. 1, 43–49 (1982).

    Google Scholar 

  93. V. D. Kubenko, P. S. Koval'chuk, and T. S. Krasnopol'skaya, Nonlinear Interaction of Flexural Vibration Modes of Cylindrical Shells [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  94. V. D. Kubenko, P. S. Koval'chuk, and V. D. Lakiza, “Experimental studies into the nonlinear vibrations of glass-fiber-reinforced plastic shells of revolution,” in: Dynamics of Structural Members, Vol. 9 of the 12-volume series Mechanics of Composites [in Russian], A.S.K., Kiev (1999), pp. 298–313.

    Google Scholar 

  95. V. D. Kubenko, P. S. Koval'chuk, and N. P. Podchasov, “Wave modes of motion of circular cylindrical shells,” Prikl. Mekh., 18, No. 9, 16–22 (1982).

    Google Scholar 

  96. V. D. Kubenko, P. S. Koval'chuk, and N. P. Podchasov, Nonlinear Vibrations of Cylindrical Shells [in Russian], Vyshcha Shkola, Kiev (1989).

    Google Scholar 

  97. V. D. Kubenko, P. S. Koval'chuk, and A. D. Reshetar', “Flexural vibration modes of spherical shells with initial imperfections,” Prikl. Mekh., 24, No. 12, 30–39 (1988).

    Google Scholar 

  98. V. D. Kubenko, V. D. Lakiza, V. S. Pavlovskii, and N. A. Pelykh, Dynamics of Elastic Gas-Liquid Systems under Vibratory Forces [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  99. A. I. Kukarina, V. I. Matsner, and V. F. Sivak, “Influence of the initial deflections on the natural vibrations of ribbed cylindrical shells,” Prikl. Mekh., 18, No. 4, 58–63 (1982).

    Google Scholar 

  100. E. V. Ladygina and Yu. V. Mikhlin, “Analysis of nonlinear vibrations of circular cylindrical shells with initial imperfections under axial compression,” in: Trans. 15th All-Union Conf. on the Theory of Shells and Plates [in Russian], Vol. 1, Izd. Kazan Univ., Kazan (1990), pp. 192–196.

  101. A. M. Lyapunov, General Problem of Motion Stability [in Russian], Gostekhteorizdat, Moscow-Leningrad (1950).

  102. I. G. Malkin, Some Problems of the Theory of Nonlinear Vibrations [in Russian], Fizmatgiz, Moscow (1956).

  103. I. G. Malkin, Theory of Motion Stability [in Russian], Nauka, Moscow (1966).

  104. L. I. Mandel'shtam, Collected Works [in Russian], Vol. 4, Izd. AN SSSR, Moscow (1955).

  105. L. I. Manevich, Yu. V. Mikhlin, and V. N. Pilipchuk, Method of Normal Vibrations for Essentially Nonlinear Systems [in Russian], Nauka, Moscow (1989).

  106. V. I. Matsner, “Study into the influence of initial deflections on the natural frequencies of shells under axial compressive forces,” Prikl. Mekh., 14, No. 5, 112–116 (1978).

    Google Scholar 

  107. A. V. Karmishin (ed.), A. I. Zhukov, V. G. Kolosov et al., Methods of Dynamic Design and Tests of Thin-Walled Structures [in Russian], Mashinostroenie, Moscow (1990).

  108. N. A. Kil'chevskii (ed.), Mechanics of Shell-Liquid-Heated-Gas Systems [in Russian], Naukova Dumka, Kiev (1970).

    Google Scholar 

  109. A. M. Militsyn and D. I. Sotnikov, “Measuring the initial deflections of thin-walled shells of revolution,” Éksp. Issled. Prochn. Nadezhn. Konstr., No. 1, 41–46 (1972).

    Google Scholar 

  110. V. E. Mineev, “Stability analysis of closed circular cylindrical shells under dynamic loading,” Tr. VVIA im. N. E. Zhukovskogo, 808, 74–92 (1959).

    Google Scholar 

  111. V. E. Mineev, “Experimental stability analysis of closed cylindrical shells under uniform dynamic compression,” Tr. VVIA im. N. E. Zhukovskogo, 808, 93–101 (1959).

