Three Dimensional Vibrations in a Rectangular Bar.
Abstract
Three dimensional vibrations become important when it is desired to look at high order modes or when the dimensions in one or two directions are not 'small'. There is value in studying such vibrations in a rectangular bar since quite complex shapes can be considered to be made up of a number of bars. Further, an analytical approach offers advantages over a finite element or finite difference approach as it is possible to gain more physical insight and also, for higher order modes, it is easier to find the solutions of transcendental equations than find eigenvalues of a large matrix. This report aims to find the possible vibrations of a rectangular bar whose three adjacent surfaces are free from any applied load. Six different vibrations occur corresponding to the corner of the body translating in three dimensions and rotating about three axes. If the bar is rectangular, limited in three directions and if the surfaces are stress free a characteristic equation is obtained for the resonant frequencies and the types of vibration studied occur in combination for some particular frequencies. These will correspond to the natural frequencies of vibration of a finite bar. This general problem has not been studied here but to illustrate the proposed method an application has been made to the relatively simple problem of determining the mode shapes and frequencies of a rubber bar (Poissons ratio 0:5).
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1978
- Accession Number
- ADA081837
Entities
People
- T. G. Ryall