Forced harmonic vibrations and dissipative heating-up of viscoelastic thin-walled elements (review)

International Applied Mechanics

Volumn 36, Issue 2, 2000, Pages 174-195

  Karnaukhov, V G ^a   Kirichok, I F ^a  

^a S P TIMOSHENKO INSTITUTE OF MECHANICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034134709     PISSN: 10637095     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02681993     Document Type: Review

References (106)

1. 1. I. Yu. Babich and N. P. Semenyuk, "Stability and initial supercritical behavior of composite shells," Prikl. Mekh., 34, No. 6, 3-38 (1998) (Int. Appl. Mech., 34, No. 2, 507-537 (1998)).
2. 1. I. Yu. Babich and N. P. Semenyuk, "Stability and initial supercritical behavior of composite shells," Prikl. Mekh., 34, No. 6, 3-38 (1998) (Int. Appl. Mech., 34, No. 2, 507-537 (1998)).
3. 2. G. I. Barenblat, "Effects of small vibrations of polymers subject to deformation," Prikl. Mat. Mekh., 30, No. 1, 73-81 (1966).
4. 3. R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems [Russian translation], Mir, Moscow (1968).
5. 4. V. L. Berdichevskii, Variation Principles of Continuum Mechanics [in Russian], Nauka, Moscow (1983).
6. 5. V. V. Bolotin, "The equations of nonstationary temperature fields in thin shells in the presence of heat sources," Prikl. Mat. Mekh., 24, No. 2, 361-364 (1960).
7. 6. V. V. Bolotin and A. I. Litvinov, "Theory of vibrodamping polymeric coatings," Mekh. Polim., No. 2, 269-277 (1978).
8. 7. V. V. Bolotin and Yu. N. Novichkov, The Mechanics of Multilayer Structures [in Russian], Mashinostroyeniye, Moscow (1980).
9. 8. A. S. Vol'mir, The Stability of Deformable Systems [in Russian], Nauka, Moscow (1967).
10. 9. A. S. Vol'mir, The Nonlinear Dynamics of Plates and Shells [in Russian], Nauka, Moscow (1972).
11. 10. I. I. Vorovich and V. G. Safronenko, "Application of variation principles to connected problems of thermoviscoelastic shells," Izv. Akad. Nauk SSSR, Ser. Mekh. Tverd. Tela, No. 4, 166-173 (1980).
12. 11. L. A. Galin, "Action of vibrational load on polymeric materials," Izv. Akad. Nauk SSSR, Ser. Mekh., No. 6, 11-15 (1965).
13. 12. É. I. Grigolyuk and F. A. Kogan, "The present state of the theory of multilayer shells," Prikl. Mekh., 8, No. 6, 3-18 (1972).
14. 13. É. I. Grigolyuk and P. P. Chulkov, Stability and Vibrations of Three-Layer Shells [in Russian], Mashinostroyeniye, Moscow (1973).
15. 14. Ya. M. Grigorenko and A. T. Vasilenko, Problems of the Statics of Anisotropic Inhomogeneous Shells [in Russian], Nauka, Moscow (1972).
16. 15. Ya. M. Grigorenko and A. T. Vasilenko, "Solution of problems and analysis of the stress-strain state of anisotropic shells (review)," Prikl. Mekh., 33, No. 11, 3-37 (1997) (Int. Appl. Mech., 33, No. 11, 851-880 (1997)).
17. 15. Ya. M. Grigorenko and A. T. Vasilenko, "Solution of problems and analysis of the stress-strain state of anisotropic shells (review)," Prikl. Mekh., 33, No. 11, 3-37 (1997) (Int. Appl. Mech., 33, No. 11, 851-880 (1997)).
18. 16. Ya. M. Grigorenko and A. P. Mukoyed, Solution of Nonlinear Problems of the Theory of Shells on a Computer [in Russian], Vyshcha Shk., Kiev (1983).
