Operational formulae for response calculations

Abstract

The paper presents systematic tables of formulae whose purpose is to facilitate the operational solution of response problems reducible to linear differential equations with constant coefficients and with simple forcing functions. The formulae enable the user to find operational equivalents of a wide class of simple functions and, inversely, to find functional equivalents of a great number of operational expressions, in the most rapid and direct manner. In such a way, it is possible to reduce to a minimum the usual heavy algebraical work involved in response calculations. The tables include only such functions whose operational equivalents are algebraic fractions, but these cover a wide field of practical applications. Operational fractions of the 1st, 2nd, 3rd and 4th order are treated in a comprehensive way, so that all possible particular cases are included. Additional tables make it possible to reduce every fraction of 5th or 6th order to a combination of fractions of lower order. The introductory text describes the method of deriving the formulae and explains how to use them in solving response problems. A number of examples are appended which show the advantages of the tables and give solutions of several typical problems.