Band-gap shift and defect-induced annihilation in prestressed elastic structures

Journal of Applied Physics

Volumn 105, Issue 6, 2009, Pages

  Gei, M ^a   Movchan, A B ^b   Bigoni, D ^a  

^a UNIVERSITY OF TRENTO   (Italy)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BAND GAPS; BAND-GAP SHIFTS; BEAM AXIS; CONCENTRATED MASS; CONSTRUCTIVE ALGORITHMS; ELASTIC BEAMS; ELASTIC FOUNDATIONS; ELASTIC STRUCTURES; FILTERING PROPERTIES; GOVERNING EQUATIONS; MASS EFFECTS; PIECE WISE; PRE STRESS; PRE-STRESSED; RESONANCE MODES; STOP BANDS;

ELASTICITY; ENERGY GAP;

MODEL STRUCTURES;

EID: 63749132882     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3093694     Document Type: Article

References (48)

1. References to phononic and photonic crystals can be found at http://www.phys.uoa.gr/phononics/PhononicDatabase.html and http://phys.lsu.edu/ ~jdowling/pbgbib.html.
2. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
3. S. John, Phys. Rev. Lett. 58, 2486 (1987).
4. M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, Phys. Rev. Lett. 71, 2022 (1993).
5. M. M. Sigalas and E. N. Economou, Solid State Commun. 86, 141 (1993).
6. M. D. Bacon, P. Dean, and J. L. Martin, Proc. Phys. Soc. London 80, 174 (1962).
7. A. B. Movchan and L. I. Slepyan, Proc. R. Soc. London, Ser. A 463, 2709 (2007).
8. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
9. J. H. Page, A. Sukhovich, S. Yang, M. L. Cowan, F. Van Der Biest, A. Tourin, M. Fink, Z. Liu, C. T. Chan, and P. Sheng, Phys. Status Solidi B 241, 3454 (2004).
10. S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 93, 024301 (2004).
11. X. Zhang and Z. Liu, Appl. Phys. Lett. 85, 341 (2004).
12. A.-C. Hladky-Hennion, J. Vasseur, B. Dubus, B. Djafari-Rouhani, D. Ekeom, and B. Morvan, J. Appl. Phys. 104, 064906 (2008).
13. P. Sheng, X. X. Zhang, Z. Liu, and C. T. Chan, Physica B 338, 201 (2003).
14. Z. Liu, C. T. Chan, and P. Sheng, Phys. Rev. B 71, 014103 (2005).
15. G. W. Milton and J. R. Willis, Proc. R. Soc. London, Ser. A 463, 855 (2007).
16. In sensor technology, active elements such as shape memory and piezoelectric inserts or patches are distributed periodically along the active device Refs. in order to enable the filtering properties of the system; ways to tune the width of stop bands are described in Refs..
17. M. Ruzzene and A. Baz, J. Vibr. Acoust. 122, 151 (2000).
18. A. Baz, J. Vibr. Acoust. 123, 472 (2001).
19. X. Zhang, Z.-Q. Zhang, L.-M. Li, C. Jin, D. Zhang, B. Man, and B. Cheng, Phys. Rev. B 61, 1892 (2000).
20. C. Goffaux and J. P. Vigneron, Phys. Rev. B 64, 075118 (2001).
21. A. Khelief, P. A. Deymier, B. Djafari-Rouhani, J. O. Vasseur, and L. Dobrzynski, J. Appl. Phys. 94, 1308 (2003).
22. W. L. Liu, T.-J. Yang, and B.-Y. Gu, J. Phys.: Condens. Matter 16, 4557 (2004).
23. L. Cremer and H. O. Leilich, Arch. Elektr. Uebertrag. 7, 261 (1953).
24. J. W. Miles, J. Engrg. Mech. Div. 82, 1 (1956).
25. Y. K. Lin, Int. J. Mech. Sci. 4, 409 (1962).
26. D. J. Mead, J. Sound Vib. 40, 19 (1975).
27. D. J. Mead, J. Sound Vib. 190, 495 (1996).
28. D. Yu, Y. Liu, H. Zhao, G. Wang, and J. Qiu, Phys. Rev. B 73, 064301 (2006).
29. D. Yu, Y. Liu, H. Zhao, G. Wang, and J. Qiu, J. Appl. Phys. 100, 124901 (2006).
30. D. Bigoni and A. B. Movchan, Int. J. Solids Struct. 39, 4843 (2002).
31. A. B. Movchan and S. Guenneau, Phys. Rev. B 70, 125116 (2004).
32. C. G. Poulton, S. Guenneau, and A. B. Movchan, Phys. Rev. B 69, 195112 (2004).
33. D. Bigoni, M. Gei, and A. B. Movchan, J. Mech. Phys. Solids 56, 2494 (2008).
34. D. Bigoni and D. Capuani, J. Mech. Phys. Solids 53, 1163 (2005).
35. D. Bigoni, D. Capuani, P. Bonetti, and S. Colli, Comput. Methods Appl. Mech. Eng. 196, 4222 (2007).
36. W. J. Parnell, IMA J. Appl. Math. 72, 223 (2007).
37. K. F. Graff, Wave Motion in Elastic Solids (Oxford University Press, New York, 1975).
38. V. V. Zalipaev (Ref.) developed an asymptotic approach to longitudinal vibrations of an elastic beam (without prestress) containing defects at its boundary and found that the "effective boundary conditions" for the first-order asymptotic problem are either of Dirichlet type (the boundary of the thin body is clamped), Robin type (stress and displacement satisfy an elastic constitutive equation), or Neumann type (the boundary, strongly damaged, becomes traction-free).
39. V. V. Zalipaev, A. B. Movchan, and I. S. Jones, Q. J. Mech. Appl. Math. 60, 457 (2007).
40. S. Nudehi, R. Mukherjee, and S. W. Shaw, J. Dyn. Syst., Meas., Control 128, 278 (2006).
41. C. Gui, R. Legtenberg, H. A. C. Tilmans, J. H. J. Fluitman, and M. Elwenspoek, J. Microelectromech. Syst. 7, 122 (1998).
42. V. Kaajakari, T. Mattila, A. Oja, and H. Seppä, J. Microelectromech. Syst. 13, 715 (2004).
43. We refer to "effective negative mass effects" as the exponentially decaying propagation modes that can be found in elastic systems in the way addressed in Ref..
44. R. Feynman, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1965), Vol. 2.
45. S. P. Timoshenko, W. Weaver, and D. H. Young, Vibration Problems in Engineering (Wiley, New York, 1974).
46. T. G. Chondros, A. D. Dimarogonas, and J. Yao, J. Sound Vib. 215, 17 (1998).
47. In the case of a homogeneous beam on an elastic foundation, all quantities introduced in Eqs. are constant along axis z. Therefore, the dispersion equation simplifies to P ω2 = (kr)4 + F- (kr)2 + S-, possessing the following features: (i) In the long-wavelength limit (kr→0), ω satisfies the cutoff limit P ω02 = S-. (ii) The frequency is monotonic for tensile (or null) prestress, F- 0, so that ωmin = ω0 in this case. (iii) For a compressive prestress, F- <0, the function of the above equation displays a minimum such that P ωmin2 = S - F- 2 4 and, consequently, buckling (ωmin =0) occurs at F- buckl =-2S with kbuckl r= S- 14.
48. (x) =0.6272 x2 -1.04533 x3 +4.5948 x4 -9.9736 x5 +20.2948 x6 -33.0351 x7 +47.1063 x8 -40.7556 x9 +19.6 x10.