19. 17. Ya. M. Grigorenko, E. I. Bespalova, A. T. Vasilenko, et al., Numerical Solution of Boundary-Value Problems of Orthotropic Shells of Revolution on an M-220 Computer [in Russian], Naukova Dumka, Kiev (1971).
20. 18. B. P. Gumenyuk, "On the effect of flexural vibration on the temperature of a viscoelastic rod," Visnyk Kyivskogo Univ., Ser. Mat. Mekh., No. 14, 100-105 (1972).
21. 19. B. P. Gumenyuk, "Toward the effect of flexural vibration on the temperature of a viscoelastic rod," Visnyk Kyivskogo Univ., Ser. Mat. Mekh., No. 15, 41-46 (1973).
22. 20. B. P. Gumenyuk and V. G. Karnaukhov, "Thermal instability in connected dynamic problems of thermoviscoelasticity," Dokl. Akad. Nauk Ukr. SSR., Ser. A, No. 7, 609-629 (1978).
23. 21. B. P. Gumenyuk and V. G. Karnaukhov, "Thermal instability of viscoelastic bodies under dynamic cyclic loads," in: Thermal Stresses of Structural Elements [in Russian], Issue 18 (1978), pp. 46-50.
24. 22. B. P. Gumenyuk and V. G. Karnaukhov, "Approximate calculation of critical thermal states in connected dynamic problems of thermoviscoelasticity," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 10, 905-908 (1977).
25. 23. B. P. Gumenyuk and V. G. Karnaukhov, "Effect of thermomechanical conjugation on the dynamic behavior of a viscoelastic rod subject to forced longitudinal vibrations," Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 2, 128-132 (1978).
26. 24. B. P. Gumenyuk and V. G. Karnaukhov, "Heat generation in a viscoelastic cylindrical shell under cyclic loading," in: Boundary-Value Problems of the Theory of Elasticity and Viscoelasticity [in Russian], Sverdlovsk (1980), pp. 42-48.
27. 25. B. P. Gumenyuk, V. G. Karnaukhov, and I. F. Kirichok, "Connected dynamic problems of thermoviscoelasticity for plates and shells subject to cyclic loads," in: Proc. 10th All-Union Conf. on The Theory of Shells and Plates [in Russian], Vol. 1, Kutaisi (1975), pp. 374-481.
28. 26. B. P. Gumenyuk, V. G. Karnaukhov, and I. F. Kirichok, "Using the quasilinearization and WKB methods to solve connected problems of thermoviscoelasticity in cyclic loads," in: The Stress-Strain State of Elastic and Viscoelastic Structures [in Russian], Sverdlovsk (1977), pp. 14-24.
29. 27. B. P. Gumenyuk, V. G. Karnaukhov, and I. K. Senchenkov, "Influence of thermomechanical coupling on the dynamic behavior of viscoelastic bodies," Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 148-155 (1980).
30. 28. A. Jagota and P. R. Dawson, "The influence of lateral wall vibrations on the ultrasonic welding of thin-walled parts," Trans. ASME, Konstr. Tekhn. Mash., Ser. B, 11, 117-128 (1988).
31. 29. A. A. Dudchenko, S. A. Lurie, and I. F. Obraztsov, "Anisotropic plates and shells," Itogi Nauki Tekh. VINITI Ser. Mekh. Def. Tverd. Tela, 15, 126-140 (1983).
32. 30. A. A. Il'yushin and B. E. Pobedrya, Fundamentals of the Mathematical Theory of Thermoviscoelasticity [in Russian], Nauka, Moscow (1970).
33. 31. Kapania, "Methods of design of laminated shells (review)," Sovr. Mashinostr., Ser. B, No. 12, 1-11 (1995).
34. 32. V. G. Karnaukhov, Connected Problems of Thermoviscoelasticity [in Russian], Naukova Dumka, Kiev (1982).
35. 33. V. G. Karnaukhov and B. P. Gumenyuk, "Vibrations of a viscoelastic rod with thermomechanical conjugation," Inzh. Fiz. Zh., 35, No. 4, 692-697 (1978).
