An introduction to the study of wave mechanics by Louis De Broglie

By Louis De Broglie

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86) is a set of antisymmetric eigenvalues k0A, k1A, k2A, . . 86) is not easy, because the parameters p and q are also dependent on the wavenumber. These equations can be analysed as relationships ω(k) or c(ω) describing dispersion curves, where ω is the angular frequency and c is the phase velocity. 86). These solutions can be real, imaginary or complex. However, in the case of the nonloaded plate problem it is sufficient to consider real wavenumber k values only. 92) is presented below [4]: P1: TIX/XYZ JWST119-c01 P2: ABC JWST119-Ostachowicz December 1, 2011 9:37 Introduction to the Theory of Elastic Waves Printer Name: Yet to Come 27 1.

1965) Backward wave transmission of stress pulses in elastic cylinders and plates. The Journal of Acoustical Society of America, 38, 835–842. 18. , Bettucci, A. and Germano, M. (2000) Anomalous propagation characteristics of evanescent waves. Ultrasonics, 38, 817–820. 19. L. (2003) Negative group velocity Lamb waves on plates and applications to the scattering of sound by shells. The Journal of the Acoustical Society of America, 113, 2659–2662. 20. Bancroft, D. (1941) The velocity of longitudinal waves in cylindrical bars.

1) Accuracy or error of this approximation Rn (x, a ) can be expressed in the form of the Lagrange residual: Rn (x, a ) = (x − a )n+1 (n+1) f (ξ ), (n + 1)! 3) In the general case of an approximating function f (x) one can consider a class of certain base functions { pn (x)}(n = 0, 1, 2, . ), which are polynomials, or a class of periodic functions, which can be trigonometric functions {sin(nx), cos(nx)}(n = 0, 1, 2, . ). There are also other classes of base functions, which can be useful in specific approximation cases, for example rational functions, exponential functions [1, 5] and so on.

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