Energy Band and Wave Modes for a Super - Cell of a Defected Periodic Viaduct
|International Journal of Engineering Trends and Technology (IJETT)||
|© 2013 by IJETT Journal|
|Year of Publication : 2013|
|Authors : Cheng-Yong He , Li Lei , Jian-Fei Lu|
Cheng-Yong He , Li Lei , Jian-Fei Lu. "Energy Band and Wave Modes for a Super - Cell of a Defected Periodic Viaduct". International Journal of Engineering Trends and Technology (IJETT). V4(6):2253-2260 Jun 2013. ISSN:2231-5381. www.ijettjournal.org. published by seventh sense research group.
In this study, the influence of different defects on the energy bands of a s uper cell of a defected periodic viaduct (DPV) when considering the pile - soil - structure interaction is investigated. By using the coupled boundary element method (BEM) model for the piles supporting the superstructure of the DPV , the compliances of the pil e foundation s are obtained . By using the compliances of the piles and the transfer matrices for the beams and piers, the transfer matrix for each span of the DPV is determined. T he eigenvalue equation for the super cell of the DPV can be developed by using the transfer matri ces for the spans of the super cell and the Bloch theorem, the solution of which yields the energy bands for the super - cell. Numerical results show that the defected span may give rise to the defect state for the super cell of the DPV.
 M.M. Sigalas . Defect states of acoustic waves in two - dimensional lattice of solid cylinders, J Appl Phys. vol. 84, pp. 3026 – 3030, 1998.
 C.H. Hodges . Confinement of vibration by structure irregularity, J Sound Vib. vol. 82, pp. 411 – 424, 1982.
 L. Brilloui n . Wave propagation in periodic structures, Dover Public Inc, New York. 1946.
 D.J. Mead . Free wave propagation in periodically supported infinite beams, J Sound Vib. vol. 11, pp. 181 – 197, 1970.
 D.J. Mead . Wave propagation in continuous periodic structures: Research contributions from Southampton, J Sound Vib. vol. 190, pp. 495 – 524, 1996.
 D.J. Mead . A general theory of harmonic wave propagation in linear periodic systems with multiple coupling, J Sound Vib. vol. 27, pp. 235 – 260, 1973.
 Y.K. Lin . Free vibratio ns of a continuous beam on elastic supports, Int J Mech Sci. vol.4, pp. 409 – 423, 1962.
 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, 2 001.
 F.G. Wu . Point defect states in two - dimensional phononic crystals, Phys Lett. vol. 292, pp. 198 – 202, 2001.
 Y.K. Lin, J.N. Yang . Free vibration of a disordered periodic beam, J Appl Mech. vol. 41, pp. 383 – 391, 1974.
 J.N. Yang, Y.K. Lin . Frequency respo nse function of a disordered periodic beam, J Sound Vib. vol. 38, pp. 317 – 340, 1975.
 D.J. Mead . Wave propagation and natural modes in periodic systems: Mono - coupled systems, J Sound Vib. vol. 40, pp. 1 – 18, 1975.
 D.J. Mead . Wave propagation and natural mode s in periodic systems: Multi - coupled systems, with and without damping, J Sound Vib. vol. 40, pp. 19 – 39, 1975.
 D.J. Mead, A.S. Bansal . Mono - coupled periodic systems with a single disorder: Free wave propagation, J Sound Vib. vol. 61, pp. 481 – 496, 1978.
 A.S . Bansal . Free wave motion in periodic systems with multiple disorders, J Sound Vib. vol. 60, pp. 389 – 400, 1978.
 D.J. Mead, A.S. Bansal, Mono - coupled periodic systems with a single disorder: Response to convected lodaings, J Sound Vib. vol. 61, pp. 497 – 515 , 1978.
 K.F. Graff , Wave motion in elastic solids. Clarendon Press, Oxford, 1975.
 A.V. Oppenheim , A.S. Willsky, I.T. Young. Signals and systems, 2nd ed, Prentice Hall Englewood Cliffs, New Jersey, 1983.
 D. Clouteau , M.L. Elhabre, D. Aubry . Periodic BEM and FEM - BEM Coupling, COMPUT MECH. vol. 25, pp. 567 – 577, 2000.
 G.D. Manolis , D.E. Beskos . Boundary element methods in elastodynamics, Unwin Hyman, London, 1988.
 J.F. Lu, H.Y. Yuan . The sequence Fourier transform method for the analysis of a p eriodic viaduct subjected to non - uniform seismic. ACTA MECH , 2013.
 C. Kittel . Introduction to solid state physics, 7th ed, John Wiley & Sons, Inc, New York, 1996.
 G. Beer , L. Smith, C. Duenser . The boundary element method with programming: For engineers an d scientists, Springer, Berlin, 2008.
Defected periodic viaduct (DPV); super - cell method; the boundary element method (BEM); the pile - soil - structure interaction.