    Google Scholar 

  112. V. E. Mineev, “Stability analysis of closed cylindrical shells under uniform dynamic compression,” in: Studies in the Theory of Plates and Shells [in Russian], Issue 6–7, Kazan (1970), pp. 596–623.

  113. Yu. A. Mitropol'skii, Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).

    Google Scholar 

  114. N. N. Moiseev, Asymptotic Methods of Nonlinear Mechanics [in Russian], Nauka, Moscow (1969).

  115. V. I. Mossakovskii, “Influence of nonuniform stress and initial imperfections on the stability of a cylindrical shell,” in: Trans. 7th All-Union Conf. on the Theory of Shells and Plates (Dnepropetrovsk, 1969) [in Russian], Nauka, Moscow (1970), pp. 831–839.

  116. V. I. Mossakovskii, L. I. Manevich, and A. M. Mil'tsyn, Modeling the Load-Bearing Capacity of Cylindrical Shells [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  117. Kh. M. Mushtari, “Elastic equilibrium of a thin shell with an initial imperfection in the median surface,” Prikl. Mat. Mekh., 15, No. 6, 743–750 (1951).

    Google Scholar 

  118. Kh. M. Mushtari and K. Z. Galimov, Nonlinear Theory of Elastic Shells [in Russian], Tatknigoizdat, Kazan (1957).

  119. A. V. Karmishin (ed.), Nonstationary Aeroelasticity of Thin-Walled Structures [in Russian], Mashinostroenie, Moscow (1982).

  120. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations, John Wiley and Sons, New York (1977).

    Google Scholar 

  121. Yu. N. Novichkov, “Flutter of plates and shells,” in: Solid Mechanics [in Russian], Issue 11, VINITI, Moscow (1978), pp. 67–122.

    Google Scholar 

  122. V. V. Novozhilov, Theory of Thin Shells [in Russian], Sudpromizat, Leningrad (1962).

    Google Scholar 

  123. V. T. Palamarchuk and P. S. Polyakov, “Rational reinforcement of a stringer shell with initial deflections,” Prikl. Mekh., 12, No. 3, 21–27 (1976).

    Google Scholar 

  124. A. S. Pal'chevskii and V. T. Kirichenko, “Predicting the critical axial force for an imperfect cylindrical shell,” Prikl. Mekh., 31, No. 8, 48–53 (1995).

    Google Scholar 

  125. J. M. T. Thompson and G. W. Hunt (ed.), Collapse: The Buckling of Structures in Theory and Practice, Cambridge University Press, Cambridge (1982).

    Google Scholar 

  126. O. P. Protsenko, “Influence of the initial deflection on the natural frequencies of a cylindrical shell,” Prikl. Mekh., 10, No. 2, 143–148 (1964).

    Google Scholar 

  127. O. P. Protsenko, “Stability of a cylindrical shell with an initial deflection under aperiodic axial compression,” Prikl. Mekh., 1, No. 3, 27–34 (1965).

    Google Scholar 

  128. O. P. Protsenko and V. S. Pavlovskii, “Dynamic stability of a closed cylindrical shell under a compounds time-aperiodic load,” in: Stability Problems in Structural Mechanics [in Russian], Moscow (1965), pp. 293–305.

  129. M. T. Rabinovich and D. I. Trubetskov, An Introduction to the Theory of Vibrations and Waves [in Russian], Nauka, Moscow (1984).

  130. J. W. Strutt (Baron Rayleigh), The Theory of Sound, 2nd ed., Dover, New York (1945).

    Google Scholar 

  131. A. D. Reshetar', “Influence of initial imperfections on the natural frequencies of spherical shells,” in: Trans. 11th Sci. Conf. of Young Scientists of the Inst. of Mech Acad. Sci. USSR, Kiev, Vol. 1, Deposited at VINITI No. 5507-V86 (1986), pp. 190–195.

    Google Scholar 

  132. A. D. Reshetar', Vibrations of Shallow Spherical Shells with Initial Imperfections and Geometric Nonlinearity [in Russian], Author's Abstract of PhD Thesis, Kiev (1988).

