HIGH PRECISION CALCULATIONS OF PARAMETERS FOR FREQUENCIES AND MODE SHAPES OF UNIFORM BEAMS

摘要

This report summarizes the expressions for the normal modes of vibration of ten uniform beams and gives the numerical results of double precision calculations for the frequencies, mode shape coefficients and related parameters in tabular form.nIn Section II, general properties of the beam equation, boundary conditions, and modes of vibration are discussed. Section III relates the ten beam problems to three standard problems. The transcendental equations determining the normal modes and frequencies are given for each type of beam. The method of calculating the frequencies to a high degree of accuracy is stated briefly in Section IV. In Section V the numerical data is tabulated and the formulas discussed earlier are summarized.