You are here

Home » Content

Analytic solution of one-dimensional problem for partial integro-differential equations which have partial continuous coefficients in thermoviscoelasticity theory

Journal Name:

  • İstanbul Üniversitesi Fen Fakültesi Matematik, Fizik ve Astronomi Dergisi

Publication Year:

  • 1998-1999
Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
in this paper, a non-stationary problem on thermomechanic wave propagation is solved in an environment, which is, consists of a finite thick plate connected with a semiinfinile space. Materials of the plate and the space are in conformity with linear viscoelaslicity laws. Mathematical model of (he problem consists of: linear equations of viscoelasticity and heat transfer for each environment independently, initial conditions and on the connection surface of environments conditions of increasing temperature and normal stress, depending only on time which are given as known functions, it is assumed that temperature and mechanical fields depend on each other. As a system, parabolic type partial inlegro-differential equation of temperature and hyperbolic type partial integro-differential equation of wave are solved, it is assumed that kernels of integral operators are difference kernels. Depending on boundary conditions, functions of temperature and mechanical magnitudes become only functions of time and a space axis, which is perpendicular to free surface. In this case the problem turns out to be a one-dimensional one.
Bookmark/Search this post with
FULL TEXT (PDF): 
PDF icon arastrmx_190866_57-58_pp_113-161.pdf
113-161
  • English

REFERENCES

References: 

[1]
ACHE
N BACH ,J.D.,SUN ,C.T. and HERRMAN , G.: On the vibration of the a laminated body ,LAp\?\. Mech., 35 (1968), 467-475.
[2]
BARKER,L.M
: :A model for stress wave propagation in composite materials , J.of Comp. Mater, 5 (1971), 140-162.
[3| BRILLOIJIN , L.: Wave propagation in periodic structures .Dover publishing, 182(1952)
[4j CARSLAW ,H.S. and JAEGER,J.C: Operational Methods in Applied
Mechanics, Oxford University Press. 1941.
|5j CHE EN, C.C. and CLIFTON, R.J: Asymptotic bilaminates, Proc. 14th Midwestern Mechanics Conf. University of Oklahoma , 1975,399-417 |6| CHEN,P.J. and GURT1N,M.E.: On the propagation od one-dimensional deceleration waves in laminated composites. J.Appl.Mech. N40 {1973), 1055¬1060.
|7| CHRISTINSEN, K.M.-.Wave propagation in layered elastic media, J.Appl. Mech.42 (1975). 153-158.
|8] CHRISTENSEN,R.M.:Theory of Viscoelasticiiy,Academic press. 1971.
|9j CRISTESCU,N.:Dynamik'plasticity, North-Holland Publishers, 1967.
.JlOj CRACH, S. '.Wave propagation in a viscoelastic material with temperature-dependent properties and thermomechanical coupling. Transactions of ASME ,J
Of Appl . Mech ., 86 (1964) .423-429.
fll| GUTERMAN,M.M and NITECKI ,:Z.H.: Differential Equations The
Saunders Series,1984.
112] HEGEMIER ,G.A. and NAYFEH, A.H.: A Continuum theory for wave propagation in laminated composites,J.Appl. Mech.,40 (1973), 503-510..8 1nj^HETNARSKS, R.B.: Solution of Coupled Thermae last ic Problem in the form of series of function. Arch. Mech. Stos.,6, N4 (1964), 32-39.
[14|..HETNARSKI, R.B.: Coupled Thermoelastic Problem for the halfspace^uW. Acad. Polan. ScuSer. Sci. Techn., 12, Nl (1964)J20-128.
115] IGN ACZAG,J.: Thermal displacement in a non-homogeneous elastic semifmite space, caused by sudden heating of the boundary, Arch.Meech. Stos.,10 N2 (1958), 152-159.
[16| KARMAN,Th.:^/7 the propagation of elastic deformation in solid, -NDRC report No,A-29, OSRDNo.365 (I942).
[17] LEE,E.H.:Dynamics of Composite Materials, ASME Appl.Mech.Divisions Series, Book No.H0078(1972).
[18] LEE,E.H.and KANTER^J.: Wave propagation in finite roads of Viscoelastic Materials, Journal of Appl. Physics, 24, N9 (1953) 1115.
[19] LEE,E.H. and ROGERS J".G.-.Solution of viscoelastic stress analysis problems using measured creep or relaxation functions. Brown University Technical Report DA-G-54/I, J. Appl. Mech, 30 Trans.ASME,85 (1963), 127-133,Series E.
[20] MORLAND,L.W.and LEE,E.H.:Slress analysis for linear viscoelastic materials with temperature variation, Transactions of the Society of Rheology, 4 (1960), 223.
[21] MUKI , R. and STERNBERG^ .-.On transient thermal stresses in viscoelastic materials with temperature dependent properties. Journal of Applied Mechanics,28,Trans. ASME ,83.( 1961). Scries E.
[22] PECK, J.C and GURTMAN,G.A. \Dispertive pulse propagation parallel to the interfaces of a laminated Composite, J.Appl. Mech., 36 (1969),479-484.
[23] SNEDDON,I.N.: The propagation of thermal stresses in thin Metallic rods. Proc. Roy. Soe. Sec. A, 9,65 (1959), 115-121.
[24] SOOS,E.:77;ii Green 'functions (for short time) in the linear theory of Coupled thermoelastieitv. Arch. Mech. Stos.,18, Nl, 12-18.
[25] SVE,C :Stress wave attenuation in Composite Materials, J.Appl. Mech., 39 (1972),1151-1153.
[26] TAYLOR,G.I.: Propagation of earth waves from an explosion, British official Report .R.C5570. (1940)21.
[27] TING, T.C.T.: Simple waves in an extensible String J. Appl.Mech.,36 (1969),893-896.
[28] TING,T,C.T.-.Dynamical response of Composites, Applied. Mech. reviews, 33 ,NI2 (1980).
[29] TING, T.C.T and MUKUNOKI, I :A theory of viscoelastic analogy for wave propagation normal to the layering of a layered medium, J. Appl. Mech. reviews, 46, N3 (1979),329-336.
[30] TING, T.C.T and MUKUNOKI, I -.Transient wave propagation normal to the layering of finite layered medium, Int. J. Solids Structures, 16 (1980), 239-251.
[31] VALANIS, K.C and L1AN1S, G.A.: Method of analysis of transient -thermal stresses in thermorheologically simple viscoelastic solids,Transactions of the ASME. J of Appl. Mech.,86 (1964), 47-53.
[32] VALANIS, K.C.: Method of analysis of transient thermal stresses in thermorheoiogiea/ly simple viscoelastic solids,Mechanical Engineering, 86 (1964), 64.
[33] VALANIS, K.C and LIANIS, G.'.Error analysis of approximate solutions of thermal viscoelastic stresses, Purdue University Report A and ES 62-13, (1962).
Hdl VAI.ANIS. K.C: Studies in Stress Analvsis of Viscoelastic Solids Under Non-Steadv
Temperature Gravitational and Inertial Loads, PhD thesis, Purdue University, 1963.

Thank you for copying data from http://www.arastirmax.com