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FREE VIBRATIONS of VISCOELASTIC MATERIALS FOR ARBITRARY KERNEL

Journal Name:

  • İstanbul Üniversitesi Fen Fakültesi Matematik, Fizik ve Astronomi Dergisi

Publication Year:

  • 2004-2005

Key Words:

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
For an isotropic viscoelastic constitutive relation in Boltzmann-Volterra form the problems of vibrations of linear viscoelastic materials reduce to the solution of a certain integro-differential equation which coincides with the equation of vibrations of a viscoelastic system with single degree of freedom. Full solution of this equation for arbitrary kernel of relaxation is constructed in the present article. Iteration processes for calculating frequency and damping coefficient are given. There are two special cases of the relaxation kernel that a solution for the problem involved is given. One is the case of the sum of exponents, in the other the kernel is the sum of Dirac delta and an exponent. Analysis of obtained solutions and their comparisons with results available in literature are performed.
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REFERENCES

References: 

1.
Ishlinskii
, A.Yu., "Longitudinal Vibrations of a Bar with a Linear Law of After-effect and Relaxation", Prikl. Math. Mech. 4(1) ,79-92 (1940) (in Russian).
2. Rozovskii,
M.I.
, "Radial Vibrations of a Hollow Sphere with a Singular Elastic After-effect Kernel", D.A.N. SSSR, 105(4), 672-675 (1955) (in Russian).
3.
Rabotnov
, Yu.N., Elements of Hereditary Solid Mechanics, Mir pub., M. (1980).
4.
Christensen,
R.M.
, Theory of Viscoelasticity (An introduction), A.P., N.Y.&L. (1971).
5.11yushin A.A., Larionov G.S., Filatov A.N., "On Averaging in a Systems of Integra-differential Equations", D.A.N. SSSR,188(1), (1969) (in Russian).
6.
Bogolyubov
, N.N., On some Statistical Methods in Mathematical Physics, Izd.A.N. USSR (1945).
7.
Ilyasov,M.H.
, Gurbanov,N.T., "To the Solution of Integra-differential Equation of Free Vibrations of Viscoelastic System",D.A.N.Azerb.,No.5,(1984) (in Russian).
8.
Ilyasov,M.H.
, Aköz,A.Y., "The Vibration and Dynamic Stability of Viscoelastic Plates", Int.J.Engin.Science 38 (2000) 695-714.9. Newman,M.K.,"Viscous Damping in Flexural Vibrations of Bars", J.AppLMech., v.26,Trans.ASME,v.81,ser.E,sept.(1959),pp.367-376.
10. Lee,H.C./'Forced Lateral Vibration of a Uniform Cantilever Beam with Internal and External Damping",J.Appl.Mech.,v.27,Trans.ASME, v.82, ser.E, sept.(1960), pp. 551-556.
11. Pan,H.H., "Vibration of a Viscoelastic Timoshenko Beam",J.Engin.Mech. Division, Proc.A S C E, (1966), pp. 213-233.
12. Huang,T.C, Huang,C.C.,"Free Vibrations of Viscoelastic Timoshenko Beams", J. Appl. Mech., Trans.ASME, ser.E, june (1971), pp.515-521.
13. Struik,L.C.E.,"Free Damped Vibrations of Linear Viscoelastic Materials", Rheol. Acta 6, 119 (1967).
14. Flugge,W,Viscoelasticity,Sprmger Verlag, (1975).
15 Ilyushin,A.A., Pobedrya,B.E.,77?e Foundations of Mathematical Theory ofThermovisco-elasticity, Nauka, M.(1970) (in Russian).
16. Ogibalov,P.M., Lomakin,V.A., Kishkin,B.P., Mechanics of Polymers, Izd.Mosk. Univ.,M.(1975) (in Russian).
17. Moskvitin,V.V., Strength of Viscoelastic Materials, Nauka, M.(1972) (in Russian).
18. Larionov,G.S.,"Investigation of Vibrations of Relaxation Systems by Averaging Method",Mec.of Polimers,5 (1969) (in Russian).
19. Matyash,V.L,"Vibrations of Isotropic Viscoelastic Shells", Mec.of Polymers,6 (1971) (in Russian).
20. Sneddon,I.N ., Fourier Transforms, McGRAW- HILL Company, INC, N.Y., T.,L.,(1951)
21. Ilyasov,M.H., Some Dynamical Problems of Linear Viscoelasticity, Doctoral Dissertation, Moscow Gos. Univ., Moscow (1985),
22. Ilyasova, N.M. "Free Damped Vibrations of Viscoelastic Materials", Istanbul Univ. Fen Fak. Mat. Dergisi 61-62 (2002-2003), 29-40.

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