Influence of Different Defects on the Energy Bands for the Super Cell of a Defected Periodic Viaduct
 |
International Journal of Engineering Trends and Technology (IJETT) | 
|
| © 2013 by IJETT Journal | ||
| Volume-4 Issue-5 |
||
| Year of Publication : 2013 | ||
| Authors : Cheng-yong He , Li Lei |
Citation
Cheng-yong He , Li Lei. "Influence of Different Defects on the Energy Bands for the Super Cell of a Defected Periodic Viaduct". International Journal of Engineering Trends and Technology (IJETT). V4(5):2194-2204 May 2013. ISSN:2231-5381. www.ijettjournal.org. published by seventh sense research group.
Abstract
In this study, the influence of different defects on the energy bands for the super cell of a defected periodic viaduct (DPV) when considering the pile - soil - structure interaction is investigated. By developing a coupled boundary element method (BEM) model for the piles supporting the superstructure of the DPV , the compliances of the pile foundation can be obtained , combined with the transfer matrices for the beams and piers, the transfer matrix for each span of the viaduct can be determined. Then, the eigenvalue equation for the super cell of the DPV can be derived by utilizing the Bloch theorem , solution of which yields the energy bands of the super - cell. Num erical results show that some defects may give rise to the defect state for the super cell of the DPV.
References
[1] M . M . Sigalas . Defect states of acoustic waves in two - dimensional lattice of solid cylinders , J Appl Phys. vol. 84 , pp. 3026 – 3030 , 19 98 .
[2] C.H. Hodges . Confinement of vibration by structu re irregularity , JS ound V i b. vol. 82 , pp. 411 – 424 , 19 82.
[3] L . Brillouin . Wave propagation in periodic structures , Dover Public Inc, New York. 1946.
[4] D . J . Mead . Free wave propagation in periodically supported infinite beams , J Sound Vib. vol. 11 , pp. 181 – 197 , 19 70.
[5] D . J . Mead . Wave propagation in continuous periodic structures: Research contributions from Southampton , J S ound V ib. vol. 190 , pp. 495 – 524 , 19 96 .
[6] D . J . Mead . A general theory of harmonic wave propagation in linear periodic systems with multiple coupl ing , J S ound V ib. vol. 27 , pp. 235 – 260 , 19 73 .
[7] Y . K . Lin . Free vibrations of a continuous beam on elastic supports , Int J Mech Sci . vol. 4 , pp. 409 – 423 , 19 6 2.
[8] F . G . Wu, Z . Y . Liu, Y . Y . Liu . Stop gaps and single defect states of acoustic waves in two - dimensional lattice of liquid cylinders , Chin Phys Lett . vol. 18 , pp. 785 – 787 , 2001 .
[9] F . G . Wu . Point defect states in two - dimensional phononic crystals , Phys Lett . vol. 292 , pp. 198 – 202, 2001 .
[10] Y . K . Lin, J . N . Yang . Free vibration of a disordered periodic beam , J Appl M ech . vol. 41 , pp. 383 – 391 , 19 74 .
[11] J . N . Yang, Y . K . Lin . Frequency response function of a disordered periodic beam , J S ound V ib. vol. 38 , pp. 317 – 340 , 19 75 .
[12] D . J . Mead . Wave propagation and natural modes in periodic systems: Mono - coupled systems , J S ound V ib. vol. 40 , pp. 1 – 18 , 19 75 .
[13] D . J . Mead . Wave propagation and natural modes in periodic systems: Multi - coupled systems, with and without damping , J S ound V ib. vol. 40 , pp. 19 – 39 , 19 75 .
[14] D . J . Mead, A . S . Bansal . Mono - coupled periodic systems with a single d isorder : Free wave propagation, J S ound V ib. vol. 61 , pp. 481 – 496 , 19 78 .
[15] A . S . Bansal . Free wave motion in periodic systems with multiple disorders, J S ound V ib. vol. 60 , pp. 389 – 400 , 19 78 .
[16] D . J . Mead, A . S . Bansal , Mono - coupled periodic systems with a single d isord er : Response to convected lodaings , J S ound V ib. vol. 61 , pp. 497 – 515 , 19 78 .
[17] K . F . Graff , Wave motion in elastic solids . Clarendon P ress, Oxford , 1975.
[18] A . V . Oppenheim , A . S . Willsky , I . T . Young . Signals and systems , 2nd ed , Prentice Hall Englewood Cliffs, Ne w Jersey , 1983 .
[19] D . Clouteau , M . L . Elhabre , D . Aubry . Periodic BEM and FEM - BEM Coupling , COMPUT MECH . vol. 25, pp. 567 – 577 , 2000 .
[20] G . D . Manolis , D . E . Beskos . Boundary element methods in elastodynamics , Unwin Hyman, London , 1988 .
[21] J.F. Lu, H.Y. Yuan . The seque nce Fourier transform method for the analysis of a periodic viaduct subjected to non - uniform seismic . ACTA MECH , 2013.
[22] G. Beer , L. Smith, C. Duenser . The boundary element method with programming : For engineers and scientists, Springer, Berlin, 2008.
[23] C . Ki ttel . Introduction to solid state physics , 7th ed , John Wiley & Sons, Inc , New York , 1996 .
Keywords
Defected periodic viaduct (DPV); super - cell method ; the boundary element method (BEM); the pile - soil - structure interaction.