Two Papers on Natural Frequencies of Continuous Beams.

摘要

A rapid approximate method is presented for calculating the fundamental frequencies of flexural vibration of two span beams and of particular arrangements of three span beams which are continuous over non-deflecting supports and are elastically restrained against rotation at their end supports. The stiffnesses of the end restraints are assumed to be positive. The mass per unit of length and the flexural rigidity of the cross section of the beams may vary from one span to the next, but in any one span these quantities are considered constant. The application of the method is illustrated by two numerical examples. The purpose of this paper is to present a method for calculating the undamped natural frequencies of flexural vibration of continuous beams on flexible supports. The supports are represented by a set of mutually independent, linearly elastic, deflectional and rotational springs. The effects of concentrated masses, attached either directly to the beam or through a spring, are also considered.