Abstract
The laws governing the propagation, growth and decay of acceleration waves in directed models of elastic beams are deduced for materials with zero and non-zero heat flux, that is non-conductors and conductors of heat. The equations depend explicitly on the geometric and inertial characteristic of the beam section and on the mechanical properties of the material. Solutions are derived for the velocities of propagation and the evolution (amplitude variation) of each type of wave (extension, bending, shear, twist). Results are discussed and some numerical examples presented.
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References
Nunziato, J.W. and Cowin, S.C., 'A non-linear theory of elastic materials with voids', Arch. Ration. Mech. Anal. 72 (1979) 175-201.
Capriz, G., Continua with Microstructure, Springer-Verlag, Berlin, 1989.
Mariano, P.M. and Augusti, G., 'Multifield description of microcracked continua: a local model', Math. Mech. Solids 3 (1998) 237-254.
Eriksen, J.L. and Truesdell, C.A., 'Exact theory of stress and strain in rods and shell', Arch. Ration. Mech. Anal. 1 (1958) 296-323.
Antman, S.S., The Theory of Rods, Handbuch der Physik, Band VI a/2, Springer-Verlag, Berlin, 1960.
Antman, S.S., Non-linear Problems of Elasticity, Springer-Verlag, New York, 1995.
Green, A.E. and Naghdi, P.M., 'Non-isotermal theory of rods, plates and shells', Int. J. Solids Struc. 6 (1970) 209-244.
Reissner, E., 'On a simple variational analysis of small finite deformations of prismatical beams', ZAMP 34 (1983) 642-648.
Simo, J.C. and Vu-Quoc, L., 'On the dynamics in space of rods undergoing large motions, a geometrically exact approach', Comput. Meth. Appl. Mech. Engng. 66 (1988) 125-161.
Simo, J.C. and Vu-Quoc, L., 'A geometrically exact rod model incorporating shear and torsion-warping deformation', Int. J. Solids Struc. 27(3) (1991) 371-393.
Villaggio, P., Mathematical Models of Elastic Structures, Cambridge University Press, 1997.
Bailey, P.B. and Chen, P.J.: 'On the local and global behaviour of acceleration waves', Arch. Ration. Mech. Anal. 41 (1971) 121-131.
Bailey, P.B. and Chen, P.J.: 'On the local and global behaviour of acceleration waves: addendum asymptotic behaviour', Arch. Ration. Mech. Anal. 44 (1972) 212-216.
Wright, T.W., 'Acceleration waves in simple elastic materials', Arch. Ration. Mech. Anal. 50 (1973) 237-277.
Manacorda, T., Introduzione alla Termomeccanica dei Continui, Pitagora, Bologna, 1979.
Šilhavý , M., The Mechanics and Thermodynamics of Continuous Media, Springer-Verlag, Berlin, 1997.
Mariano, P.M. and Sabatini, L., 'Homothermal acceleration waves in multifield descriptions of continua', Int. J. Non-linear Mech. 35 (2000) 963-977.
Sabatini, L., 'Propagazione di onde di accelerazione in modelli multicampo di continui', Ph. D. Thesis in Structural Engineering, Università di Roma 'La Sapienza' (in Italian), 2000.
Chadwick, P. and Currie, P.K., 'The propagation and growth of acceleration waves in heat conducting elastic materials', Arch. Ration. Mech. Anal. 49 (1972) 137-158.
Baldacci, R., Scienza delle Costruzioni, UTET, Torino, 1976.
Courant, R. and Hilbert, D., Methods of Mathematical Physics II, Wiley (Interscience), New York, 1962.
Varley, E. and Cumberbatch, E., 'Non-linear theory of wave fronts propagation', J. Inst.Math. Appl. 1 (1965) 101-112.
Ruberti, A. and Isidori, A., Teoria dei sistemi, Siderea, Roma, 1975.
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Sabatini, L., Augusti, G. Acceleration Waves in Thermoelastic Beams. Meccanica 35, 519–546 (2000). https://doi.org/10.1023/A:1010592409020
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DOI: https://doi.org/10.1023/A:1010592409020