無限遠点と原点とにおける複素周波数関数の対数的特異性 : スペクトル表式に関わって

概要

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Singularity at the infinity point on the complex frequency plane poses frequently perplexing mathematical difficulties when treating linear hereditary cause-to-effect relations. Beginning with reexamination of Fourier and Laplace-type spectral formulations for the impulse and step response time functions, the current study is intended to get a steady engineering insight into particular situations characterized by logarithmic features at the infinity and origin points. A well-defined distribution is advantageously introduced for describing alternatively time or frequency domain properties, which occupies intermediate positions in a sequential chain formed by the Dirac's delta and Heaviside's step. By classifying the degree of singularity at the two points for a practical use, fundamental illustrations follow from the interests of applied mechanics. The latter includes models for constant-Q material damping and foundation-soil rocking impedance.
2006-03-20