  133. J. J. Rushchitsky and S. I. Tsurpal, Waves in Microstructural Materials [in Ukrainian], Oranta, Kiev (1998).

  134. P. Seide, “Modification of Koiter's theory of initial postbuckling behavior and sensitivity of a structure to imperfections,” in: Y. C. Fung and E. E. Sechler (eds.), Thin Shell Structures: Theory, Experiment, and Design, Prentice Hall, Englewood Cliffs, N. J. (1974).

    Google Scholar 

  135. V. F. Sivak, “Experimental investigation of the nonlinear resonance properties of cylindrical shells,” Int. Appl. Mekh., 36, No. 2, 247–250 (2000).

    Google Scholar 

  136. L. S. Srubshchik, Buckling and Postbuckling Behavior of Shells [in Russian], Izd. Rostov, Rostov (1981).

  137. R. O. Stearman, “Influence of flow conditions of a compressible liquid on the static and dynamic stability of thin cylindrical shell structures,” in: Y. C. Fung and E. E. Sechler (eds.), Thin Shell Structures: Theory, Experiment and Design, Prentice Hall, Englewood Cliffs, N. J. (1974).

    Google Scholar 

  138. J. J. Stocker, Nonlinear Oscillations in Mechanical and Electrical Systems, Interscience, New York (1950).

    Google Scholar 

  139. O. I. Terebushko, “Influence of reinforcement on the dynamic stability of a cylindrical shell,” Prikl. Mekh., 13, No. 3, 10–16 (1977).

    Google Scholar 

  140. O. I. Terebushko, “Stability of reinforced and anisotropic shells,” in: Proc. 8th All-Union Conf. on the Theory of Shells and Plates (Dnepropetrovsk, 1969) [in Russian], Nauka, Moscow (1970), pp. 884–897.

  141. S. Yu. Fialko, “Study into the influence of the initial deflection on the natural frequencies of ribbed conic shells,” Prikl. Mekh., 18, No. 11, 118–122 (1982).

    Google Scholar 

  142. S. Yu. Fialko, “Modes of natural vibrations of imperfect conic shells,” Prikl. Mekh., 20, No. 12, 109–112 (1984).

    Google Scholar 

  143. S. Yu. Fialko, “Modes of natural vibrations of ribbed conic shells,” Prikl. Mekh., 20, No. 11, 51–55 (1984).

    Google Scholar 

  144. H. Haken, Synergetics, an Introduction, Springer, Berlin (1977).

    Google Scholar 

  145. R. L. Halfman, Dynamics, Addison-Wesley, New York (1962).

    Google Scholar 

  146. J. W. Hutchinson and W. T. Koiter, “Postbuckling theory,” Appl. Mech. Rev., 23, No. 12, 1353–1366 (1970).

    Google Scholar 

  147. C. Hayashi, Nonlinear Oscillations in Physical Systems, Princeton University Press, Princeton, N.J. (1985).

    Google Scholar 

  148. V. N. Chelomei, “A possibility of increasing the stability of elastic systems through vibrations,” Dokl. AN SSSR, 110, No. 3, 345–348 (1956).

    Google Scholar 

  149. A. N. Chuiko, “Load-bearing capacity of thin-walled shells under impulsive radial pressure,” Prikl. Mekh., 8, No. 5, 21–27 (1972).

    Google Scholar 

  150. G. Schmidt, Parametererregte Schwingungen, DVW, Berlin (1975).

    Google Scholar 

  151. M. A. Shumik, “Dynamic stability of an orthotropic cylindrical shell under external pressure,” Prikl. Mekh., 27, No. 5, 124–128 (1991).

    Google Scholar 

  152. M. Amabili and M. P. Paidoussis, “Review of studies on geometrically nonlinear vibration and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction,” Appl. Mech. Rev., 56, No. 4, 349–381 (2003).

    Google Scholar 

  153. J. Arbocz, “The effect of initial imperfections on shell stability,” in: Y. C. Fung and E. E. Sechler (eds.), Thin Shell Structures: Theory, Experiment and Design, Prentice Hall, Englewood Cliffs, N.J. (1974), pp. 205–245.

    Google Scholar 

  154. J. Arbocz, “Shell stability analysis in theory and practice,” Chapter 4 in: J. M. T. Thompson and G. W. Hunt (eds.), Collapse: The Buckling of Structures in Theory and Practice, Cambridge University Press, Cambridge (1983), pp. 43–74.

