Wave Propagation in Linear Planar Beams

Abstract

In Chap. 10 we derived the equations governing the dynamic response of planar beams. A simpler set of equations emanated from the linearization of the equations of motion. Further, we introduced assumptions to yield Timoshenko, Rayleigh, and Bernoulli–Euler beam theories. Timoshenko beam theory is the most complete, including rotary inertia effects and shear deformation. Rayleigh beam theory neglects shear deformation but includes rotary inertia. Bernoulli–Euler beam theory neglects both shear deformations and rotary inertia. While these differences are usually not very important in the context of static response, they have significant consequences in dynamics. In this chapter we explore the phenomenon of wave propagation in beams through classical solutions of the linearized equations of motion of these three theories.

Electronic Supplementary Material The online version of this chapter (https://doi.org/10.1007/978-3-030-89944-8_11) contains supplementary material, which is available to authorized users.