CHAPTER 3 - Vibrations of Beams—I

Abstract

This chapter presents vibrations of beams. The extensional or longitudinal and torsional vibrations of bars are considered in the chapter. Extensional and torsional vibrations are treated, because the governing equations are simpler than that for flexural vibrations. For extension and torsion only free undamped vibrations are considered. For flexure natural frequenciesandthe responseto applied forces for uniform and non-uniformbeams are obtained. The three types of deformation are considered separately in this chapter. For non-uniform beams approximate methods of analysis are usually necessary. From the many available methods the Rayleigh-Ritz and finite element methods have been chosen, because, in addition to their suitability for beam problems, they can be used for more complex elastic bodies, such as, plates and shells. It is shown that with these methods elastic bodies, which possess an infinite number of degrees of freedom, are replaced effectively by approximate multi-degree-of-freedom systems, governed by the equations.