    Google Scholar 

  155. J. Arbocz and H. Abramovich, The Initial Imperfection Data Bank at the Delft University of Technology, Report LR-290, Delft University of Technology, The Netherlands (1979), pp. 37–46.

    Google Scholar 

  156. J. Arbocz and C. D. Babcock, “The effect on the buckling cylindrical shells,” J. Appl. Mech., Trans. ASME, 36, No. 1, 28–38 (1969).

    Google Scholar 

  157. J. Arbocz and C. D. Babcock, “Computerized stability analysis using measured initial imperfections,” in: Proc. 12th Congr. ICAS, Munich (1980), pp. 688–701.

  158. J. Arbocz and J. G. Williams, “Imperfection surveys on a 10 ft-diameter shell structure,” AIAA J., 15, No. 7, 949–956 (1977).

    Google Scholar 

  159. R. E. Ball and J. A. Burt, “Dynamic buckling of shallow spherical shells,” Trans. ASME, E40, No. 20, 411–416 (1973).

    Google Scholar 

  160. G. W. Barr and R. O. Stearman, “Aeroelastic stability characteristics of cylindrical shells considering imperfections and edge constraint,” AIAA J., 7, 912–919 (1967).

    Google Scholar 

  161. G. W. Barr and R. O. Stearman, “Aeroelastic stability characteristics of cylindrical shells,” AIAA J., 8, 993–1000 (1970).

    Google Scholar 

  162. A. Blaquiere, Nonlinear System Analysis, Academic Press, New York-London (1966).

    Google Scholar 

  163. H. H. Bleich and J. H. Ginsberg, “Nonlinear forced vibrations of infinitely long cylindrical shells,” in: Techn. Rept. No. 46, Dept. of Civil Engineering and Engineering Mechanics, Columbia University, New York (1970).

    Google Scholar 

  164. B. Budiansky, “Dynamic buckling of elastic structures: criteria and estimates,” in: G. Herrmann (ed.), Proc. Intern. Conf. on Dynamic Stability of Structures, Pergamon, Elmsford, N.Y. (1967), pp. 83–106.

    Google Scholar 

  165. B. Budiansky and J. W. Hutchinson, “Dynamic buckling of imperfection sensitive structures,” in: Proc. 11th IUTAM Congr., Springer-Verlag, Berlin (1964), pp. 634–651.

    Google Scholar 

  166. B. Budiansky and J. W. Hutchinson, “Dynamic buckling of imperfect-sensitive structures,” in: Applied Mechanics, Springer Verlag (1966), pp. 636–657.

  167. J. C. Chen, “Nonlinear vibration of cylindrical shells,” Ph. D. Thesis, Institute of Technology, Pasadena, California (1972).

    Google Scholar 

  168. J. C. Chen and C. D. Babcock, “Nonlinear vibration of cylindrical shells,” AIAA J., 13, No. 7, 868–876 (1975).

    Google Scholar 

  169. A. P. Coppa, “Measurement of initial geometrical imperfections of cylindrical shells,” AIAA J., 4, No. 1, 172–175 (1966).

    Google Scholar 

  170. L. H. Donnell and C. C. Wan, “The effect of imperfection on buckling of thin cylinders and columns under axial compression,” Trans. ASME, J. Appl. Mech., 72, No. 2, 73–83 (1950).

    Google Scholar 

  171. D. A. Evensen, “A theoretical and experimental study of the nonlinear flexural vibrations of thin circular rings,” J. Appl. Mech., No. 33, 553–560 (1966).

    Google Scholar 

  172. W. Flügge, Stresses in Shells, Springer Verlag, Berlin (1973).

    Google Scholar 

  173. R. Gryboš, Stateznoš è Konstrukcij pod Obciazeniem Uderzoniowym, Pol. Akad. Nauk, Warsaw-Poznan (1980).

  174. N. J. Hoff, “Dynamic stability of structures,” in: Dynamic Stability of Structures, Pergamon Press, Oxford (1967), pp. 7–41.