36. 34. V. G. Karnaukhov and I. F. Kirichok, Connected Problems of the Theory of Viscoelastic Plates and Shells [in Russian], Naukova Dumka, Kiev (1986).
37. 35. V. G. Karnaukhov and I. F. Kirichok, "The quasilinearization method in connected dynamic problems of thermoviscoelasticity," Vopr. Dinam. Prochn., No. 42, 3-11 (1983).
38. 36. V. G. Karnaukhov and I. F. Kirichok, "The thermomechanical theory of three-layer shells with a viscoelastic damping layer under cyclic loading," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 6, 46-49 (1981).
39. 37. V. G. Karnaukhov and I. F. Kirichok, "The thermomechanical theory of three-layer orthotropic shells with a viscoelastic filler," Prikl. Mekh., 19, No. 7, 31-37 (1983).
40. 38. V. G. Karnaukhov and I. F. Kirichok, "One variant of constructing the thermomechanical theory of structural flexible viscoelastic shells subject to harmonic deformation," Prikl. Mekh., 27, No. 5, 57-63 (1991).
41. 39. V. G. Karnaukhov and I. F. Kirichok, "The thermomechanical theory of flexible shallow three-layer shells with a viscoelastic damping layer," in: Energy Dissipation in Mechanical Systems Subject to Vibrations [in Russian], Naukova Dumka, Kiev (1982), pp. 31-40.
42. 40. V. G. Karnaukhov and I. F. Kirichok, "Thermomechanical behavior of flexible viscoelastic plates and shells under cyclic loads," Probl. Prochn., No. 3, 10-14 (1979).
43. 41. V. G. Karnaukhov, I. F. Kirichok, and B. P. Gumenyuk, "The quasilinearization and WKB methods in connected dynamic problems of thermoviscoelasticity," in: Thermal Stresses of Structural Elements [in Russian], Issue 15 (1975), pp. 36-44.
44. 42. V. G. Karnaukhov, I. F. Kirichok, and B. P. Gumenyuk, "Influence of a cyclic load on the thermomechanical behavior of a viscoelastic round plate of variable thickness," in: Thermal Stresses of Structural Elements [in Russian], Issue 16, (1976), pp. 17-22.
45. 43. V. G. Karnaukhov, V. V. Mikhailenko, and F. Ts. Franovskii, "Development of the theory of constitutive equations for physically nonlinear viscoelastic bodies under cyclic strain," Prikl. Mekh., 32, No. 10, 46-51 (1996).
46. 44. V. G. Karnauhov, I. K. Senchenkov, and B. P. Gumenyuk, The Thermomechanical Behavior of Viscoelastic Bodies under Harmonic Loading [in Russian], Naukova Dumka, Kiev (1985).
47. 45. V. G. Karnaukhov, G. A. Yakovlev, and L. P. Goncharov, "Investigation of the self-heating of viscoelastic materials under cyclic loads," Probl. Prochn., No. 2, 26-29 (1975).
48. 46. A. M. Kiiko and O. B. Rudakova, "The connected problem of thermoviscoelasticity on free nonlinear vibrations of a rectangular plate," Mekh. Tverd. Tela, No. 5, 145-148 (1989).
49. 47. I. F. Kirichok, "The thermomechanical behavior of a composite rod with viscoelastic layers," Prikl. Mekh., 8, No. 4, 107-115 (1982).
50. 48. I. F. Kirichok, "The linear thermomechanical theory of cyclically deformed viscoelastic shells," Dokl. Akad. Nauk Ukr. SSR Ser. A, No. 3, 34-38 (1984).
51. 49. I. F. Kirichok, "The vibrations of prestressed three-layer shells with a viscoelastic filler with allowance for heat generation," Prikl. Mekh., 21, No. 10, 37-46 (1985).
52. 50. I. F. Kirichok, "Influence of shear strain and rotary inertia on the thermomechanical behavior of rods subject to flexural vibrations," Prikl. Mekh., 27, No. 1, 107-115 (1991).
