A class of reduced-order models in the theory of waves and stability.
This paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental. The approximations have two defining characteristics: (i) they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the (frequency, wavenumber) plane and (ii) the approximate dispersion relations are polynomials that pass exactly through points on this grid. Thus, the method is interpolatory in nature, but the interpolation takes place in (frequency, wavenumber) space, rather than in physical space. Full details are presented for a non-trivial example, that of antisymmetric elastic waves in a layer. The method is related to partial fraction expansions and barycentric representations of functions. An asymptotic analysis is presented, involving Stirling's approximation to the psi function, and a logarithmic correction to the polynomial dispersion relation.
Department of Mathematics , University of Keele , Staffordshire ST5 BG, UK.
C J
0000-0002-1530-1426
CJ
Chapman
Department of Mechanical and Manufacturing Engineering , Aalborg University , Fibigerstraede 16, 9220 Aalborg, Denmark.
S V
SV
Sorokin
Euler truncation; Fourier series; Lamb wave; Rayleigh wave; barycentric representation; elastic wave