پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 158 |
| تعداد شمارهها | 6,225 |
| تعداد مقالات | 67,685 |
| تعداد مشاهده مقاله | 114,965,935 |
| تعداد دریافت فایل اصل مقاله | 89,639,691 |
Analytical D’Alembert Series Solution for Multi-Layered One-Dimensional Elastic Wave Propagation with the Use of General Dirichlet Series | ||
| Civil Engineering Infrastructures Journal | ||
| مقاله 10، دوره 51، شماره 1، شهریور 2018، صفحه 169-198 اصل مقاله (1.81 M) | ||
| نوع مقاله: Research Papers | ||
| شناسه دیجیتال (DOI): 10.7508/ceij.2018.01.010 | ||
| نویسندگان | ||
| Mohamad Emami1؛ Morteza Eskandari-Ghadi* 2 | ||
| 1School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran. | ||
| 2School of Civil Engineering, College of Engineering, University of Tehran, I.R. Iran. | ||
| چکیده | ||
| A general initial-boundary value problem of one-dimensional transient wave propagation in a multi-layered elastic medium due to arbitrary boundary or interface excitations (either prescribed tractions or displacements) is considered. Laplace transformation technique is utilised and the Laplace transform inversion is facilitated via an unconventional method, where the expansion of complex-valued functions in the Laplace domain in the form of general Dirichlet series is used. The final solutions are presented in the form of finite series involving forward and backward travelling wave functions of the d’Alembert type for a finite time interval. This elegant method of Laplace transform inversion used for the special class of problems at hand eliminates the need for finding singularities of the complex-valued functions in the Laplace domain and it does not need utilising the tedious calculations of the more conventional methods which use complex integration on the Bromwich contour and the techniques of residue calculus. Justification for the solutions is then considered. Some illustrations of the exact solutions as time-histories of stress or displacement of different points in the medium due to excitations of arbitrary form or of impulsive nature are presented to further investigate and interpret the mathematical solutions. It is shown via illustrations that the one-dimensional wave motions in multi-layered elastic media are generally of complicated forms and are affected significantly by the changes in the geometrical and mechanical properties of the layers as well as the nature of the excitation functions. The method presented here can readily be extended for three-dimensional problems. It is also particularly useful in seismology and earthquake engineering since the exact time-histories of response in a multi-layered medium due to arbitrary excitations can be obtained as finite sums. | ||
| کلیدواژهها | ||
| Analytical D’alembert Solution؛ General Dirichlet Series؛ Inverse Laplace Transform؛ Multi-Layered؛ One-Dimensional؛ Wave Propagation | ||
| مراجع | ||
|
Achenbach, J.D., (1975). Wave propagation in elastic solids, Applied Mathematics and Mechanics, Vol. 16,Amsterdam: North-Holland, Elsevier Science Publishers.
Achenbach, J. D., Hemann, J. H. and Ziegler, F., (1968). "Tensile failure of interface bonds in a composite body subjected to compressive loads", AIAA Journal (The American Institute of Aeronautics and Astronautics), 6(10), 2040-2043.
Ahlfors, L. V., (1966). Complex analysis, International Series in Pure and Applied Mathematics, Second Edition, McGraw-Hill, Inc.
Apostol, T. M., (1974). Mathematical analysis. Second Edition. Addison-Wesley Publishing Company, Inc.
Ardeshir-Behrestaghi, A., Eskandari-Ghadi, M. and Vaseghi-Amiri, J., (2013). "Analytical solution for a two-layer transversely isotropic half-space affected by an arbitrary shape dynamic surface load", Civil Engineering Infrastructures Journal, 46(1), 1-14.
Beddoe, B., (1966). "Vibration of a sectionally uniform string from an initial state", Journal of Sound and Vibration, 4(2), 215-223.
Berlyand, L. and Burridge, R., (1995). "The accuracy of the O'Doherty-Anstey Approximation for wave propagation in highly disordered stratified media", Wave Motion, 21(4), 357-373.
Boström, A., (2000). "On wave equations for elastic rods", ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 80(4), 245-51.
Brown, J.W. and Churchill, R.V., (2012). Fourier series and boundary value problems, Eight Edition, McGraw-Hill, Inc.
Bruck, H.A., (2000). A one-dimensional model for designing functionally graded materials to manage stress waves", International Journal of Solids and Structures, 37(44), 6383-6395.
Burridge, R. (1988). "One-dimensional wave propagation in a highly discontinuous medium", Wave Motion, 10(1), 19-44.
Cheshmehkani, S. and Eskandari-Ghadi, M. (2017). "Three-dimensional dynamic ring load and point load Green's functions for continuously inhomogeneous viscoelastic transversely isotropic half-space", Engineering Analysis with Boundary Elements, 76, 10-25.
Cheung, Y.K., Tham, L.G. and Lei, Z.X. (1995). "Transient response of single piles under horizontal excitations", Earthquake Engineering and Structural Dynamics, 24(7), 1017-1038.
