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Complex Root-Finding Program with Application to the Dispersion Relation of Waves Propagating in a Fluid-Loaded Plate

机译:复杂寻根程序应用于流体加载板中波传播的色散关系

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A method of finding complex roots is described, applicable to the situation where the given equation depends on a parameter in such a way that there exists a real root for a certain value of this parameter. This real root should be determined first by a real root-finding routine. By incrementing the parameter by adjustable steps to the desired value one can follow the progression of the corresponding root from the real axis into the complex plane. Alternately, one may apply this method to the case where it is desired to refine an approximate complex root obtained by other means, or track its progression through the complex plane when a parameter of the equation is varied. The method is a two-dimensional counterpart to the one-dimensional technique whereby the change of sign of the pertinent function delimits the location of a root. The complex root is similarly enclosed in a nested set of squares of diminishing size. The method is illustrated by a typical example, the dispersion relation for the propagation of straight-crested waves in a homogeneous plate. Without fluid loading the propagation speed is real; loading the plate by a fluid moves this real root into the complex plane, which physically corresponds to the appearance of radiation into the fluid. The real and imaginary parts of the relative wave speed are presented, calculated according to exact elasticity theory and thick-plate theory, for antisymmetric and symmetric waves separately and simultaneously, as a function of the dimensionless wave number. Flow diagram, source program listing, and computation examples of the FORTRAN program are given. (Author)

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