53. 51. I. F. Kirichok and V. G. Karnaukhov, "The thermomechanical behavior of flexible viscoelastic plates and shells under cyclic loads," Probl. Prochn., No. 3, 10-14 (1979).
54. 52. M. Kishkilov, "The finite-element method for investigation of a beam under the effect of continuous vibrational loading," Teor. Pril. Mekh., No. 2, 74-80 (1990).
55. 53. A. D. Kovalenko and V. G. Karnaukhov, "Equations and solution of some problems of the theory of viscoelastic shells," in: Thermal Stresses of Structural Elements [in Russian], Issue 7 (1967), pp. 11-24.
56. 54. A. D. Kovalenko and V. G. Karnaukhov, "The main features of the behavior of simple material," in: Thermal Stresses of Structural Elements [in Russian], Issue 12, (1972), pp. 5-18.
57. 55. A. D. Kovalenko and V. G. Karnaukhov, "The effect of cyclic loading on the temperature of a viscoelastic cylinder," Dop. Akad. Nauk Ukr. RSR, No. 9, 1135-1140 (1966).
58. 56. A. D. Kovalenko and V. G. Karnaukhov, "Heat generation in viscoelastic shells of revolution under periodic actions," in: Thermal Stresses of Structural Elements [in Russian], Issue 11 (1971), pp. 5-11.
59. 57. A. D. Kovalenko and V. G. Karnaukhov, "Heat generation in viscoelastic bodies under periodic actions," Prikl. Mekh, 5, No. 2, 28-35 (1969).
60. 58. A. D. Kovalenko and V. G. Karnaukhov, "Heat generation in viscoelastic bodies," Dop. Akad. Nauk Ukr RSR, No. 11, 1029-1033 (1968).
61. 59. A. D. Kovalenko, V. G. Karnaukhov, G. A. Yakovlev, B. P. Gumenyuk, and L. P. Goncharov, "Heating of a viscoelastic rod in transversal vibrations, "in: Thermal Stresses of Structural Elements [in Russian], Issue 12 (1972), pp. 36-39.
62. 60. A. D. Kovalenko, V. G. Karnaukhov, G. A. Yakovlev, B. P. Gumenyuk, and L. P. Goncharov, "Heat generation in viscoelastic rods subject to forced transversal vibrations," in: Thermal Stresses of Structural Elements [in Russian], Issue 13 (1973), pp. 11-14.
63. 61. V. I. Kozlov, "Vibrations and dissipative heating-up of a multilayer viscoelastic shell of revolution," Prikl. Mekh., 32, No. 6, 82-89 (1996) (Int. Appl. Mech., 32, No. 6, 480-486 (1996)).
64. 61. V. I. Kozlov, "Vibrations and dissipative heating-up of a multilayer viscoelastic shell of revolution," Prikl. Mekh., 32, No. 6, 82-89 (1996) (Int. Appl. Mech., 32, No. 6, 480-486 (1996)).
65. 62. V. V. Vasil'ev, V. D. Protasov, V. V. Bolotin, et al., Composite Materials: A Reference Book [in Russian] (V. V. Vasil'ev and Yu. M. Tarnopol'skii, general editors), Mashinostroyeniye, Moscow (1990).
66. 63. B. J. Korites and F. C. Nelson, "The influence of dissipative heating on the loss factor of a viscoelastically damped beam," Trans. ASME, Konstr. Tekhn. Mash., Ser. B, No. 4, 56-61 (1969).
67. 64. A. I. Lukomskaya and V. F. Evstratov, Fundamentals of Predicting the Mechanical Behavior of Rubber [in Russian], Khimiya, Moscow (1975).
68. 65. G. I. Marchuk and V. I. Agoshkov, An Introduction to Projection-Net Methods [in Russian], Nauka, Moscow (1981).
69. 66. V. V. Moskvitin, Resistance of Viscoelastic Materials [in Russian], Nauka, Moscow (1972).