    Google Scholar 

  175. J. W. Hutchison and B. Budiansky, “Dynamic buckling estimates,” AIAA J., 4, No. 3, 525–530 (1966).

    Google Scholar 

  176. J. W. Hutchison and W. T. Koiter, “Postbucking theory,” Appl. Mech. Rev., Vol. 23, 1353–1366 (1970).

    Google Scholar 

  177. W. T. Koiter, “Elastic stability and post-buckling behavior,” Proc. Symp. Nonlinear Problems, University of Wisconsin Press., Madison (1963), pp. 257–276.

    Google Scholar 

  178. W. T. Koiter, “The effect of axisymmetric imperfections on the buckling of cylindrical shells under axial compression,” Koniklike Nederlandishe Academie van Wetenshappen, B66, No. 5, 265–279 (1963).

    Google Scholar 

  179. W. T. Koiter, “On the stability of elastic equilibrium,” Doct. Thesis, Amsterdam (1945) (English translation: NASA TT F-10 (1967), p. 883).

  180. L. Koval, “Note of the effect of dynamic asymmetry of the vibrations of cylindrical shells,” J. Acoust. Soc. Amer., 35, No. 2, 57–60 (1963).

    Google Scholar 

  181. P. S. Koval'chuk, N. P. Podchasov, and V. V. Kholopova, “Periodic modes in the forced nonlinear vibrations of filled cylindrical shells with an initial deflection,” Int. Appl. Mech., 38, No. 6, 716–722 (2002).

    Google Scholar 

  182. P. S. Koval'chuk, N. P. Podchasov, and V. V. Kholopova, “Analysis of nonlinear bulging of liquid-filled cylindrical shells under local dynamic loading,” Int. Appl. Mech., 39, No. 3, 312–317 (2003).

    Google Scholar 

  183. V. D. Kubenko, P. S. Koval'chuk, and L. A. Kruk, “On multimode nonlinear vibrations of filled cylindrical shells,” Int. Appl. Mech., 39, No. 1, 85–92 (2003).

    Google Scholar 

  184. A. Rosen and J. Singer, “The effect of axisymmetric initial imperfections on the vibrations of cylindrical shells,” AIAA J., 12, 995–997 (1974).

    Google Scholar 

  185. A. Rosen and J. Singer, “Influence of asymmetric imperfections of the vibrations of axially compressed cylindrical shells,” Israel J. Techn., 14, No. 1, 29–36 (1976).

    Google Scholar 

  186. J. Singer, “Buckling of integrally stiffened cylindrical shells—a review of experiment and theory,” in: Contributions to the Theory of Aircraft Structures, Delft University Press, Rotterdam (1972), pp. 325–357.

    Google Scholar 

  187. J. Singer, H. Abramowich, and R. Yaffe, “Initial imperfection measurements of stiffened shells and buckling predictions,” Israel J. Techn., 17, No. 5–6, 324–338 (1979).

    Google Scholar 

  188. J. Singer, J. Arbocz, and C. D. Babcock, “Bucking of imperfect stiffened cylindrical shells under axial compression,” AIAA J., 9, 68–75 (1971).

    Google Scholar 

  189. Y. S. Tamura and C. D. Babcock, “Dynamic stability of cylindrical shells under step loading,” Trans. ASME, Ser. E, 42, No. 1, 190–195 (1975).

    Google Scholar 

  190. R.C. Tennyson, “Interaction of cylindrical shell buckling experiments with theory,” in: Theory of Shells, North-Holland, Amsterdam (1980), pp. 65–116.

    Google Scholar 

  191. Y. C. Fung and E. E. Sechler (eds.), Thin Shell Structures. Theory, Experiment and Design, Prentice Hall, Englewood Cliffs, N.J. (1974).

    Google Scholar 

  192. S. P. Timoshenko, Theory of Plates and Shells, McGraw-Hill, New York (1940).

    Google Scholar 

  193. S. A. Tobjas, “A theory of imperfection for the vibration of elastic bodies of revolution,” Eng., No. 172, 409–420 (1951).

    Google Scholar 

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Kubenko, V.D., Koval'chuk, P.S. Influence of Initial Geometric Imperfections on the Vibrations and Dynamic Stability of Elastic Shells. International Applied Mechanics 40, 847–877 (2004). https://doi.org/10.1023/B:INAM.0000048679.54437.f8

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