Elastic wave transmission at an abrupt junction in a thin plate with application to heat transport and vibrations in mesoscopic systems

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 8, 2001, Pages

  Cross, M C ^a   Lifshitz, Ron ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; ELASTICITY; GEOMETRY; HEAT TRANSFER; LOW TEMPERATURE; MATHEMATICAL MODEL; OSCILLATOR; THERMAL ANALYSIS; VIBRATION;

EID: 0035880838     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.085324     Document Type: Article

References (21)

1. D. Angelescu, M. Cross, and M. Roukes, Superlattices Microstruct.23, 673 (1998).
2. L. Rego and G. Kirczenow, Phys. Rev. Lett.81, 232 (1998).
3. M P. Blencowe, Phys. Rev. B59, 4992 (1999).
4. R. Landauer, IBM J. Res. Dev.1, 223 (1957).
5. K. Schwab, E. Henriksen, J. Worlock, and M L. Roukes, Nature (London)404, 974 (2000).
6. R. Mihailovich and J. Parpia, Phys. Rev. Lett.68, 3052 (1992).
7. D S. Greywall, B. Yurke, P A. Busch, and S C. Arney, Europhys. Lett.34, 37 (1996).
8. D. Carr and H. Craighead, J. Vac. Sci. Technol. B15, 2760 (1997).
9. D. Carr, S. Evoy, L. Sekaric, H. Craighead, and J. Parpia, Appl. Phys. Lett.75, 920 (1999).
10. D. Harrington, P. Mohanty, and M. Roukes, Physica B15, 2145 (2000).
11. P. Mohanty, D. Harrington, K. Ekinci, Y. Yang, M. Murphy, and M. Roukes (unpublished).
12. T. Tighe, J. Worlock, and M. Roukes, Appl. Phys. Lett.70, 2687 (1997).
13. A. Cleland and M. Roukes, Appl. Phys. Lett.69, 2653 (1996).
14. A. Szafer and A. Stone, Phys. Rev. Lett.62, 300 (1989).
15. D H. Santamore and M C. Cross, Phys. Rev. Lett. (to be published).
16. L. Landau and E. Lifshitz, Theory of Elasticity, 3rd ed. (Butterworth-Heinemann, Oxford, 1986).
17. G. Miller and H. Pursey, Proc. R. Soc. London, Ser. A223, 521 (1954).
18. K. Graff, Wave Motion in Elastic Solids (Dover, New York, 1991).
19. S. Timoshenko, Theory of Elastic Stability (McGraw-Hill, New York, 1961).
20. The Rayleigh-Lamb equations usually occur in the somewhat different context of the analysis of the modes in a plate which is considered infinite in the (formula presented) plane, with propagation in the x direction and no dependence on the y coordinate. The wave numbers (formula presented) then give the variation across the thickness of the plate. The equations take the same form, with the wave speed ratio r given by the expression for two-dimensional elasticity theory, (formula presented). For example Rego and Kirczenow (Ref. 2) plot dispersion curves for these modes across the thickness of an infinite plate.
21. The sign convention for the moments (formula presented) is that (formula presented) is positive if it tends to produce compression in the negative z side of the plate. The angular displacements (formula presented) are defined with the same convention. This is the usual definition in the elasticity literature (Ref. 18).