70. 67. M. A. Narbut, "The ray-path method of calculation of the intensity of wave fields in viscoelastic media," in: Problems of the Dynamic Theory of Propagation of Seismic Waves [in Russian], Issue 12, (1974), pp.61-68.
71. 68. A. D. Nashif, D. I. G. Jones, and J. P. Henderson, Vibration Damping, John Wiley and Sons, New York (1985).
72. 69. P. F. Nedorezov, "Determination of the temperature field in forced longitudinal vibrations of a viscoelastic rod," in: The Mechanics of Deformable Media [in Russian], Issue 5 (1978), pp. 8-17.
73. 70. P. F. Nedorezov, "Determination of the temperature field in a polymeric cylindrical shell under cyclic loading: engineering theory," in: Applied Theory of Elasticity [in Russian], Izd. Saratov. Univ., Saratov (1980), pp. 28-33.
74. 71. Yu. N. Nemish and Yu. I. Khoma, "The stress-strain state of nonthin shells and plates. A generalized theory (review)," Prikl. Mekh., 29, No. 11, 3-34 (1993) (Int. Appl. Mech., 29, No. 11, 873-902 (1993)).
75. 71. Yu. N. Nemish and Yu. I. Khoma, "The stress-strain state of nonthin shells and plates. A generalized theory (review)," Prikl. Mekh., 29, No. 11, 3-34 (1993) (Int. Appl. Mech., 29, No. 11, 873-902 (1993)).
76. 72. W. C. Rheinboldt and J. Ortega, Iterative Solution of Nonlinear Systems in Several Variables [Russian translation], Mir, Moscow (1975).
77. 73. Ya. S. Podstrigach and R. N. Shvets, Thermoelasticity of Thin Shells [in Russian], Naukova Dumka, Kiev (1978).
78. 74. V. M. Porksheyan, "Some features of the solution of the heat conduction equation with allowance for the coupling of thermomechanical processes," Izv. Sev.-Kavkaz. Nauch. Tsentra Vyssh. Shk. Estest. Nauk, No. 2, 29-33 (1984).
79. 75. V. M. Porksheyan, "Heating-up of thermoviscoelastic rods and circular plate under cyclic strains," Prikl. Mekh., 20, No. 1, 94-100 (1984).
80. 76. A. P. Prusakov and Yu. K. Rasteryaev, "Bending of shallow multilayer shells in a high-temperature field," in: Proc. 8th All-Union Conf. on The Theory of Shells and Plates (Rostov-on-Don, 1971) [in Russian], Nauka, Moscow (1973), pp. 756-672.
81. 77. S. B. Ratner and V. I. Korobov, "Self-heating of polymers subject to multiple strain," Dokl. Akad. Nauk Ukr. SSR, No. 4, 161-166 (1965).
82. 78. S. B. Ratner and V. I. Korobov, "Self-heating of plastic subject to cyclic strain," Mekh. Polim., No. 3, 93-100 (1965).
83. 79. O. B. Rudakova, "The problem of thermoviscoelasticity on free nonlinear vibrations of a rectangular plate," Izv. Akad. Nauk Ukr. SSR Mekh. Tverd. Tela., No. 5, 183-187 (1990).
84. 80. V. G. Safronenko, "Application of the variation principle to the formulation of connected problems for thermoviscoelastic shells," in: Design of Plates and Shells [in Russian], Izd. Rostov. Univ., Rostov-on-Don (1980), pp. 12-22.
85. 81. V. G. Safronenko, "Variation formulation of connected problems for thermoviscoelastic shells," Izv. Sev.-Kavkaz. Nauch. Tsentr, No. 4, 21-27 (1976).
86. 82. I. K. Senchenkov, "The dynamic behavior of a rod with allowance for the temperature dependences of the properties of the material," Prikl. Mekh., 20, No. 2, 85-92 (1984).
87. 83. I. K. Senchenkov, "Longitudinal vibrations and heating-up of a rod made from nonlinear viscoelastic material," Prikl. Mekh., 21, No. 9, 79-85 (1985).