Chiu, T.C. and Erdogan, F. (1999). "One-dimensional wave propagation in a functionally graded elastic medium", Journal of Sound and Vibration, 222(3), 453-487.
Churchill, R.V. (1936). "Temperature distribution in a slab of two layers", Duke Math Journal, 2(1), 405-414.
Churchill, R.V. (1937). "The inversion of Laplace transformation by a direct expansion in series and its application to boundary-value problems", Mathematische Zeitschrift, 42(1), 567-579.
Churchill, R.V. (1958). Operational mathematics, Second Edition, McGraw-Hill.
Cohen, A.M. (2007). Numerical methods for Laplace transform inversion, Springer.
De Hoop, A.T. (1960). "A modification of Cagniard's method for solving seismic pulse problems", Applied Scientific Research, Section B, 8(1), 349-356.
Duffy, D.G. (1993). 'On the numerical inversion of Laplace transforms: Comparison of three new methods on characteristic problems from applications", ACM Transactions on Mathematical Software (TOMS), 19(3), 333-359.
Durbin, F. (1974). Numerical inversion of Laplace transforms: An efficient improvement to Dubner and Abate's method" The Computer Journal, 17(4), 371-376.
Eskandari-Ghadi, M., Hassanpour Charmhini, A. and Ardeshir-Behrestaghi, A. (2014). "A method of function space for vertical impedance function of a circular rigid foundation on a transversely isotropic ground", Civil Engineering Infrastructures Journal, 47(1), 13-27.
Eskandari-Ghadi, M., Rahimian, M., Mahmoodi, A. and Ardeshir-Behrestaghi, A. (2013). "Analytical solution for two-dimensional coupled thermoelastodynamics in a cylinder", Civil Engineering Infrastructures Journal, 46(2), 107-123.
Eskandari-Ghadi, M. and Sattar, S. (2009). "Axisymmetric transient waves in transversely isotropic half-space", Soil Dynamics and Earthquake Engineering, 29, 347-355.
Hardy, G.H. (1915). The general theory of Dirichlet's series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 18,Cambridge: Cambridge University Press.
Hassani, S., (2013). Mathematical physics: A modern introduction to its foundations, 2nd Edition, Springer International Publishing Switzerland.
Kobayashi, M.H. and Genest, R. (2014). "On an extension of the d’Alembert solution to initial–boundary value problems in multi-layered, multi-material domains", Wave Motion, 51(5), 768-784.
Kreyszig, E. (2011). Advanced engineering mathematics, Tenth Edition, John Wiley & Sons, Inc.
Lang, S. (1999). Complex analysis, Graduate Texts in Mathematics, 103, Fourth Edition, Springer.
Lin, W.H. and Daraio, C. (2016). Wave propagation in one-dimensional microscopic granular chains", Physical Review E, 94(5), 052907(1-6).
Macaulay, W.H. (1919). "Note on the deflection of beams. The Messenger of Mathematics, 48, 129-130.
O'Doherty, R.F. and Anstey, N.A. (1971). "Reflections on amplitudes", Geophysical Prospecting, 19(3), 430-458.
Ponge, M.F. and Croënne, C. (2016). "Control of elastic wave propagation in one-dimensional piezomagnetic phononic crystals, The Journal of the Acoustical Society of America, 139(6), 3288-3295.
Raoofian Naeeni, M. and Eskandari-Ghadi, M. (2016). "A potential method for body and surface wave propagation in transversely isotropic half- and full-spaces", Civil Engineering Infrastructures Journal, 49(2), 263-288.
Raoofian Naeeni, M. and Eskandari-Ghadi, M. (2016). "Analytical solution of the asymmetric transient wave in a transversely isotropic half-space due to both buried and surface impulses", Soil Dynamics and Earthquake Engineering, 81, 42-57.
Shafiei, M. and Khaji, N. (2015). "An adaptive physics-based method for the solution of one-dimensional wave motion problems", Civil Engineering Infrastructures Journal, 48(2), 217-234.
Sneddon, I.N. (1995). Fourier transforms, New York: Dover Publications, Inc., (reprinted).
Thambiratnam, D.P. (1986). "Transient waves in a rod subjected to impulsive end loading", Earthquake Engineering and Structural Dynamics, 14(3), 475-485.
Van Der Hijden, J.H. (2016). Propagation of transient elastic waves in stratified anisotropic media, Applied Mathematics and Mechanics, Vol. 32,Amsterdam: North-Holland, Elsevier Science Publishers.
Weinberger, H.F., (1995). A first course in partial differential equations with complex variables and transform methods, New York: Dover Publications, Inc. (reprinted).
Yang, H. and Yin, X. (2015). "Transient responses of girder bridges with vertical poundings under near‐fault vertical earthquake", Earthquake Engineering & Structural Dynamics, 44(15), 2637-2657.
Yang, K. (2008). "A unified solution for longitudinal wave propagation in an elastic rod", Journal of Sound and Vibration, 314(1), 307-329. | ||
|
آمار تعداد مشاهده مقاله: 469 تعداد دریافت فایل اصل مقاله: 542 |
||