Application of a New Complex Root-Finding Technique to the Dispersion Relations for Elastic Waves in a Fluid-Loaded Plate

1983 ◽  
Vol 43 (5) ◽  
pp. 1127-1139 ◽  
Author(s):  
Pieter S. Dubbelday
Keyword(s):  
Elastic Waves ◽  
Dispersion Relations ◽  
Complex Root ◽  
Root Finding ◽  
Loaded Plate

Variational Methods for Dispersion Relations and Elastic Properties of Composite Materials

1972 ◽  
Vol 39 (2) ◽  
pp. 327-336 ◽  
Author(s):  
W. Kohn ◽  
J. A. Krumhansl ◽  
E. H. Lee
Keyword(s):  
Composite Materials ◽  
Elastic Properties ◽  
Elastic Waves ◽  
Variational Principles ◽  
Lattice Structure ◽  
Dispersion Relations ◽  
Bravais Lattice ◽  
Layered Composites ◽  
Crystal Lattices ◽  
Ritz Procedure

The propagation of harmonic elastic waves through composite media with a periodic structure is analyzed. Methods utilizing the Floquet or Bloch theory common in the study of the quantum mechanics of crystal lattices are applied. Variational principles in the form of integrals over a single cell of the composite are developed, and applied in some simple illustrative cases. This approach covers waves moving in any direction relative to the lattice structure, and applies to structures of the Bravais lattice groups which include, for example, parallel rods in a square or hexagonal pattern, and an arbitrary parallelepiped cell. More than one type of inclusion can be considered, and the elastic properties and density of the inclusion and matrix can vary with position, as long as they are periodic from cell to cell. The Rayleigh-Ritz procedure can be applied to the solution of the variational equations, which provides a means of calculating dispersion relations and elastic properties of specific composite materials. Detailed calculations carried out on layered composites confirm the effectiveness of the method.

Algorithm 365: complex root finding [C5]

1969 ◽  
Vol 12 (12) ◽  
pp. 686-687 ◽  
Author(s):  
H. Bach
Keyword(s):  
Complex Root ◽  
Root Finding

scholarly journals The deferred limit method for long waves in a curved waveguide

2017 ◽  
Vol 473 (2200) ◽  
pp. 20160900 ◽  
Author(s):  
C. J. Chapman ◽  
S. V. Sorokin
Keyword(s):  
Dispersion Relation ◽  
Elastic Waves ◽  
Bessel Functions ◽  
Dispersion Relations ◽  
High Order ◽  
Long Waves ◽  
Strongly Coupled ◽  
Curved Waveguide

This paper presents a technique, based on a deferred approach to a limit, for analysing the dispersion relation for propagation of long waves in a curved waveguide. The technique involves the concept of an analytically satisfactory pair of Bessel functions, which is different from the concept of a numerically satisfactory pair, and simplifies the dispersion relations for curved waveguide problems. Details are presented for long elastic waves in a curved layer, for which symmetric and antisymmetric waves are strongly coupled. The technique gives high-order corrections to a widely used approximate dispersion relation based a kinematic hypothesis, and determines rigorously which of its coefficients are exact.

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