88. 84. I. K. Senchenkov, "Approximate formulation of connected problems of nonlinear thermoviscoelasticity under harmonic actions," Prikl. Mekh., 21, No. 2, 91-99 (1985).
89. 85. I. K. Senchenkov and B. P. Gumenyuk, "The thermomechanical behavior of a viscoelastic spring-rod with an amplitude-dependent module," Prikl. Mekh., 16, No. 5, 107-112 (1980).
90. 86. I. K. Senchenkov and V. G. Karnaukhov, "Some general variation principles of thermomechanics," in: Mechanics of Elastomers [in Russian], Krasnodar. Politekh. Inst., Krasnodar (1981), pp. 43-50.
91. 87. I. K. Senchenkov, V. G. Karnaukhov, and B. P. Gumenyuk, "Influence of vibrational heating-up on the mechanical stability of a viscoelastic rod," in: Mechanics and Strength of Machines [in Russian], Issue 34, (1981), pp. 109-113.
92. 88. I. K. Senchenkov and I. F. Kirichok, "Forced nonlinear vibrations and dissipative heating-up of a viscoelastic beam," Prikl. Mekh., 23, No. 1, 91-97 (1987).
93. 89. L. R. Soshevskaya, "Determination of the temperature field in a plate subject to steady-state transversal vibrations," in: Mechanics of Deformable Media [in Russian], Issue 6, 34-44 (1979).
94. 90. I. A. Sprishevskaya, "Two problems of determination of the temperature field of a cyclically deformable medium," Vestnik Moskovskogo Univ., No. 4, 91-95 (1968).
95. 91. S. P. Timoshenko and S. Voinovskii-Kriger, Plates and Shells [in Russian], Fizmatgiz, Moscow (1963).
96. 92. J. F. Tormey and S. C. Britton, "Effect of cyclic loading on solid propellant grain structures," Raketn. Tekhn. Kosmon., No. 8, 70-82 (1963).
97. 93. Yu. N. Shevchenko and I. V. Prokhorenko, The Theory of Elastoplastic Shells under Nonisothermal Loads [in Russian], Naukova Dumka, Kiev (1981).
98. 94. R. A. Shapery, "The effect of cyclic loading on the temperature in viscoelastic media with variable properties," Raketn. Tekhn. Kosmon., No. 5, 55-60 (1964).
99. 95. R. A. Shapery, "Thermomechanical behavior of viscoelastic media with variable properties subjected to cyclic loading," Trans. ASME, Prikl. Mekh., Ser. E, No. 3, 150-161 (1965).
100. 96. R. A. Shapery and D. E. Cantey, "Thermomechanical response studies of solid propellants subjected to cyclic and random loading," Raketn. Tekhn. Kosmon., No. 2, 255-264 (1966).
101. 97. J. Constable, J. G. Williams, and D. J. Burns, "Fatigue and cyclic thermal softening of thermoplastics," J. Mech. Eng, Schi., 12, No. 1, 20-29 (1970).
102. 98. D. D. Joseph and E. M. Sparrow, "Nonlinear diffusion induced by nonlinear sources," Quart. Appl. Math., 28, No. 3, 327-341 (1970).
103. 99. D. D. Joseph and T. S. Lundgren, "Quasilinear Dirichlet problems driven by positive sources," Arch. Ration. Mech. Anal., 43, No. 4, 241-269 (1973).
104. 100. N. C. Huang and E. N. Lee, "Thermomechanical coupling behavior of viscoelastic rods subjected to cyclic loading," Trans. ASME Ser. E, 34, No 1, 127-132 (1967).
105. 101. F. S. Karal Jr. and J. B. Keller, "Elastic wave propagation in homogeneous and inhomogeneous media," J. Acoust. Soc. Amer., 31, No. 6, 1241-1255 (1959).
106. 102. S. Mukherjee, "Variational principle in dynamic thermoviscoelasticity," Int. J. Sol. Struct., 9, No. 10, 1301-1316 (1973).