RESEARCH ARTICLE
New decay results in linear thermoelastodynamics
Francesca Passarella,
Vincenzo Tibullo,
Francesca Passarella
Dipartimento di Matematica, Università di Salerno, Italy
Search for more papers by this authorCorresponding Author
Vincenzo Tibullo
Dipartimento di Matematica, Università di Salerno, Italy
Correspondence
Vincenzo Tibullo, Dipartimento di Matematica, Università di Salerno, Italy.
Email: [email protected]
Communicated by: H. Ammari
Search for more papers by this authorFrancesca Passarella,
Vincenzo Tibullo,
Francesca Passarella
Dipartimento di Matematica, Università di Salerno, Italy
Search for more papers by this authorCorresponding Author
Vincenzo Tibullo
Dipartimento di Matematica, Università di Salerno, Italy
Correspondence
Vincenzo Tibullo, Dipartimento di Matematica, Università di Salerno, Italy.
Email: [email protected]
Communicated by: H. Ammari
Search for more papers by this authorAbstract
This paper is concerned with the linear theory of thermoelastodynamics for the class of homogeneous and isotropic media with a semi-strongly elliptic elasticity tensor. For this class of materials, some results about the spatial behavior of solutions for the initial-boundary value problem are obtained by using an appropriate family of surface integral measures.
REFERENCES
- 1Horgan CO, Knowles JK. Recent developments concerning Saint-Venant's principle. Adv Appl Mech. 1983; 23: 179-269.
- 2Horgan CO. Recent developments concerning Saint-Venant's principle: An update. Appl Mech Rev. 1989; 42: 295-303.
10.1115/1.3152414 Google Scholar
- 3Horgan CO. Recent developments concerning Saint-Venant's principle: A second update. Appl Mech Rev. 1996; 49: S101-S111.
10.1115/1.3101961 Google Scholar
- 4Edelstein WS. A spatial decay estimate for the heat equation. Z Angew Math Phys. 1969; 20: 900-907.
- 5Knowles JK. On the spatial decay of solutions of the heat equation. Z Angew Math Phys. 1971; 22: 1050-1056.
- 6Flavin JN, Knops RJ. Some spatial decay estimates in continuum dynamics. J Elast. 1987; 17: 249-264.
- 7Flavin JN, Knops RJ, Payne LE. Energy bounds in dynamical problems for a semi-infinite elastic beam. In: G Eason, RW Ogden, eds. Elasticity: Mathematical Methods and Applications. Chichester: Ellis-Horwood; 1989: 101-111.
- 8Gurtin ME. The linear theory of elasticity. In: CA Truesdell, ed. Handbuch Der Physik, Vol. VIa/2. Berlin: Springer; 1972: 1-295.
- 9Ericksen JL, Toupin RA. Implications of Hadamard's conditions for elastic stability with respect to uniqueness theorems. Can J Math. 1956; 8: 432-436.
10.4153/CJM-1956-051-2 Google Scholar
- 10Gurtin ME, Sternberg E. A note on uniqueness in classical elastodynamics. Q Appl Math. 1961; 19: 169-171.
10.1090/qam/129226 Google Scholar
- 11Gurtin ME, Toupin RA. A uniqueness theorem for the displacement boundary-value problem of linear elastodynamics. Q Appl Math. 1965; 23: 79-81.
- 12Toupin RA, Bernstein B. Sound waves in deformed perfectly elastic materials. Acousto-elastic effect. J Acoust Soc. 1961; 33: 216-225.
- 13Chiriţǎ S. Saint Venant's principle in linear thermoelasticity. J Therm Stresses. 1995; 18: 485-496.
- 14Chiriţǎ S, Ciarletta M. Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua. Eur J Mech A Solids. 1999; 18: 915-933.
- 15Park JB, Lakes RS. Biomaterials: An Introduction. 3rd ed. Berlin: Springer; 2007.
- 16Wang YC, Lakes RS. Analytical parametric analysis of the contact problem of human buttocks and negative Poisson's ratio foam cushions. Int J Solids Struct. 2002; 39: 4825-4838.
- 17Lakes R. Foam structures with a negative Poisson's ratio. 1987; 235: 1038-1040.
- 18Lakes RS. Saint Venant end effects for materials with negative Poisson's ratios. J Appl Mech. 1992; 59: 744-746.
- 19Chiriţǎ S. Further results on the spatial beaviour in linear elastodynamics, An. Ştiinţ Univ. Al.I. Cuza Iaşi, Mat. (N. S.). 2004; 50: 289-304.
- 20Chiriţǎ S, Ciarletta M. Some further growth and decay results in linear thermoelastodynamics. J Therm Stresses. 2003; 26: 889-903.
- 21Ciarletta M, Passarella F. On the spatial behaviour in dynamics of elastic mixtures. Eur J Mech A Solids. 2001; 20: 969-979.
- 22Ciarletta M, Chiriţǎ S, Passarella F. Some results on the spatial behaviour in linear porous elasticity. Arch Mech. 2005; 57: 43-65.
- 23Passarella F, Tibullo V, Zampoli V. Decay properties of solutions of a Mindlin-type plate model for rhombic systems. J Mech Mater Struct. 2010; 5: 323-339.
- 24Passarella F, Tibullo V. Some results in linear theory of thermoelasticity backward in time for microstretch materials. J Therm Stresses. 2010; 33: 559-576.
- 25Passarella F. New results for semi-strongly elliptic materials in linear elastodynamics. Mech Res Commun. 2018; 94: 53-57.
- 26Tibullo V. Novel results in porous elasticity for semi-strongly elliptic materials. submitted to ZAMP.
- 27Carlson DE. Linear Thermoelasticity; In: CA Truesdell, ed. Handbuch Der Physik, Vol. VIa/2. Berlin: Springer; 1972: 297-345.
